NTCIR10-FS-11

Results for NTCIR10-FS-11

Query

Original Query

NTCIR10-FS-11 Formula Search Query <query> <TeXquery>\int _{{\qvar{g}\neq 0}}|\nabla\qvar{f}|^{q}d\qvar{x}\leq\qvar{c}\int _{{\qvar{g}\neq 0}}|\nabla(\qvar{f}+\qvar{g})|^{\qvar{q}}d\qvar{x}</TeXquery> <pquery> <m:math> <m:mrow xml:id="m18.1.25.pmml" xref="m18.1.25"> <m:mrow xml:id="m18.1.25.1.pmml" xref="m18.1.25.1"> <m:msub xml:id="m18.1.25.1.1.pmml" xref="m18.1.25.1.1"> <m:mo xml:id="m18.1.1.pmml" xref="m18.1.1">∫</m:mo> <m:mrow xml:id="m18.1.2.1.pmml" xref="m18.1.2.1"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> <m:mo xml:id="m18.1.2.1.2.pmml" xref="m18.1.2.1.2">≠</m:mo> <m:mn xml:id="m18.1.2.1.3.pmml" xref="m18.1.2.1.3">0</m:mn> </m:mrow> </m:msub> <m:mrow xml:id="m18.1.25.1.2.pmml" xref="m18.1.25.1.2"> <m:msup xml:id="m18.1.25.1.2.2.pmml" xref="m18.1.25.1.2.2"> <m:mrow xml:id="m18.1.25.1.2.2.2.pmml" xref="m18.1.25.1.2.2.2"> <m:mo fence="true" xml:id="m18.1.25.1.2.2.2a.pmml" xref="m18.1.25.1.2.2.2">|</m:mo> <m:mrow xml:id="m18.1.25.1.2.2.2.2.pmml" xref="m18.1.25.1.2.2.2.2"> <m:mo xml:id="m18.1.4.pmml" xref="m18.1.4">∇</m:mo> <m:mo xml:id="m18.1.25.1.2.2.2.2a.pmml" xref="m18.1.25.1.2.2.2.2">⁡</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="f"/> </m:mrow> <m:mo fence="true" xml:id="m18.1.25.1.2.2.2b.pmml" xref="m18.1.25.1.2.2.2">|</m:mo> </m:mrow> <m:mi xml:id="m18.1.7.1.pmml" xref="m18.1.7.1">q</m:mi> </m:msup> <m:mo xml:id="m18.1.25.1.2.1.pmml" xref="m18.1.25.1.2.1">⁢</m:mo> <m:mi xml:id="m18.1.8.pmml" xref="m18.1.8">d</m:mi> <m:mo xml:id="m18.1.25.1.2.1a.pmml" xref="m18.1.25.1.2.1">⁢</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="x"/> </m:mrow> </m:mrow> <m:mo xml:id="m18.1.10.pmml" xref="m18.1.10">≤</m:mo> <m:mrow xml:id="m18.1.25.2.pmml" xref="m18.1.25.2"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="c"/> <m:mo xml:id="m18.1.25.2.1.pmml" xref="m18.1.25.2.1">⁢</m:mo> <m:mrow xml:id="m18.1.25.2.2.pmml" xref="m18.1.25.2.2"> <m:msub xml:id="m18.1.25.2.2.1.pmml" xref="m18.1.25.2.2.1"> <m:mo xml:id="m18.1.12.pmml" xref="m18.1.12">∫</m:mo> <m:mrow xml:id="m18.1.13.1.pmml" xref="m18.1.13.1"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> <m:mo xml:id="m18.1.13.1.2.pmml" xref="m18.1.13.1.2">≠</m:mo> <m:mn xml:id="m18.1.13.1.3.pmml" xref="m18.1.13.1.3">0</m:mn> </m:mrow> </m:msub> <m:mrow xml:id="m18.1.25.2.2.2.pmml" xref="m18.1.25.2.2.2"> <m:msup xml:id="m18.1.25.2.2.2.2.pmml" xref="m18.1.25.2.2.2.2"> <m:mrow xml:id="m18.1.25.2.2.2.2.2.pmml" xref="m18.1.25.2.2.2.2.2"> <m:mo fence="true" xml:id="m18.1.25.2.2.2.2.2a.pmml" xref="m18.1.25.2.2.2.2.2">|</m:mo> <m:mrow xml:id="m18.1.25.2.2.2.2.2.2.pmml" xref="m18.1.25.2.2.2.2.2.2"> <m:mo xml:id="m18.1.15.pmml" xref="m18.1.15">∇</m:mo> <m:mo xml:id="m18.1.25.2.2.2.2.2.2a.pmml" xref="m18.1.25.2.2.2.2.2.2">⁡</m:mo> <m:mrow xml:id="m18.1.25.2.2.2.2.2.2b.pmml" xref="m18.1.25.2.2.2.2.2.2"> <m:mo xml:id="m18.1.25.2.2.2.2.2.2c.pmml" xref="m18.1.25.2.2.2.2.2.2">(</m:mo> <m:mrow xml:id="m18.1.25.2.2.2.2.2.2.1.pmml" xref="m18.1.25.2.2.2.2.2.2.1"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="f"/> <m:mo xml:id="m18.1.18.pmml" xref="m18.1.18">+</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> </m:mrow> <m:mo xml:id="m18.1.25.2.2.2.2.2.2d.pmml" xref="m18.1.25.2.2.2.2.2.2">)</m:mo> </m:mrow> </m:mrow> <m:mo fence="true" xml:id="m18.1.25.2.2.2.2.2b.pmml" xref="m18.1.25.2.2.2.2.2">|</m:mo> </m:mrow> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="q"/> </m:msup> <m:mo xml:id="m18.1.25.2.2.2.1.pmml" xref="m18.1.25.2.2.2.1">⁢</m:mo> <m:mi xml:id="m18.1.23.pmml" xref="m18.1.23">d</m:mi> <m:mo xml:id="m18.1.25.2.2.2.1a.pmml" xref="m18.1.25.2.2.2.1">⁢</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="x"/> </m:mrow> </m:mrow> </m:mrow> </m:mrow> </m:math> </pquery> <cquery> <m:math> <m:apply xml:id="m18.1.25" xref="m18.1.25.pmml"> <m:leq xml:id="m18.1.10" xref="m18.1.10.pmml"/> <m:apply xml:id="m18.1.25.1" xref="m18.1.25.1.pmml"> <m:apply xml:id="m18.1.25.1.1" xref="m18.1.25.1.1.pmml"> <m:csymbol cd="ambiguous" xml:id="m18.1.25.1.1.1">subscript</m:csymbol> <m:int xml:id="m18.1.1" xref="m18.1.1.pmml"/> <m:apply xml:id="m18.1.2.1" xref="m18.1.2.1.pmml"> <m:neq xml:id="m18.1.2.1.2" xref="m18.1.2.1.2.pmml"/> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> <m:cn type="integer" xml:id="m18.1.2.1.3" xref="m18.1.2.1.3.pmml">0</m:cn> </m:apply> </m:apply> <m:apply xml:id="m18.1.25.1.2" xref="m18.1.25.1.2.pmml"> <m:times xml:id="m18.1.25.1.2.1" xref="m18.1.25.1.2.1.pmml"/> <m:apply xml:id="m18.1.25.1.2.2" xref="m18.1.25.1.2.2.pmml"> <m:csymbol cd="ambiguous" xml:id="m18.1.25.1.2.2.1">superscript</m:csymbol> <m:apply xml:id="m18.1.25.1.2.2.2" xref="m18.1.25.1.2.2.2.pmml"> <m:abs xml:id="m18.1.25.1.2.2.2.1"/> <m:apply xml:id="m18.1.25.1.2.2.2.2" xref="m18.1.25.1.2.2.2.2.pmml"> <m:ci xml:id="m18.1.4" xref="m18.1.4.pmml">normal-∇</m:ci> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="f"/> </m:apply> </m:apply> <m:ci xml:id="m18.1.7.1" xref="m18.1.7.1.pmml">q</m:ci> </m:apply> <m:ci xml:id="m18.1.8" xref="m18.1.8.pmml">d</m:ci> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="x"/> </m:apply> </m:apply> <m:apply xml:id="m18.1.25.2" xref="m18.1.25.2.pmml"> <m:times xml:id="m18.1.25.2.1" xref="m18.1.25.2.1.pmml"/> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="c"/> <m:apply xml:id="m18.1.25.2.2" xref="m18.1.25.2.2.pmml"> <m:apply xml:id="m18.1.25.2.2.1" xref="m18.1.25.2.2.1.pmml"> <m:csymbol cd="ambiguous" xml:id="m18.1.25.2.2.1.1">subscript</m:csymbol> <m:int xml:id="m18.1.12" xref="m18.1.12.pmml"/> <m:apply xml:id="m18.1.13.1" xref="m18.1.13.1.pmml"> <m:neq xml:id="m18.1.13.1.2" xref="m18.1.13.1.2.pmml"/> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> <m:cn type="integer" xml:id="m18.1.13.1.3" xref="m18.1.13.1.3.pmml">0</m:cn> </m:apply> </m:apply> <m:apply xml:id="m18.1.25.2.2.2" xref="m18.1.25.2.2.2.pmml"> <m:times xml:id="m18.1.25.2.2.2.1" xref="m18.1.25.2.2.2.1.pmml"/> <m:apply xml:id="m18.1.25.2.2.2.2" xref="m18.1.25.2.2.2.2.pmml"> <m:csymbol cd="ambiguous" xml:id="m18.1.25.2.2.2.2.1">superscript</m:csymbol> <m:apply xml:id="m18.1.25.2.2.2.2.2" xref="m18.1.25.2.2.2.2.2.pmml"> <m:abs xml:id="m18.1.25.2.2.2.2.2.1"/> <m:apply xml:id="m18.1.25.2.2.2.2.2.2" xref="m18.1.25.2.2.2.2.2.2.pmml"> <m:ci xml:id="m18.1.15" xref="m18.1.15.pmml">normal-∇</m:ci> <m:apply xml:id="m18.1.25.2.2.2.2.2.2.1" xref="m18.1.25.2.2.2.2.2.2.1.pmml"> <m:plus xml:id="m18.1.18" xref="m18.1.18.pmml"/> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="f"/> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> </m:apply> </m:apply> </m:apply> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="q"/> </m:apply> <m:ci xml:id="m18.1.23" xref="m18.1.23.pmml">d</m:ci> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="x"/> </m:apply> </m:apply> </m:apply> </m:apply> </m:math> </cquery> </query> <relevance> here <m:math alttext="f" display="inline" xml:id="m19.1" xref="m19.1.pmml"> <m:semantics xml:id="m19.1a" xref="m19.1.pmml"> <m:ci xml:id="m19.1.1" xref="m19.1.1.pmml">f</m:ci> <m:annotation-xml encoding="MathML-Presentation" xml:id="m19.1.pmml" xref="m19.1"> <m:mi xml:id="m19.1.1.pmml" xref="m19.1.1">f</m:mi> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m19.1b" xref="m19.1.pmml">f</m:annotation> </m:semantics> </m:math> is actually a function, <m:math alttext="f^{{(k)}}" display="inline" xml:id="m20.1" xref="m20.1.pmml"> <m:semantics xml:id="m20.1a" xref="m20.1.pmml"> <m:apply xml:id="m20.1.3" xref="m20.1.3.pmml"> <m:csymbol cd="ambiguous" xml:id="m20.1.3.1">superscript</m:csymbol> <m:ci xml:id="m20.1.1" xref="m20.1.1.pmml">f</m:ci> <m:ci xml:id="m20.1.2.1" xref="m20.1.2.1.pmml">k</m:ci> </m:apply> <m:annotation-xml encoding="MathML-Presentation" xml:id="m20.1.pmml" xref="m20.1"> <m:msup xml:id="m20.1.3.pmml" xref="m20.1.3"> <m:mi xml:id="m20.1.1.pmml" xref="m20.1.1">f</m:mi> <m:mrow xml:id="m20.1.2.1.pmml" xref="m20.1.2.1"> <m:mo xml:id="m20.1.2.1a.pmml" xref="m20.1.2.1">(</m:mo> <m:mi xml:id="m20.1.2.1b.pmml" xref="m20.1.2.1">k</m:mi> <m:mo xml:id="m20.1.2.1c.pmml" xref="m20.1.2.1">)</m:mo> </m:mrow> </m:msup> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m20.1b" xref="m20.1.pmml">f^{{(k)}}</m:annotation> </m:semantics> </m:math> is the <m:math alttext="k" display="inline" xml:id="m21.1" xref="m21.1.pmml"> <m:semantics xml:id="m21.1a" xref="m21.1.pmml"> <m:ci xml:id="m21.1.1" xref="m21.1.1.pmml">k</m:ci> <m:annotation-xml encoding="MathML-Presentation" xml:id="m21.1.pmml" xref="m21.1"> <m:mi xml:id="m21.1.1.pmml" xref="m21.1.1">k</m:mi> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m21.1b" xref="m21.1.pmml">k</m:annotation> </m:semantics> </m:math>-th derivative of <m:math alttext="f" display="inline" xml:id="m22.1" xref="m22.1.pmml"> <m:semantics xml:id="m22.1a" xref="m22.1.pmml"> <m:ci xml:id="m22.1.1" xref="m22.1.1.pmml">f</m:ci> <m:annotation-xml encoding="MathML-Presentation" xml:id="m22.1.pmml" xref="m22.1"> <m:mi xml:id="m22.1.1.pmml" xref="m22.1.1">f</m:mi> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m22.1b" xref="m22.1.pmml">f</m:annotation> </m:semantics> </m:math>, <m:math alttext="z" display="inline" xml:id="m23.1" xref="m23.1.pmml"> <m:semantics xml:id="m23.1a" xref="m23.1.pmml"> <m:ci xml:id="m23.1.1" xref="m23.1.1.pmml">z</m:ci> <m:annotation-xml encoding="MathML-Presentation" xml:id="m23.1.pmml" xref="m23.1"> <m:mi xml:id="m23.1.1.pmml" xref="m23.1.1">z</m:mi> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m23.1b" xref="m23.1.pmml">z</m:annotation> </m:semantics> </m:math> is the variable and <m:math alttext="a" display="inline" xml:id="m24.1" xref="m24.1.pmml"> <m:semantics xml:id="m24.1a" xref="m24.1.pmml"> <m:ci xml:id="m24.1.1" xref="m24.1.1.pmml">a</m:ci> <m:annotation-xml encoding="MathML-Presentation" xml:id="m24.1.pmml" xref="m24.1"> <m:mi xml:id="m24.1.1.pmml" xref="m24.1.1">a</m:mi> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m24.1b" xref="m24.1.pmml">a</m:annotation> </m:semantics> </m:math> and <m:math alttext="c" display="inline" xml:id="m25.1" xref="m25.1.pmml"> <m:semantics xml:id="m25.1a" xref="m25.1.pmml"> <m:ci xml:id="m25.1.1" xref="m25.1.1.pmml">c</m:ci> <m:annotation-xml encoding="MathML-Presentation" xml:id="m25.1.pmml" xref="m25.1"> <m:mi xml:id="m25.1.1.pmml" xref="m25.1.1">c</m:mi> </m:annotation-xml> <m:annotation encoding="application/x-tex" xml:id="m25.1b" xref="m25.1.pmml">c</m:annotation> </m:semantics> </m:math> are constants. </relevance> </topic> </blockcode></div> <h3>Compiled by FSE</h3> <h4>Token-Filter</h4> <ul><li>TeXFilter:<code>[d x 2, int x 2, leq, +, (, ), neq x 2, 0 x 2, nabla x 2, q, \ x 7, _ x 2, | x 4, ^ x 2]</code></li><li>Presentation-MathML:<code>[≠ x 2, ∇ x 2, d x 2, 0 x 2, ≤, q, +, | x 4, ∫ x 2]</code></li></ul> <h4>MathML-Filter</h4> <blockcode linenumbers="off" title="compressed Presentation-MathML regular expression"> mrow[mrow[msub[mo[∫];mrow[(.*?);mo[≠];mn[0]]];mrow[msup[mrow[mo[|];mrow[mo[∇];(.*?)];mo[|]];mi[q]];mi[d];(.*?)]];mo[≤];mrow[(.*?);mrow[msub[mo[∫];mrow[1;mo[≠];mn[0]]];mrow[msup[mrow[mo[|];mrow[mo[∇];mfenced[mrow[2;mo[+];1]]];mo[|]];(.*?)];mi[d];3]]]]</blockcode> <blockcode linenumbers="off" title="compressed Content-MathML regular expression"> apply[leq;apply[apply[csymbol[subscript];int;apply[neq;(.*);cn[0]]];apply[times;apply[csymbol[superscript];apply[abs;apply[ci[normal-∇];(.*)]];ci[q]];ci[d];(.*)]];apply[times;(.*);apply[apply[csymbol[subscript];int;apply[neq;1;cn[0]]];apply[times;apply[csymbol[superscript];apply[abs;apply[ci[normal-∇];apply[plus;2;1]]];(.*)];ci[d];3]]]]</blockcode> <h4>Word filter</h4> No words found specifified. Rendered Presentation-MathML: <m:math> <m:mrow xml:id="m18.1.25.pmml" xref="m18.1.25"> <m:mrow xml:id="m18.1.25.1.pmml" xref="m18.1.25.1"> <m:msub xml:id="m18.1.25.1.1.pmml" xref="m18.1.25.1.1"> <m:mo xml:id="m18.1.1.pmml" xref="m18.1.1">∫</m:mo> <m:mrow xml:id="m18.1.2.1.pmml" xref="m18.1.2.1"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> <m:mo xml:id="m18.1.2.1.2.pmml" xref="m18.1.2.1.2">≠</m:mo> <m:mn xml:id="m18.1.2.1.3.pmml" xref="m18.1.2.1.3">0</m:mn> </m:mrow> </m:msub> <m:mrow xml:id="m18.1.25.1.2.pmml" xref="m18.1.25.1.2"> <m:msup xml:id="m18.1.25.1.2.2.pmml" xref="m18.1.25.1.2.2"> <m:mrow xml:id="m18.1.25.1.2.2.2.pmml" xref="m18.1.25.1.2.2.2"> <m:mo fence="true" xml:id="m18.1.25.1.2.2.2a.pmml" xref="m18.1.25.1.2.2.2">|</m:mo> <m:mrow xml:id="m18.1.25.1.2.2.2.2.pmml" xref="m18.1.25.1.2.2.2.2"> <m:mo xml:id="m18.1.4.pmml" xref="m18.1.4">∇</m:mo> <m:mo xml:id="m18.1.25.1.2.2.2.2a.pmml" xref="m18.1.25.1.2.2.2.2">⁡</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="f"/> </m:mrow> <m:mo fence="true" xml:id="m18.1.25.1.2.2.2b.pmml" xref="m18.1.25.1.2.2.2">|</m:mo> </m:mrow> <m:mi xml:id="m18.1.7.1.pmml" xref="m18.1.7.1">q</m:mi> </m:msup> <m:mo xml:id="m18.1.25.1.2.1.pmml" xref="m18.1.25.1.2.1">⁢</m:mo> <m:mi xml:id="m18.1.8.pmml" xref="m18.1.8">d</m:mi> <m:mo xml:id="m18.1.25.1.2.1a.pmml" xref="m18.1.25.1.2.1">⁢</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="x"/> </m:mrow> </m:mrow> <m:mo xml:id="m18.1.10.pmml" xref="m18.1.10">≤</m:mo> <m:mrow xml:id="m18.1.25.2.pmml" xref="m18.1.25.2"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="c"/> <m:mo xml:id="m18.1.25.2.1.pmml" xref="m18.1.25.2.1">⁢</m:mo> <m:mrow xml:id="m18.1.25.2.2.pmml" xref="m18.1.25.2.2"> <m:msub xml:id="m18.1.25.2.2.1.pmml" xref="m18.1.25.2.2.1"> <m:mo xml:id="m18.1.12.pmml" xref="m18.1.12">∫</m:mo> <m:mrow xml:id="m18.1.13.1.pmml" xref="m18.1.13.1"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> <m:mo xml:id="m18.1.13.1.2.pmml" xref="m18.1.13.1.2">≠</m:mo> <m:mn xml:id="m18.1.13.1.3.pmml" xref="m18.1.13.1.3">0</m:mn> </m:mrow> </m:msub> <m:mrow xml:id="m18.1.25.2.2.2.pmml" xref="m18.1.25.2.2.2"> <m:msup xml:id="m18.1.25.2.2.2.2.pmml" xref="m18.1.25.2.2.2.2"> <m:mrow xml:id="m18.1.25.2.2.2.2.2.pmml" xref="m18.1.25.2.2.2.2.2"> <m:mo fence="true" xml:id="m18.1.25.2.2.2.2.2a.pmml" xref="m18.1.25.2.2.2.2.2">|</m:mo> <m:mrow xml:id="m18.1.25.2.2.2.2.2.2.pmml" xref="m18.1.25.2.2.2.2.2.2"> <m:mo xml:id="m18.1.15.pmml" xref="m18.1.15">∇</m:mo> <m:mo xml:id="m18.1.25.2.2.2.2.2.2a.pmml" xref="m18.1.25.2.2.2.2.2.2">⁡</m:mo> <m:mrow xml:id="m18.1.25.2.2.2.2.2.2b.pmml" xref="m18.1.25.2.2.2.2.2.2"> <m:mo xml:id="m18.1.25.2.2.2.2.2.2c.pmml" xref="m18.1.25.2.2.2.2.2.2">(</m:mo> <m:mrow xml:id="m18.1.25.2.2.2.2.2.2.1.pmml" xref="m18.1.25.2.2.2.2.2.2.1"> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="f"/> <m:mo xml:id="m18.1.18.pmml" xref="m18.1.18">+</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="g"/> </m:mrow> <m:mo xml:id="m18.1.25.2.2.2.2.2.2d.pmml" xref="m18.1.25.2.2.2.2.2.2">)</m:mo> </m:mrow> </m:mrow> <m:mo fence="true" xml:id="m18.1.25.2.2.2.2.2b.pmml" xref="m18.1.25.2.2.2.2.2">|</m:mo> </m:mrow> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="q"/> </m:msup> <m:mo xml:id="m18.1.25.2.2.2.1.pmml" xref="m18.1.25.2.2.2.1">⁢</m:mo> <m:mi xml:id="m18.1.23.pmml" xref="m18.1.23">d</m:mi> <m:mo xml:id="m18.1.25.2.2.2.1a.pmml" xref="m18.1.25.2.2.2.1">⁢</m:mo> <mws:qvar xmlns:mws="http://www.mathweb.org/mws/ns" name="x"/> </m:mrow> </m:mrow> </m:mrow> </m:mrow> </m:math> <h2>Results<h2> <h3>Summary<h3> <h4>Reviewer score 2</h4><ul> <li>Items reviewd: 42</li> <li>Accumulated score: 108924</li> <li>Formulasearchengine found: 9</li> </ul><h4>Reviewer score 0</h4><ul> <li>Items reviewd: 58</li> <li>Accumulated score: 48357</li> <li>Formulasearchengine found: 4</li> </ul><table><tr><th></th><th>++</th><th>+</th><th>o</th><th>∑</th></tr><tr><th>200000+</th><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><th>5000-200000</th><td>0</td><td>9</td><td>4</td><td>13</td></tr><tr><th><5000</th><td>0</td><td>33</td><td>54</td><td>87</td></tr><tr><th>∑</th><td>0</td><td>42</td><td>58</td>.<td>100</td></tr></table>50000000:0 200000:0 10000:13 5000:13 <div id="graph-info" style="height:20px;overflow:auto;"></div> <div id="graph" style="width: 90%"></div> <div id="graph-results"></div> <script type="text/javascript"> g = new Dygraph( 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"id56383"; hitids[55] = "id56602"; hitids[56] = "id57618"; hitids[57] = "id58711"; hitids[58] = "id59617"; hitids[59] = "id59625"; hitids[60] = "id61588"; hitids[61] = "id62117"; hitids[62] = "id62997"; hitids[63] = "id64046"; hitids[64] = "id64438"; hitids[65] = "id65276"; hitids[66] = "id66859"; hitids[67] = "id67369"; hitids[68] = "id68373"; hitids[69] = "id68839"; hitids[70] = "id69078"; hitids[71] = "id69338"; hitids[72] = "id69509"; hitids[73] = "id69716"; hitids[74] = "id70138"; hitids[75] = "id71017"; hitids[76] = "id74990"; hitids[77] = "id76441"; hitids[78] = "id83387"; hitids[79] = "id83839"; hitids[80] = "id86390"; hitids[81] = "id86443"; hitids[82] = "id87496"; hitids[83] = "id89073"; hitids[84] = "id89966"; hitids[85] = "id96632"; hitids[86] = "id99016"; hitids[87] = "idp14495376"; hitids[88] = "idp163776"; hitids[89] = "idp18333472"; hitids[90] = "idp21309088"; hitids[91] = "idp21578768"; hitids[92] = "idp24874944"; hitids[93] = "idp24982064"; hitids[94] = "idp25115664"; hitids[95] = "idp2688720"; hitids[96] = "idp275712"; hitids[97] = "idp31639936"; hitids[98] = "idp36087904"; hitids[99] = "idp58080"; hitids[100] = "idp618880"; hitinfo[1] =" id: idp733616, Relevance: 2internal score: 12291";hitinfo[2] =" id: idp10775264, Relevance: 2internal score: 12234";hitinfo[4] =" id: idp18482720, Relevance: 2internal score: 12145";hitinfo[7] =" id: idp22331808, Relevance: 2internal score: 12086";hitinfo[8] =" id: idp15078368, Relevance: 2internal score: 12057";hitinfo[9] =" id: idp21387280, Relevance: 2internal score: 12056";hitinfo[10] =" id: idp22368352, Relevance: 2internal score: 12056";hitinfo[11] =" id: idp8107968, Relevance: 2internal score: 12016";hitinfo[12] =" id: idp22985904, Relevance: 2internal score: 11983";hitinfo[14] =" id: id124859, Relevance: 2internal score: 0";hitinfo[15] =" id: id67365, Relevance: 2internal score: 0";hitinfo[16] =" id: id70843, Relevance: 2internal score: 0";hitinfo[17] =" id: id91042, Relevance: 2internal score: 0";hitinfo[18] =" id: idp13677424, Relevance: 2internal score: 0";hitinfo[19] =" id: idp13993328, Relevance: 2internal score: 0";hitinfo[20] =" id: idp15748240, Relevance: 2internal score: 0";hitinfo[21] =" id: idp192576, Relevance: 2internal score: 0";hitinfo[22] =" id: idp20708592, Relevance: 2internal score: 0";hitinfo[23] =" id: idp21496224, Relevance: 2internal score: 0";hitinfo[24] =" id: idp21648032, Relevance: 2internal score: 0";hitinfo[25] =" id: idp2190864, Relevance: 2internal score: 0";hitinfo[26] =" id: idp23618192, Relevance: 2internal score: 0";hitinfo[27] =" id: idp24425744, Relevance: 2internal score: 0";hitinfo[28] =" id: idp24527840, Relevance: 2internal score: 0";hitinfo[29] =" id: idp24672480, Relevance: 2internal score: 0";hitinfo[30] =" id: idp24959520, Relevance: 2internal score: 0";hitinfo[31] =" id: idp25578864, Relevance: 2internal score: 0";hitinfo[32] =" id: idp26606096, Relevance: 2internal score: 0";hitinfo[33] =" id: idp26662016, Relevance: 2internal score: 0";hitinfo[34] =" id: idp26815008, Relevance: 2internal score: 0";hitinfo[35] =" id: idp26879344, Relevance: 2internal score: 0";hitinfo[36] =" id: idp27231392, Relevance: 2internal score: 0";hitinfo[37] =" id: idp27625952, Relevance: 2internal score: 0";hitinfo[38] =" id: idp28303744, Relevance: 2internal score: 0";hitinfo[39] =" id: idp28342608, Relevance: 2internal score: 0";hitinfo[40] =" id: idp28800976, Relevance: 2internal score: 0";hitinfo[41] =" id: idp328512, Relevance: 2internal score: 0";hitinfo[42] =" id: idp33982064, Relevance: 2internal score: 0";hitinfo[43] =" id: idp6182384, Relevance: 2internal score: 0";hitinfo[44] =" id: idp6231536, Relevance: 2internal score: 0";hitinfo[45] =" id: idp833216, Relevance: 2internal score: 0";hitinfo[46] =" id: idp90880, Relevance: 2internal score: 0";hitinfo[3] =" id: idp8511248, Relevance: 0internal score: 12146";hitinfo[5] =" id: idp10149248, Relevance: 0internal score: 12140";hitinfo[6] =" id: idp20569264, Relevance: 0internal score: 12099";hitinfo[13] =" id: idp21821328, Relevance: 0internal score: 11972";hitinfo[47] =" id: id121336, Relevance: 0internal score: 0";hitinfo[48] =" id: id129515, Relevance: 0internal score: 0";hitinfo[49] =" id: id53746, Relevance: 0internal score: 0";hitinfo[50] =" id: id54191, Relevance: 0internal score: 0";hitinfo[51] =" id: id54417, Relevance: 0internal score: 0";hitinfo[52] =" id: id54778, Relevance: 0internal score: 0";hitinfo[53] =" id: id56024, Relevance: 0internal score: 0";hitinfo[54] =" id: id56383, Relevance: 0internal score: 0";hitinfo[55] =" id: id56602, Relevance: 0internal score: 0";hitinfo[56] =" id: id57618, Relevance: 0internal score: 0";hitinfo[57] =" id: id58711, Relevance: 0internal score: 0";hitinfo[58] =" id: id59617, Relevance: 0internal score: 0";hitinfo[59] =" id: id59625, Relevance: 0internal score: 0";hitinfo[60] =" id: id61588, Relevance: 0internal score: 0";hitinfo[61] =" id: id62117, Relevance: 0internal score: 0";hitinfo[62] =" id: id62997, Relevance: 0internal score: 0";hitinfo[63] =" id: id64046, Relevance: 0internal score: 0";hitinfo[64] =" id: id64438, Relevance: 0internal score: 0";hitinfo[65] =" id: id65276, Relevance: 0internal score: 0";hitinfo[66] =" id: id66859, Relevance: 0internal score: 0";hitinfo[67] =" id: id67369, Relevance: 0internal score: 0";hitinfo[68] =" id: id68373, Relevance: 0internal score: 0";hitinfo[69] =" id: id68839, Relevance: 0internal score: 0";hitinfo[70] =" id: id69078, Relevance: 0internal score: 0";hitinfo[71] =" id: id69338, Relevance: 0internal score: 0";hitinfo[72] =" id: id69509, Relevance: 0internal score: 0";hitinfo[73] =" id: id69716, Relevance: 0internal score: 0";hitinfo[74] =" id: id70138, Relevance: 0internal score: 0";hitinfo[75] =" id: id71017, Relevance: 0internal score: 0";hitinfo[76] =" id: id74990, Relevance: 0internal score: 0";hitinfo[77] =" id: id76441, Relevance: 0internal score: 0";hitinfo[78] =" id: id83387, Relevance: 0internal score: 0";hitinfo[79] =" id: id83839, Relevance: 0internal score: 0";hitinfo[80] =" id: id86390, Relevance: 0internal score: 0";hitinfo[81] =" id: id86443, Relevance: 0internal score: 0";hitinfo[82] =" id: id87496, Relevance: 0internal score: 0";hitinfo[83] =" id: id89073, Relevance: 0internal score: 0";hitinfo[84] =" id: id89966, Relevance: 0internal score: 0";hitinfo[85] =" id: id96632, Relevance: 0internal score: 0";hitinfo[86] =" id: id99016, Relevance: 0internal score: 0";hitinfo[87] =" id: idp14495376, Relevance: 0internal score: 0";hitinfo[88] =" id: idp163776, Relevance: 0internal score: 0";hitinfo[89] =" id: idp18333472, Relevance: 0internal score: 0";hitinfo[90] =" id: idp21309088, Relevance: 0internal score: 0";hitinfo[91] =" id: idp21578768, Relevance: 0internal score: 0";hitinfo[92] =" id: idp24874944, Relevance: 0internal score: 0";hitinfo[93] =" id: idp24982064, Relevance: 0internal score: 0";hitinfo[94] =" id: idp25115664, Relevance: 0internal score: 0";hitinfo[95] =" id: idp2688720, Relevance: 0internal score: 0";hitinfo[96] =" id: idp275712, Relevance: 0internal score: 0";hitinfo[97] =" id: idp31639936, Relevance: 0internal score: 0";hitinfo[98] =" id: idp36087904, Relevance: 0internal score: 0";hitinfo[99] =" id: idp58080, Relevance: 0internal score: 0";hitinfo[100] =" id: idp618880, Relevance: 0internal score: 0";</script> <h3>Short result list</h3> <h3>Detailed results for reviewer score 2</h3> <div id="idp733616"><h4>Hit idp733616</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 1</li> <li>Formulasearchengine score: 12291</li> <li>Reference to collection: _PREFIX_/19/f007349.xhtml#idp733616</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\begin{split}||\nabla\psi\cdot\nabla(\varphi _{\epsilon}-1)||^{2}\leq M_{3}^{2}\int _{{\mathbb{R}^{d}}}|\nabla\varphi(\frac{x}{\epsilon})|^{2}dx=\epsilon^{{-2}}M_{3}^{2}&\int _{{\mathbb{R}^{d}}}|(\nabla\varphi)(\frac{x}{\epsilon})|^{2}dx\\ &=\epsilon^{{d-2}}M_{3}^{2}|||\nabla\varphi|||^{2}\rightarrow 0\mbox{ as }\epsilon\rightarrow 0,\end{split}$ at pos:86176(8%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.75 * TOKEN_SCORE[int] + 1.5 * TOKEN_SCORE[leq] + 1.0 * TOKEN_SCORE[+] + 1.9375 * TOKEN_SCORE[(] + 1.9375 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.75 * TOKEN_SCORE[0] + 1.96875 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999999995343387 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[_] + 1.99993896484375 * TOKEN_SCORE[|] + 1.99951171875 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.75*0.279351653691737+1.5*2.71610004241772+1.0*0.0160883895861106+1.9375*0.00418257496311516+1.9375*0.00417601612706465+1.0*4.28403503219485+1.75*0.0483458611105983+1.96875*6.39416349760091+1.0*0.855340292115138+1.9999999995343387*5.92879328325965E-4+1.984375*0.00257082788077282+1.99993896484375*0.0975909302497933+1.99951171875*0.00338742677192689 = 12291.334095438282' final score ~ 12291 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp733616" alttext="\begin{split}||\nabla\psi\cdot\nabla(\varphi _{\epsilon}-1)||^{2}\leq M_{3}^{2}\int _{{\mathbb{R}^{d}}}|\nabla\varphi(\frac{x}{\epsilon})|^{2}dx=\epsilon^{{-2}}M_{3}^{2}&\int _{{\mathbb{R}^{d}}}|(\nabla\varphi)(\frac{x}{\epsilon})|^{2}dx\\ &=\epsilon^{{d-2}}M_{3}^{2}|||\nabla\varphi|||^{2}\rightarrow 0\mbox{ as }\epsilon\rightarrow 0,\end{split}" display="block"><semantics id="idp733168"><mrow id="idp733296"><mrow id="idp733424"><msup id="idp734704"><mrow id="idp734832"><mo id="idp734960" fence="true">||</mo><mrow id="idp735456"><mrow id="idp735584"><mo id="idp735712">∇</mo><mo id="idp735968">⁡</mo><mi id="idp736224">ψ</mi></mrow><mo id="idp736480">⋅</mo><mrow id="idp736768"><mo id="idp736896">∇</mo><mo id="idp737184">⁡</mo><mrow id="idp737472"><mo id="idp737600">(</mo><mrow id="idp737856"><msub id="idp737984"><mi id="idp738112">φ</mi><mi id="idp738400">ϵ</mi></msub><mo id="idp738688">-</mo><mn id="idp738944">1</mn></mrow><mo id="idp739200">)</mo></mrow></mrow></mrow><mo id="idp739456" fence="true">||</mo></mrow><mn id="idp739984">2</mn></msup><mo id="idp740240">≤</mo><mrow id="idp740528"><msubsup id="idp740656"><mi id="idp740784">M</mi><mn id="idp741040">3</mn><mn id="idp741296">2</mn></msubsup><mo id="idp741552">⁢</mo><mrow id="idp741840"><msub id="idp741968"><mo id="idp742096">∫</mo><msup id="idp742384"><mi id="idp742512" mathvariant="double-struck">R</mi><mi id="idp743040">d</mi></msup></msub><mrow id="idp743296"><msup id="idp743424"><mrow id="idp743552"><mo id="idp743680" fence="true">|</mo><mrow id="idp744208"><mrow id="idp744336"><mo id="idp744464">∇</mo><mo id="idp744752">⁡</mo><mi id="idp745040">φ</mi></mrow><mo id="idp745328">⁢</mo><mrow id="idp745616"><mo id="idp745744">(</mo><mfrac id="idp746000"><mi id="idp746128">x</mi><mi id="idp746384">ϵ</mi></mfrac><mo id="idp746672">)</mo></mrow></mrow><mo 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id="idp764624">φ</mi></mrow><mo id="idp764912" fence="true">|</mo></mrow><mo id="idp765440" fence="true">||</mo></mrow><mn id="idp765968">2</mn></msup></mrow><mo id="idp766224">→</mo><mrow id="idp766512"><mn id="idp766640">0</mn><mo id="idp766896">⁢</mo><mtext id="idp767184"> as </mtext><mo id="idp767472">⁢</mo><mi id="idp767760">ϵ</mi></mrow><mo id="idp768048">→</mo><mn id="idp768336">0</mn></mrow><mo id="idp768592">,</mo></mrow><annotation-xml id="idp768848" encoding="MathML-Content"><apply id="idp769248"><and id="idp769376"/><apply id="idp769504"><leq id="idp769632"/><apply id="idp769760"><csymbol id="idp769888" cd="ambiguous">superscript</csymbol><apply id="idp770448"><csymbol id="idp770576" cd="latexml">norm</csymbol><apply id="idp771136"><ci id="idp771264">⋅</ci><apply id="idp771552"><ci id="idp771680">∇</ci><ci id="idp771968">ψ</ci></apply><apply id="idp772256"><ci id="idp772384">∇</ci><apply id="idp772672"><minus id="idp772800"/><apply id="idp772928"><csymbol id="idp773056" cd="ambiguous">subscript</csymbol><ci id="idp773616">φ</ci><ci id="idp773904">ϵ</ci></apply><cn id="idp774192" type="integer">1</cn></apply></apply></apply></apply><cn id="idp774720" type="integer">2</cn></apply><apply id="S1.Ex6.m1.sh1ah.cmml"><times id="S1.Ex6.m1.sh1.cmml"/><apply id="S1.Ex6.m1.sh1g.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh1a.cmml">superscript</csymbol><apply id="S1.Ex6.m1.sh1e.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh1b.cmml">subscript</csymbol><ci id="S1.Ex6.m1.sh1c.cmml">M</ci><cn type="integer" id="S1.Ex6.m1.sh1d.cmml">3</cn></apply><cn type="integer" id="S1.Ex6.m1.sh1f.cmml">2</cn></apply><apply id="S1.Ex6.m1.sh1ag.cmml"><apply id="S1.Ex6.m1.sh1n.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh1h.cmml">subscript</csymbol><int id="S1.Ex6.m1.sh1i.cmml"/><apply id="S1.Ex6.m1.sh1m.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh1j.cmml">superscript</csymbol><ci id="S1.Ex6.m1.sh1k.cmml">R</ci><ci id="S1.Ex6.m1.sh1l.cmml">d</ci></apply></apply><apply 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id="S1.Ex6.m1.sh3d.cmml">d</ci><cn type="integer" id="S1.Ex6.m1.sh3e.cmml">2</cn></apply></apply><apply id="S1.Ex6.m1.sh3n.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh3h.cmml">superscript</csymbol><apply id="S1.Ex6.m1.sh3l.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh3i.cmml">subscript</csymbol><ci id="S1.Ex6.m1.sh3j.cmml">M</ci><cn type="integer" id="S1.Ex6.m1.sh3k.cmml">3</cn></apply><cn type="integer" id="S1.Ex6.m1.sh3m.cmml">2</cn></apply><apply id="S1.Ex6.m1.sh3x.cmml"><csymbol cd="ambiguous" id="S1.Ex6.m1.sh3o.cmml">superscript</csymbol><apply id="S1.Ex6.m1.sh3v.cmml"><csymbol cd="latexml" id="S1.Ex6.m1.sh3p.cmml">norm</csymbol><apply id="S1.Ex6.m1.sh3u.cmml"><abs id="S1.Ex6.m1.sh3q.cmml"/><apply id="S1.Ex6.m1.sh3t.cmml"><ci id="S1.Ex6.m1.sh3r.cmml">∇</ci><ci id="S1.Ex6.m1.sh3s.cmml">φ</ci></apply></apply></apply><cn type="integer" id="S1.Ex6.m1.sh3w.cmml">2</cn></apply></apply></apply><apply id="idp832064"><ci id="idp832192">→</ci><share id="idp832480" href="#S1.Ex6.m1.sh3.cmml"/><apply id="S1.Ex6.m1.sh4d.cmml"><times id="S1.Ex6.m1.sh4.cmml"/><cn type="integer" id="S1.Ex6.m1.sh4a.cmml">0</cn><mtext id="S1.Ex6.m1.sh4b.cmml"> as </mtext><ci id="S1.Ex6.m1.sh4c.cmml">ϵ</ci></apply></apply><apply id="idp835600"><ci id="idp835728">→</ci><share id="idp836016" href="#S1.Ex6.m1.sh4.cmml"/><cn type="integer" id="S1.Ex6.m1.sh5.cmml">0</cn></apply></apply></annotation-xml><annotation id="idp837216" encoding="application/x-tex">\begin{split}||\nabla\psi\cdot\nabla(\varphi _{\epsilon}-1)||^{2}\leq M_{3}^{2}\int _{{\mathbb{R}^{d}}}|\nabla\varphi(\frac{x}{\epsilon})|^{2}dx=\epsilon^{{-2}}M_{3}^{2}&\int _{{\mathbb{R}^{d}}}|(\nabla\varphi)(\frac{x}{\epsilon})|^{2}dx\\ &=\epsilon^{{d-2}}M_{3}^{2}|||\nabla\varphi|||^{2}\rightarrow 0\mbox{ as }\epsilon\rightarrow 0,\end{split}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp10775264"><h4>Hit idp10775264</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 2</li> <li>Formulasearchengine score: 12234</li> <li>Reference to collection: _PREFIX_/62/f024501.xhtml#idp10775264</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\int _{{\mathcal{C}}}|\nabla\psi(x)|^{2}\, dx\leq(2\pi)^{d}h^{{d-2}}\frac{\int _{{\mathbb{R}^{d}\times{\mathcal{C}}}}\left|\left(\nabla _{x}+\nabla _{y}\right)\alpha(x,y)\right|^{2}\, dx\, dy}{\int|\alpha _{0}(x)|^{2}dx}\,.$ at pos:1357590(45%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.5 * TOKEN_SCORE[leq] + 1.5 * TOKEN_SCORE[+] + 1.96875 * TOKEN_SCORE[(] + 1.96875 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.5 * TOKEN_SCORE[0] + 1.875 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999999403953552 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[_] + 1.984375 * TOKEN_SCORE[|] + 1.984375 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.875*0.279351653691737+1.5*2.71610004241772+1.5*0.0160883895861106+1.96875*0.00418257496311516+1.96875*0.00417601612706465+1.0*4.28403503219485+1.5*0.0483458611105983+1.875*6.39416349760091+1.0*0.855340292115138+1.9999999403953552*5.92879328325965E-4+1.96875*0.00257082788077282+1.984375*0.0975909302497933+1.984375*0.00338742677192689 = 12234.341567312667' final score ~ 12234 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp10775264" alttext="\int _{{\mathcal{C}}}|\nabla\psi(x)|^{2}\, dx\leq(2\pi)^{d}h^{{d-2}}\frac{\int _{{\mathbb{R}^{d}\times{\mathcal{C}}}}\left|\left(\nabla _{x}+\nabla _{y}\right)\alpha(x,y)\right|^{2}\, dx\, dy}{\int|\alpha _{0}(x)|^{2}dx}\,." display="block"><semantics id="idp10776224"><mrow id="idp10776352"><mrow id="idp10776480"><mrow id="idp10776608"><msub id="idp10776736"><mo id="idp10776864">∫</mo><mi id="idp10777120" mathvariant="script">C</mi></msub><mrow id="idp10777616"><msup id="idp10777744"><mrow id="idp10777872"><mo id="idp10778000" fence="true">|</mo><mrow id="idp10778528"><mrow id="idp10778656"><mo id="idp10778784">∇</mo><mo id="idp10779072">⁡</mo><mi id="idp10779360">ψ</mi></mrow><mo id="idp10779648">⁢</mo><mrow id="idp10779936"><mo id="idp10780064">(</mo><mi id="idp10780320">x</mi><mo id="idp10780576">)</mo></mrow></mrow><mo id="idp10780832" fence="true">|</mo></mrow><mn id="idp10781360">2</mn></msup><mo id="idp10781616">⁢</mo><mi id="idp10781904">d</mi><mo id="idp10782160">⁢</mo><mi id="idp10782448">x</mi></mrow></mrow><mo id="idp10782704">≤</mo><mrow id="idp10782992"><msup id="idp10783120"><mrow id="idp10783248"><mo id="idp10783376">(</mo><mrow id="idp10783632"><mn id="idp10783760">2</mn><mo id="idp10784016">⁢</mo><mi id="idp10784304">π</mi></mrow><mo id="idp10784592">)</mo></mrow><mi id="idp10784848">d</mi></msup><mo id="idp10785104">⁢</mo><msup id="idp10785392"><mi id="idp10785520">h</mi><mrow id="idp10785776"><mi id="idp10785904">d</mi><mo id="idp10786160">-</mo><mn id="idp10786416">2</mn></mrow></msup><mo id="idp10786672">⁢</mo><mpadded id="idp10786960" width="+1.666667pt"><mfrac id="idp10787360"><mrow id="idp10787488"><msub id="idp10787616"><mo id="idp10787744">∫</mo><mrow id="idp10788032"><msup id="idp10788160"><mi id="idp10788288" mathvariant="double-struck">R</mi><mi id="idp10788816">d</mi></msup><mo id="idp10789072">×</mo><mi id="idp10789360" mathvariant="script">C</mi></mrow></msub><mrow id="idp10789888"><msup id="idp10790016"><mrow id="idp10790144"><mo id="idp10790272" fence="true">|</mo><mrow id="idp10790800"><mrow id="idp10790928"><mo id="idp10791056">(</mo><mrow id="idp10791312"><msub id="idp10791440"><mo id="idp10791568">∇</mo><mi id="idp10791856">x</mi></msub><mo id="idp10792112">+</mo><msub id="idp10792368"><mo id="idp10792496">∇</mo><mi id="idp10792784">y</mi></msub></mrow><mo id="idp10793040">)</mo></mrow><mo id="idp10793296">⁢</mo><mi id="idp10793584">α</mi><mo id="idp10793872">⁢</mo><mrow id="idp10794160"><mo id="idp10794288">(</mo><mrow id="idp10794544"><mi id="idp10794672">x</mi><mo id="idp10794928">,</mo><mi id="idp10795184">y</mi></mrow><mo id="idp10795440">)</mo></mrow></mrow><mo id="idp10795696" fence="true">|</mo></mrow><mn id="idp10796224">2</mn></msup><mo id="idp10796480">⁢</mo><mi id="idp10796768">d</mi><mo id="idp10797024">⁢</mo><mpadded id="idp10797312" width="+1.666667pt"><mi id="idp10797712">x</mi></mpadded><mo id="idp10797968">⁢</mo><mi id="idp10798256">d</mi><mo id="idp10798512">⁢</mo><mi id="idp10798800">y</mi></mrow></mrow><mrow id="idp10799056"><mo id="idp10799184">∫</mo><mrow id="idp10799472"><msup id="idp10799600"><mrow id="idp10799728"><mo id="idp10799856" fence="true">|</mo><mrow id="idp10800384"><msub id="idp10800512"><mi id="idp10800640">α</mi><mn id="idp10800928">0</mn></msub><mo id="idp10801184">⁢</mo><mrow id="idp10801472"><mo id="idp10801600">(</mo><mi id="idp10801856">x</mi><mo id="idp10802112">)</mo></mrow></mrow><mo id="idp10802368" fence="true">|</mo></mrow><mn id="idp10802896">2</mn></msup><mo id="idp10803152">⁢</mo><mi id="idp10803440">d</mi><mo id="idp10803696">⁢</mo><mi id="idp10803984">x</mi></mrow></mrow></mfrac></mpadded></mrow></mrow><mo id="idp10804240">.</mo></mrow><annotation-xml id="idp10804496" encoding="MathML-Content"><apply id="idp10804896"><leq id="idp10805024"/><apply id="idp10805152"><apply id="idp10805280"><csymbol id="idp10805408" cd="ambiguous">subscript</csymbol><int id="idp10805968"/><ci id="idp10806096">C</ci></apply><apply id="idp10806352"><times id="idp10806480"/><apply id="idp10806608"><csymbol id="idp10806736" cd="ambiguous">superscript</csymbol><apply id="idp10807296"><abs id="idp10807424"/><apply id="idp10807552"><times id="idp10807680"/><apply id="idp10807808"><ci id="idp10807936">∇</ci><ci id="idp10808224">ψ</ci></apply><ci id="idp10808512">x</ci></apply></apply><cn id="idp10808768" type="integer">2</cn></apply><ci id="idp10809296">d</ci><ci id="idp10809552">x</ci></apply></apply><apply id="idp10809808"><times id="idp10809936"/><apply id="idp10810064"><csymbol id="idp10810192" cd="ambiguous">superscript</csymbol><apply id="idp10810752"><times id="idp10810880"/><cn id="idp10811008" type="integer">2</cn><ci id="idp10811536">π</ci></apply><ci id="idp10811824">d</ci></apply><apply id="idp10812080"><csymbol id="idp10812208" cd="ambiguous">superscript</csymbol><ci id="idp10812768">h</ci><apply id="idp10813024"><minus id="idp10813152"/><ci id="idp10813280">d</ci><cn id="idp10813536" type="integer">2</cn></apply></apply><apply id="idp10814064"><divide id="idp10814192"/><apply id="idp10814320"><apply id="idp10814448"><csymbol id="idp10814576" cd="ambiguous">subscript</csymbol><int id="idp10815136"/><apply id="idp10815264"><times id="idp10815392"/><apply id="idp10815520"><csymbol id="idp10815648" cd="ambiguous">superscript</csymbol><ci id="idp10816208">R</ci><ci id="idp10816464">d</ci></apply><ci id="idp10816720">C</ci></apply></apply><apply id="idp10816976"><times id="idp10817104"/><apply id="idp10817232"><csymbol id="idp10817360" cd="ambiguous">superscript</csymbol><apply id="idp10817920"><abs id="idp10818048"/><apply id="idp10818176"><times id="idp10818304"/><apply id="idp10818432"><plus id="idp10818560"/><apply id="idp10818688"><csymbol id="idp10818816" cd="ambiguous">subscript</csymbol><ci id="idp10819376">∇</ci><ci id="idp10819664">x</ci></apply><apply id="idp10819920"><csymbol id="idp10820048" cd="ambiguous">subscript</csymbol><ci id="idp10820608">∇</ci><ci id="idp10820896">y</ci></apply></apply><ci id="idp10821152">α</ci><apply id="idp10821440"><interval id="idp10821568" closure="open"/><ci id="idp10821968">x</ci><ci id="idp10822224">y</ci></apply></apply></apply><cn id="idp10822480" type="integer">2</cn></apply><ci id="idp10823008">d</ci><ci id="idp10823264">x</ci><ci id="idp10823520">d</ci><ci id="idp10823776">y</ci></apply></apply><apply id="idp10824032"><int id="idp10824160"/><apply id="idp10824288"><times id="idp10824416"/><apply id="idp10824544"><csymbol id="idp10824672" cd="ambiguous">superscript</csymbol><apply id="idp10825232"><abs id="idp10825360"/><apply id="idp10825488"><times id="idp10825616"/><apply id="idp10825744"><csymbol id="idp10825872" cd="ambiguous">subscript</csymbol><ci id="idp10826432">α</ci><cn id="idp10826720" type="integer">0</cn></apply><ci id="idp10827248">x</ci></apply></apply><cn id="idp10827504" type="integer">2</cn></apply><ci id="idp10828032">d</ci><ci id="idp10828288">x</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp10828544" encoding="application/x-tex">\int _{{\mathcal{C}}}|\nabla\psi(x)|^{2}\, dx\leq(2\pi)^{d}h^{{d-2}}\frac{\int _{{\mathbb{R}^{d}\times{\mathcal{C}}}}\left|\left(\nabla _{x}+\nabla _{y}\right)\alpha(x,y)\right|^{2}\, dx\, dy}{\int|\alpha _{0}(x)|^{2}dx}\,.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp18482720"><h4>Hit idp18482720</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 4</li> <li>Formulasearchengine score: 12145</li> <li>Reference to collection: _PREFIX_/17/f006598.xhtml#idp18482720</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\frac{\int _{\mathcal{F}}||\nabla F||^{2}d\mu}{\int _{\mathcal{F}}||F||^{2}d\mu}=\frac{\int _{\mathcal{F}}||\nabla\phi _{0}||^{2}+\phi _{0}^{2}||\nabla u||^{2}d\mu}{\int _{\mathcal{F}}|\phi _{0}|^{2}d\mu}\geq\lambda _{0}+\frac{\int _{\mathcal{F}}\phi _{0}^{2}||\nabla u||^{2}d\mu}{\int _{\mathcal{F}}\phi _{0}^{2}d\mu}.$ at pos:2376894(75%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.984375 * TOKEN_SCORE[d] + 1.984375 * TOKEN_SCORE[int] + 1.0 * TOKEN_SCORE[leq] + 1.75 * TOKEN_SCORE[+] + 1.0 * TOKEN_SCORE[(] + 1.0 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.984375 * TOKEN_SCORE[0] + 1.9375 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999999997671694 * TOKEN_SCORE[\] + 1.999755859375 * TOKEN_SCORE[_] + 1.999999761581421 * TOKEN_SCORE[|] + 1.998046875 * TOKEN_SCORE[^] =+100.0+0.0+1.984375*0.158568544552516+1.984375*0.279351653691737+1.0*2.71610004241772+1.75*0.0160883895861106+1.0*0.00418257496311516+1.0*0.00417601612706465+1.0*4.28403503219485+1.984375*0.0483458611105983+1.9375*6.39416349760091+1.0*0.855340292115138+1.9999999997671694*5.92879328325965E-4+1.999755859375*0.00257082788077282+1.999999761581421*0.0975909302497933+1.998046875*0.00338742677192689 = 12145.38914892102' final score ~ 12145 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp18482720" alttext="\frac{\int _{\mathcal{F}}||\nabla F||^{2}d\mu}{\int _{\mathcal{F}}||F||^{2}d\mu}=\frac{\int _{\mathcal{F}}||\nabla\phi _{0}||^{2}+\phi _{0}^{2}||\nabla u||^{2}d\mu}{\int _{\mathcal{F}}|\phi _{0}|^{2}d\mu}\geq\lambda _{0}+\frac{\int _{\mathcal{F}}\phi 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type="integer" id="S11.Ex234.m1.sh1x.cmml">2</cn></apply><apply id="S11.Ex234.m1.sh1ag.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh1z.cmml">superscript</csymbol><apply id="S11.Ex234.m1.sh1ae.cmml"><csymbol cd="latexml" id="S11.Ex234.m1.sh1aa.cmml">norm</csymbol><apply id="S11.Ex234.m1.sh1ad.cmml"><ci id="S11.Ex234.m1.sh1ab.cmml">∇</ci><ci id="S11.Ex234.m1.sh1ac.cmml">u</ci></apply></apply><cn type="integer" id="S11.Ex234.m1.sh1af.cmml">2</cn></apply><ci id="S11.Ex234.m1.sh1ah.cmml">d</ci><ci id="S11.Ex234.m1.sh1ai.cmml">μ</ci></apply></apply><apply id="S11.Ex234.m1.sh1bc.cmml"><apply id="S11.Ex234.m1.sh1ao.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh1al.cmml">subscript</csymbol><int id="S11.Ex234.m1.sh1am.cmml"/><ci id="S11.Ex234.m1.sh1an.cmml">F</ci></apply><apply id="S11.Ex234.m1.sh1bb.cmml"><times id="S11.Ex234.m1.sh1ap.cmml"/><apply id="S11.Ex234.m1.sh1ay.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh1aq.cmml">superscript</csymbol><apply 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id="S11.Ex234.m1.sh2f.cmml">subscript</csymbol><int id="S11.Ex234.m1.sh2g.cmml"/><ci id="S11.Ex234.m1.sh2h.cmml">F</ci></apply><apply id="S11.Ex234.m1.sh2ab.cmml"><times id="S11.Ex234.m1.sh2j.cmml"/><apply id="S11.Ex234.m1.sh2q.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh2k.cmml">superscript</csymbol><apply id="S11.Ex234.m1.sh2o.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh2l.cmml">subscript</csymbol><ci id="S11.Ex234.m1.sh2m.cmml">ϕ</ci><cn type="integer" id="S11.Ex234.m1.sh2n.cmml">0</cn></apply><cn type="integer" id="S11.Ex234.m1.sh2p.cmml">2</cn></apply><apply id="S11.Ex234.m1.sh2y.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh2r.cmml">superscript</csymbol><apply id="S11.Ex234.m1.sh2w.cmml"><csymbol cd="latexml" id="S11.Ex234.m1.sh2s.cmml">norm</csymbol><apply id="S11.Ex234.m1.sh2v.cmml"><ci id="S11.Ex234.m1.sh2t.cmml">∇</ci><ci id="S11.Ex234.m1.sh2u.cmml">u</ci></apply></apply><cn type="integer" id="S11.Ex234.m1.sh2x.cmml">2</cn></apply><ci id="S11.Ex234.m1.sh2z.cmml">d</ci><ci id="S11.Ex234.m1.sh2aa.cmml">μ</ci></apply></apply><apply id="S11.Ex234.m1.sh2as.cmml"><apply id="S11.Ex234.m1.sh2ag.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh2ad.cmml">subscript</csymbol><int id="S11.Ex234.m1.sh2ae.cmml"/><ci id="S11.Ex234.m1.sh2af.cmml">F</ci></apply><apply id="S11.Ex234.m1.sh2ar.cmml"><times id="S11.Ex234.m1.sh2ah.cmml"/><apply id="S11.Ex234.m1.sh2ao.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh2ai.cmml">superscript</csymbol><apply id="S11.Ex234.m1.sh2am.cmml"><csymbol cd="ambiguous" id="S11.Ex234.m1.sh2aj.cmml">subscript</csymbol><ci id="S11.Ex234.m1.sh2ak.cmml">ϕ</ci><cn type="integer" id="S11.Ex234.m1.sh2al.cmml">0</cn></apply><cn type="integer" id="S11.Ex234.m1.sh2an.cmml">2</cn></apply><ci id="S11.Ex234.m1.sh2ap.cmml">d</ci><ci id="S11.Ex234.m1.sh2aq.cmml">μ</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp18588352" encoding="application/x-tex">\frac{\int _{\mathcal{F}}||\nabla F||^{2}d\mu}{\int _{\mathcal{F}}||F||^{2}d\mu}=\frac{\int _{\mathcal{F}}||\nabla\phi _{0}||^{2}+\phi _{0}^{2}||\nabla u||^{2}d\mu}{\int _{\mathcal{F}}|\phi _{0}|^{2}d\mu}\geq\lambda _{0}+\frac{\int _{\mathcal{F}}\phi _{0}^{2}||\nabla u||^{2}d\mu}{\int _{\mathcal{F}}\phi _{0}^{2}d\mu}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp22331808"><h4>Hit idp22331808</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 7</li> <li>Formulasearchengine score: 12086</li> <li>Reference to collection: _PREFIX_/15/f005660.xhtml#idp22331808</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\int\left\lvert\nabla u\right\rvert^{2}d\mathit{Vol}_{g}=\int\left\lvert\nabla u_{c}^{+}\right\rvert^{2}d\mathit{Vol}_{g}+\int\left\lvert\nabla u_{c}^{-}\right\rvert^{2}d\mathit{Vol}_{g}.$ at pos:350389(22%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.0 * TOKEN_SCORE[leq] + 1.75 * TOKEN_SCORE[+] + 1.0 * TOKEN_SCORE[(] + 1.0 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.0 * TOKEN_SCORE[0] + 1.875 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999995231628418 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[_] + 1.0 * TOKEN_SCORE[|] + 1.96875 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.875*0.279351653691737+1.0*2.71610004241772+1.75*0.0160883895861106+1.0*0.00418257496311516+1.0*0.00417601612706465+1.0*4.28403503219485+1.0*0.0483458611105983+1.875*6.39416349760091+1.0*0.855340292115138+1.9999995231628418*5.92879328325965E-4+1.96875*0.00257082788077282+1.0*0.0975909302497933+1.96875*0.00338742677192689 = 12086.099843288512' final score ~ 12086 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp22331808" alttext="\int\left\lvert\nabla u\right\rvert^{2}d\mathit{Vol}_{g}=\int\left\lvert\nabla u_{c}^{+}\right\rvert^{2}d\mathit{Vol}_{g}+\int\left\lvert\nabla u_{c}^{-}\right\rvert^{2}d\mathit{Vol}_{g}." display="block"><semantics id="idp22332736"><mrow id="idp22332864"><mrow id="idp22332992"><mrow id="idp22333120"><mo id="idp22333248">∫</mo><mrow id="idp22333504"><msup id="idp22333632"><mrow id="idp22333760"><mo id="idp22333888" fence="true">|</mo><mrow id="idp22334384"><mo id="idp22334512">∇</mo><mo id="idp22334800">⁡</mo><mi id="idp22335088">u</mi></mrow><mo id="idp22335344" fence="true">|</mo></mrow><mn id="idp22335872">2</mn></msup><mo id="idp22336128">⁢</mo><mi id="idp22336416">d</mi><mo id="idp22336672">⁢</mo><msub id="idp22336960"><mi id="idp22337088" mathvariant="italic">Vol</mi><mi id="idp22337616">g</mi></msub></mrow></mrow><mo id="idp22337872">=</mo><mrow id="idp22338128"><mrow id="idp22338256"><mo id="idp22338384">∫</mo><mrow id="idp22338672"><msup id="idp22338800"><mrow id="idp22338928"><mo id="idp22339056" fence="true">|</mo><mrow id="idp22339584"><mo id="idp22339712">∇</mo><mo id="idp22340000">⁡</mo><msubsup id="idp22340288"><mi id="idp22340416">u</mi><mi id="idp22340672">c</mi><mo id="idp22340928">+</mo></msubsup></mrow><mo id="idp22341184" fence="true">|</mo></mrow><mn id="idp22341712">2</mn></msup><mo id="idp22341968">⁢</mo><mi id="idp22342256">d</mi><mo id="idp22342512">⁢</mo><msub id="idp22342800"><mi id="idp22342928" mathvariant="italic">Vol</mi><mi id="idp22343456">g</mi></msub></mrow></mrow><mo id="idp22343712">+</mo><mrow id="idp22343968"><mo id="idp22344096">∫</mo><mrow id="idp22344384"><msup id="idp22344512"><mrow id="idp22344640"><mo id="idp22344768" fence="true">|</mo><mrow id="idp22345296"><mo id="idp22345424">∇</mo><mo id="idp22345712">⁡</mo><msubsup id="idp22346000"><mi id="idp22346128">u</mi><mi id="idp22346384">c</mi><mo id="idp22346640">-</mo></msubsup></mrow><mo id="idp22346896" fence="true">|</mo></mrow><mn id="idp22347424">2</mn></msup><mo id="idp22347680">⁢</mo><mi id="idp22347968">d</mi><mo id="idp22348224">⁢</mo><msub id="idp22348512"><mi id="idp22348640" mathvariant="italic">Vol</mi><mi id="idp22349168">g</mi></msub></mrow></mrow></mrow></mrow><mo id="idp22349424">.</mo></mrow><annotation-xml id="idp22349680" encoding="MathML-Content"><apply id="idp22350080"><eq id="idp22350208"/><apply id="idp22350336"><int id="idp22350464"/><apply id="idp22350592"><times id="idp22350720"/><apply id="idp22350848"><csymbol id="idp22350976" cd="ambiguous">superscript</csymbol><apply id="idp22351536"><abs id="idp22351664"/><apply id="idp22351792"><ci id="idp22351920">∇</ci><ci id="idp22352208">u</ci></apply></apply><cn id="idp22352464" type="integer">2</cn></apply><ci id="idp22352992">d</ci><apply id="idp22353248"><csymbol id="idp22353376" cd="ambiguous">subscript</csymbol><ci id="idp22353936">Vol</ci><ci id="idp22354192">g</ci></apply></apply></apply><apply id="idp22354448"><plus id="idp22354576"/><apply id="idp22354704"><int id="idp22354832"/><apply id="idp22354960"><times id="idp22355088"/><apply id="idp22355216"><csymbol id="idp22355344" cd="ambiguous">superscript</csymbol><apply id="idp22355904"><abs id="idp22356032"/><apply id="idp22356160"><ci id="idp22356288">∇</ci><apply id="idp22356576"><csymbol id="idp22356704" cd="ambiguous">superscript</csymbol><apply id="idp22357264"><csymbol id="idp22357392" cd="ambiguous">subscript</csymbol><ci id="idp22357952">u</ci><ci id="idp22358208">c</ci></apply><plus id="idp22358464"/></apply></apply></apply><cn id="idp22358592" type="integer">2</cn></apply><ci id="idp22359120">d</ci><apply id="idp22359376"><csymbol id="idp22359504" cd="ambiguous">subscript</csymbol><ci id="idp22360064">Vol</ci><ci id="idp22360320">g</ci></apply></apply></apply><apply id="idp22360576"><int id="idp22360704"/><apply id="idp22360832"><times id="idp22360960"/><apply id="idp22361088"><csymbol id="idp22361216" cd="ambiguous">superscript</csymbol><apply id="idp22361776"><abs id="idp22361904"/><apply id="idp22362032"><ci id="idp22362160">∇</ci><apply id="idp22362448"><csymbol id="idp22362576" cd="ambiguous">superscript</csymbol><apply id="idp22363136"><csymbol id="idp22363264" cd="ambiguous">subscript</csymbol><ci id="idp22363824">u</ci><ci id="idp22364080">c</ci></apply><minus id="idp22364336"/></apply></apply></apply><cn id="idp22364464" type="integer">2</cn></apply><ci id="idp22364992">d</ci><apply id="idp22365248"><csymbol id="idp22365376" cd="ambiguous">subscript</csymbol><ci id="idp22365936">Vol</ci><ci id="idp22366192">g</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp22366448" encoding="application/x-tex">\int\left\lvert\nabla u\right\rvert^{2}d\mathit{Vol}_{g}=\int\left\lvert\nabla u_{c}^{+}\right\rvert^{2}d\mathit{Vol}_{g}+\int\left\lvert\nabla u_{c}^{-}\right\rvert^{2}d\mathit{Vol}_{g}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp15078368"><h4>Hit idp15078368</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 8</li> <li>Formulasearchengine score: 12057</li> <li>Reference to collection: _PREFIX_/15/f005756.xhtml#idp15078368</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\int _{{\Omega\setminus D}}|\nabla u_{1}|^{2}\,\delta(x)\, dx\leq C\int _{{\partial\Omega}}|(u_{1})^{*}|^{2}\, d\sigma\leq C\int _{{\partial\Omega}}|f|^{2}\, d\sigma,$ at pos:1922117(99%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.75 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.75 * TOKEN_SCORE[leq] + 1.0 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.0 * TOKEN_SCORE[0] + 1.5 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999980926513672 * TOKEN_SCORE[\] + 1.96875 * TOKEN_SCORE[_] + 1.984375 * TOKEN_SCORE[|] + 1.9375 * TOKEN_SCORE[^] =+100.0+0.0+1.75*0.158568544552516+1.875*0.279351653691737+1.75*2.71610004241772+1.0*0.0160883895861106+1.75*0.00418257496311516+1.75*0.00417601612706465+1.0*4.28403503219485+1.0*0.0483458611105983+1.5*6.39416349760091+1.0*0.855340292115138+1.9999980926513672*5.92879328325965E-4+1.96875*0.00257082788077282+1.984375*0.0975909302497933+1.9375*0.00338742677192689 = 12057.060395018694' final score ~ 12057 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp15078368" alttext="\int _{{\Omega\setminus D}}|\nabla u_{1}|^{2}\,\delta(x)\, dx\leq C\int _{{\partial\Omega}}|(u_{1})^{*}|^{2}\, d\sigma\leq C\int _{{\partial\Omega}}|f|^{2}\, d\sigma," display="block"><semantics id="idp15079264"><mrow id="idp15079392"><mrow id="idp15079520"><mrow id="idp15079648"><msub id="idp15079776"><mo id="idp15079904">∫</mo><mrow id="idp15080160"><mi id="idp15080288" mathvariant="normal">Ω</mi><mo id="idp15080816">∖</mo><mi id="idp15081104">D</mi></mrow></msub><mrow id="idp15081360"><msup id="idp15081488"><mrow id="idp15081616"><mo id="idp15081744" fence="true">|</mo><mrow id="idp15082272"><mo id="idp15082400">∇</mo><mo id="idp15082688">⁡</mo><msub id="idp15082976"><mi id="idp15083104">u</mi><mn id="idp15083360">1</mn></msub></mrow><mo id="idp15083616" fence="true">|</mo></mrow><mn id="idp15084144">2</mn></msup><mo id="idp15084400">⁢</mo><mi id="idp15084688">δ</mi><mo id="idp15084944">⁢</mo><mrow id="idp15085200"><mo id="idp15085328">(</mo><mi id="idp15085584">x</mi><mo id="idp15085840">)</mo></mrow><mo id="idp15086096">⁢</mo><mi id="idp15086352">d</mi><mo id="idp15086608">⁢</mo><mi id="idp15086896">x</mi></mrow></mrow><mo id="idp15087152">≤</mo><mrow id="idp15087440"><mi id="idp15087568">C</mi><mo id="idp15087824">⁢</mo><mrow id="idp15088112"><msub id="idp15088240"><mo id="idp15088368">∫</mo><mrow id="idp15088656"><mo id="idp15088784">∂</mo><mo id="idp15089072">⁡</mo><mi id="idp15089360" mathvariant="normal">Ω</mi></mrow></msub><mrow id="idp15089920"><msup id="idp15090048"><mrow id="idp15090176"><mo id="idp15090304" fence="true">|</mo><msup id="idp15090832"><mrow id="idp15090960"><mo id="idp15091088">(</mo><msub id="idp15091344"><mi id="idp15091472">u</mi><mn id="idp15091728">1</mn></msub><mo id="idp15091984">)</mo></mrow><mo id="idp15092240">*</mo></msup><mo id="idp15092496" fence="true">|</mo></mrow><mn id="idp15093024">2</mn></msup><mo id="idp15093280">⁢</mo><mi id="idp15093568">d</mi><mo id="idp15093824">⁢</mo><mi id="idp15094112">σ</mi></mrow></mrow></mrow><mo id="idp15094400">≤</mo><mrow id="idp15094688"><mi id="idp15094816">C</mi><mo id="idp15095072">⁢</mo><mrow id="idp15095360"><msub id="idp15095488"><mo id="idp15095616">∫</mo><mrow id="idp15095904"><mo id="idp15096032">∂</mo><mo id="idp15096320">⁡</mo><mi id="idp15096608" mathvariant="normal">Ω</mi></mrow></msub><mrow id="idp15097168"><msup id="idp15097296"><mrow id="idp15097424"><mo id="idp15097552" fence="true">|</mo><mi id="idp15098080">f</mi><mo id="idp15098336" fence="true">|</mo></mrow><mn id="idp15098864">2</mn></msup><mo id="idp15099120">⁢</mo><mi id="idp15099408">d</mi><mo id="idp15099664">⁢</mo><mi id="idp15099952">σ</mi></mrow></mrow></mrow></mrow><mo id="idp15100240">,</mo></mrow><annotation-xml id="idp15100496" encoding="MathML-Content"><apply id="idp15100896"><and id="idp15101024"/><apply id="idp15101152"><leq id="idp15101280"/><apply id="idp15101408"><apply id="idp15101536"><csymbol id="idp15101664" cd="ambiguous">subscript</csymbol><int id="idp15102224"/><apply id="idp15102352"><setdiff id="idp15102480"/><ci id="idp15102608">Ω</ci><ci id="idp15102896">D</ci></apply></apply><apply id="idp15103152"><times id="idp15103280"/><apply id="idp15103408"><csymbol id="idp15103536" cd="ambiguous">superscript</csymbol><apply id="idp15104096"><abs id="idp15104224"/><apply id="idp15104352"><ci id="idp15104480">∇</ci><apply id="idp15104768"><csymbol id="idp15104896" cd="ambiguous">subscript</csymbol><ci id="idp15105456">u</ci><cn id="idp15105712" type="integer">1</cn></apply></apply></apply><cn id="idp15106240" type="integer">2</cn></apply><ci id="idp15106768">δ</ci><ci id="idp15107056">x</ci><ci id="idp15107312">d</ci><ci id="idp15107568">x</ci></apply></apply><apply id="S8.E21.m1.sh1y.cmml"><times id="S8.E21.m1.sh1.cmml"/><ci id="S8.E21.m1.sh1a.cmml">C</ci><apply id="S8.E21.m1.sh1x.cmml"><apply id="S8.E21.m1.sh1g.cmml"><csymbol cd="ambiguous" id="S8.E21.m1.sh1b.cmml">subscript</csymbol><int id="S8.E21.m1.sh1c.cmml"/><apply id="S8.E21.m1.sh1f.cmml"><partialdiff id="S8.E21.m1.sh1d.cmml"/><ci id="S8.E21.m1.sh1e.cmml">Ω</ci></apply></apply><apply id="S8.E21.m1.sh1w.cmml"><times id="S8.E21.m1.sh1h.cmml"/><apply id="S8.E21.m1.sh1t.cmml"><csymbol cd="ambiguous" id="S8.E21.m1.sh1i.cmml">superscript</csymbol><apply id="S8.E21.m1.sh1r.cmml"><abs id="S8.E21.m1.sh1j.cmml"/><apply id="S8.E21.m1.sh1q.cmml"><csymbol cd="ambiguous" id="S8.E21.m1.sh1k.cmml">superscript</csymbol><apply id="S8.E21.m1.sh1o.cmml"><csymbol cd="ambiguous" id="S8.E21.m1.sh1l.cmml">subscript</csymbol><ci id="S8.E21.m1.sh1m.cmml">u</ci><cn type="integer" id="S8.E21.m1.sh1n.cmml">1</cn></apply><times id="S8.E21.m1.sh1p.cmml"/></apply></apply><cn type="integer" id="S8.E21.m1.sh1s.cmml">2</cn></apply><ci id="S8.E21.m1.sh1u.cmml">d</ci><ci id="S8.E21.m1.sh1v.cmml">σ</ci></apply></apply></apply></apply><apply id="idp15121456"><leq id="idp15121584"/><share id="idp15121712" href="#S8.E21.m1.sh1.cmml"/><apply id="S8.E21.m1.sh2s.cmml"><times id="S8.E21.m1.sh2.cmml"/><ci id="S8.E21.m1.sh2a.cmml">C</ci><apply id="S8.E21.m1.sh2r.cmml"><apply id="S8.E21.m1.sh2g.cmml"><csymbol cd="ambiguous" id="S8.E21.m1.sh2b.cmml">subscript</csymbol><int id="S8.E21.m1.sh2c.cmml"/><apply id="S8.E21.m1.sh2f.cmml"><partialdiff id="S8.E21.m1.sh2d.cmml"/><ci id="S8.E21.m1.sh2e.cmml">Ω</ci></apply></apply><apply id="S8.E21.m1.sh2q.cmml"><times id="S8.E21.m1.sh2h.cmml"/><apply id="S8.E21.m1.sh2n.cmml"><csymbol cd="ambiguous" id="S8.E21.m1.sh2i.cmml">superscript</csymbol><apply id="S8.E21.m1.sh2l.cmml"><abs id="S8.E21.m1.sh2j.cmml"/><ci id="S8.E21.m1.sh2k.cmml">f</ci></apply><cn type="integer" id="S8.E21.m1.sh2m.cmml">2</cn></apply><ci id="S8.E21.m1.sh2o.cmml">d</ci><ci id="S8.E21.m1.sh2p.cmml">σ</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp15132080" encoding="application/x-tex">\int _{{\Omega\setminus D}}|\nabla u_{1}|^{2}\,\delta(x)\, dx\leq C\int _{{\partial\Omega}}|(u_{1})^{*}|^{2}\, d\sigma\leq C\int _{{\partial\Omega}}|f|^{2}\, d\sigma,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp21387280"><h4>Hit idp21387280</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 9</li> <li>Formulasearchengine score: 12056</li> <li>Reference to collection: _PREFIX_/63/f024901.xhtml#idp21387280</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\displaystyle\int _{{A_{k}}}|\nabla u|^{{p(x)}}dx\leq d_{1}\int _{{A_{k}}}u^{{q_{0}(x)}}dx+d_{2}\int _{{\Gamma _{k}}}u^{{q_{1}(x)}}d\sigma,$ at pos:225820(25%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.5 * TOKEN_SCORE[leq] + 1.5 * TOKEN_SCORE[+] + 1.875 * TOKEN_SCORE[(] + 1.875 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.5 * TOKEN_SCORE[0] + 1.5 * TOKEN_SCORE[nabla] + 1.75 * TOKEN_SCORE[q] + 1.99609375 * TOKEN_SCORE[\] + 1.9990234375 * TOKEN_SCORE[_] + 1.75 * TOKEN_SCORE[|] + 1.875 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.875*0.279351653691737+1.5*2.71610004241772+1.5*0.0160883895861106+1.875*0.00418257496311516+1.875*0.00417601612706465+1.0*4.28403503219485+1.5*0.0483458611105983+1.5*6.39416349760091+1.75*0.855340292115138+1.99609375*5.92879328325965E-4+1.9990234375*0.00257082788077282+1.75*0.0975909302497933+1.875*0.00338742677192689 = 12056.315810051512' final score ~ 12056 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp21387280" alttext="\displaystyle\int _{{A_{k}}}|\nabla u|^{{p(x)}}dx\leq d_{1}\int _{{A_{k}}}u^{{q_{0}(x)}}dx+d_{2}\int _{{\Gamma _{k}}}u^{{q_{1}(x)}}d\sigma," display="inline"><semantics id="idp21388160"><mrow id="idp21388288"><mrow id="idp21388416"><mrow id="idp21388544"><mstyle id="idp21388672" displaystyle="true"><msub id="idp21389040"><mo id="idp21389168">∫</mo><msub id="idp21389424"><mi id="idp21389552">A</mi><mi id="idp21389808">k</mi></msub></msub></mstyle><mrow id="idp21390112"><msup id="idp21390240"><mrow id="idp21390368"><mo id="idp21390496" fence="true">|</mo><mrow id="idp21391024"><mo id="idp21391152">∇</mo><mo id="idp21391440">⁡</mo><mi id="idp21391728">u</mi></mrow><mo id="idp21391984" fence="true">|</mo></mrow><mrow id="idp21392512"><mi id="idp21392640">p</mi><mo id="idp21392896">⁢</mo><mrow id="idp21393184"><mo id="idp21393312">(</mo><mi id="idp21393568">x</mi><mo id="idp21393824">)</mo></mrow></mrow></msup><mo id="idp21394080">⁢</mo><mi id="idp21394368">d</mi><mo id="idp21394624">⁢</mo><mi id="idp21394912">x</mi></mrow></mrow><mo id="idp21395168">≤</mo><mrow id="idp21395456"><mrow id="idp21395584"><msub id="idp21395712"><mi id="idp21395840">d</mi><mn id="idp21396096">1</mn></msub><mo id="idp21396352">⁢</mo><mrow id="idp21396640"><mstyle id="idp21396768" displaystyle="true"><msub id="idp21397168"><mo id="idp21397296">∫</mo><msub id="idp21397584"><mi id="idp21397712">A</mi><mi id="idp21397968">k</mi></msub></msub></mstyle><mrow id="idp21398224"><msup id="idp21398352"><mi id="idp21398480">u</mi><mrow id="idp21398736"><msub id="idp21398864"><mi id="idp21398992">q</mi><mn id="idp21399248">0</mn></msub><mo id="idp21399504">⁢</mo><mrow id="idp21399792"><mo id="idp21399920">(</mo><mi id="idp21400176">x</mi><mo id="idp21400432">)</mo></mrow></mrow></msup><mo id="idp21400688">⁢</mo><mi id="idp21400976">d</mi><mo id="idp21401232">⁢</mo><mi id="idp21401520">x</mi></mrow></mrow></mrow><mo id="idp21401776">+</mo><mrow id="idp21402032"><msub id="idp21402160"><mi id="idp21402288">d</mi><mn id="idp21402544">2</mn></msub><mo id="idp21402800">⁢</mo><mrow id="idp21403088"><mstyle id="idp21403216" displaystyle="true"><msub id="idp21403616"><mo id="idp21403744">∫</mo><msub id="idp21404032"><mi id="idp21404160" mathvariant="normal">Γ</mi><mi id="idp21404720">k</mi></msub></msub></mstyle><mrow id="idp21404976"><msup id="idp21405104"><mi id="idp21405232">u</mi><mrow id="idp21405488"><msub id="idp21405616"><mi id="idp21405744">q</mi><mn id="idp21406000">1</mn></msub><mo id="idp21406256">⁢</mo><mrow id="idp21406544"><mo id="idp21406672">(</mo><mi id="idp21406928">x</mi><mo id="idp21407184">)</mo></mrow></mrow></msup><mo id="idp21407440">⁢</mo><mi id="idp21407728">d</mi><mo id="idp21407984">⁢</mo><mi id="idp21408272">σ</mi></mrow></mrow></mrow></mrow></mrow><mo id="idp21408560">,</mo></mrow><annotation-xml id="idp21408816" encoding="MathML-Content"><apply id="idp21409216"><leq id="idp21409344"/><apply id="idp21409472"><apply id="idp21409600"><csymbol id="idp21409728" cd="ambiguous">subscript</csymbol><int id="idp21410288"/><apply id="idp21410416"><csymbol id="idp21410544" cd="ambiguous">subscript</csymbol><ci id="idp21411104">A</ci><ci id="idp21411360">k</ci></apply></apply><apply id="idp21411616"><times id="idp21411744"/><apply id="idp21411872"><csymbol id="idp21412000" cd="ambiguous">superscript</csymbol><apply id="idp21412560"><abs id="idp21412688"/><apply id="idp21412816"><ci id="idp21412944">∇</ci><ci id="idp21413232">u</ci></apply></apply><apply id="idp21413488"><times id="idp21413616"/><ci id="idp21413744">p</ci><ci id="idp21414000">x</ci></apply></apply><ci id="idp21414256">d</ci><ci id="idp21414512">x</ci></apply></apply><apply id="idp21414768"><plus id="idp21414896"/><apply id="idp21415024"><times id="idp21415152"/><apply id="idp21415280"><csymbol id="idp21415408" cd="ambiguous">subscript</csymbol><ci id="idp21415968">d</ci><cn id="idp21416224" type="integer">1</cn></apply><apply id="idp21416752"><apply id="idp21416880"><csymbol id="idp21417008" cd="ambiguous">subscript</csymbol><int id="idp21417568"/><apply id="idp21417696"><csymbol id="idp21417824" cd="ambiguous">subscript</csymbol><ci id="idp21418384">A</ci><ci id="idp21418640">k</ci></apply></apply><apply id="idp21418896"><times id="idp21419024"/><apply id="idp21419152"><csymbol id="idp21419280" cd="ambiguous">superscript</csymbol><ci id="idp21419840">u</ci><apply id="idp21420096"><times id="idp21420224"/><apply id="idp21420352"><csymbol id="idp21420480" cd="ambiguous">subscript</csymbol><ci id="idp21421040">q</ci><cn id="idp21421296" type="integer">0</cn></apply><ci id="idp21421824">x</ci></apply></apply><ci id="idp21422080">d</ci><ci id="idp21422336">x</ci></apply></apply></apply><apply id="idp21422592"><times id="idp21422720"/><apply id="idp21422848"><csymbol id="idp21422976" cd="ambiguous">subscript</csymbol><ci id="idp21423536">d</ci><cn id="idp21423792" type="integer">2</cn></apply><apply id="idp21424320"><apply id="idp21424448"><csymbol id="idp21424576" cd="ambiguous">subscript</csymbol><int id="idp21425136"/><apply id="idp21425264"><csymbol id="idp21425392" cd="ambiguous">subscript</csymbol><ci id="idp21425952">Γ</ci><ci id="idp21426240">k</ci></apply></apply><apply id="idp21426496"><times id="idp21426624"/><apply id="idp21426752"><csymbol id="idp21426880" cd="ambiguous">superscript</csymbol><ci id="idp21427440">u</ci><apply id="idp21427696"><times id="idp21427824"/><apply id="idp21427952"><csymbol id="idp21428080" cd="ambiguous">subscript</csymbol><ci id="idp21428640">q</ci><cn id="idp21428896" type="integer">1</cn></apply><ci id="idp21429424">x</ci></apply></apply><ci id="idp21429680">d</ci><ci id="idp21429936">σ</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp21430224" encoding="application/x-tex">\displaystyle\int _{{A_{k}}}|\nabla u|^{{p(x)}}dx\leq d_{1}\int _{{A_{k}}}u^{{q_{0}(x)}}dx+d_{2}\int _{{\Gamma _{k}}}u^{{q_{1}(x)}}d\sigma,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp22368352"><h4>Hit idp22368352</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 10</li> <li>Formulasearchengine score: 12056</li> <li>Reference to collection: _PREFIX_/63/f024901.xhtml#idp22368352</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\displaystyle\int _{{\tilde{A}_{k}}}|\nabla u|^{{p(x)}}dx\leq d_{1}\int _{{\tilde{A}_{k}}}(-u)^{{q_{0}(x)}}dx+d_{2}\int _{{\tilde{\Gamma}_{k}}}(-u)^{{q_{1}(x)}}d\sigma,$ at pos:337375(37%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.5 * TOKEN_SCORE[leq] + 1.5 * TOKEN_SCORE[+] + 1.96875 * TOKEN_SCORE[(] + 1.96875 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.5 * TOKEN_SCORE[0] + 1.5 * TOKEN_SCORE[nabla] + 1.75 * TOKEN_SCORE[q] + 1.99951171875 * TOKEN_SCORE[\] + 1.9990234375 * TOKEN_SCORE[_] + 1.75 * TOKEN_SCORE[|] + 1.875 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.875*0.279351653691737+1.5*2.71610004241772+1.5*0.0160883895861106+1.96875*0.00418257496311516+1.96875*0.00417601612706465+1.0*4.28403503219485+1.5*0.0483458611105983+1.5*6.39416349760091+1.75*0.855340292115138+1.99951171875*5.92879328325965E-4+1.9990234375*0.00257082788077282+1.75*0.0975909302497933+1.875*0.00338742677192689 = 12056.394374487283' final score ~ 12056 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp22368352" alttext="\displaystyle\int _{{\tilde{A}_{k}}}|\nabla u|^{{p(x)}}dx\leq d_{1}\int _{{\tilde{A}_{k}}}(-u)^{{q_{0}(x)}}dx+d_{2}\int _{{\tilde{\Gamma}_{k}}}(-u)^{{q_{1}(x)}}d\sigma," display="inline"><semantics id="idp22369264"><mrow id="idp22369392"><mrow id="idp22369520"><mrow id="idp22369648"><mstyle id="idp22369776" displaystyle="true"><msub id="idp22370144"><mo id="idp22370272">∫</mo><msub id="idp22370528"><mover id="idp22370656" accent="true"><mi id="idp22371056">A</mi><mo id="idp22371312">~</mo></mover><mi id="idp22371568">k</mi></msub></msub></mstyle><mrow id="idp22371824"><msup id="idp22371952"><mrow id="idp22372080"><mo id="idp22372208" fence="true">|</mo><mrow id="idp22372736"><mo id="idp22372864">∇</mo><mo id="idp22373152">⁡</mo><mi id="idp22373440">u</mi></mrow><mo id="idp22373696" fence="true">|</mo></mrow><mrow id="idp22374224"><mi id="idp22374352">p</mi><mo id="idp22374608">⁢</mo><mrow id="idp22374896"><mo id="idp22375024">(</mo><mi id="idp22375280">x</mi><mo id="idp22375536">)</mo></mrow></mrow></msup><mo id="idp22375792">⁢</mo><mi id="idp22376080">d</mi><mo id="idp22376336">⁢</mo><mi id="idp22376624">x</mi></mrow></mrow><mo id="idp22376880">≤</mo><mrow id="idp22377168"><mrow id="idp22377296"><msub id="idp22377424"><mi id="idp22377552">d</mi><mn id="idp22377808">1</mn></msub><mo id="idp22378064">⁢</mo><mrow id="idp22378352"><mstyle id="idp22378480" displaystyle="true"><msub id="idp22378880"><mo id="idp22379008">∫</mo><msub id="idp22379296"><mover id="idp22379424" accent="true"><mi id="idp22379824">A</mi><mo id="idp22380080">~</mo></mover><mi id="idp22380336">k</mi></msub></msub></mstyle><mrow id="idp22380592"><msup id="idp22380720"><mrow id="idp22380848"><mo id="idp22380976">(</mo><mrow id="idp22381232"><mo id="idp22381360">-</mo><mi id="idp22381616">u</mi></mrow><mo id="idp22381872">)</mo></mrow><mrow id="idp22382128"><msub id="idp22382256"><mi id="idp22382384">q</mi><mn id="idp22382640">0</mn></msub><mo id="idp22382896">⁢</mo><mrow id="idp22383184"><mo id="idp22383312">(</mo><mi id="idp22383568">x</mi><mo id="idp22383824">)</mo></mrow></mrow></msup><mo id="idp22384080">⁢</mo><mi id="idp22384368">d</mi><mo id="idp22384624">⁢</mo><mi id="idp22384912">x</mi></mrow></mrow></mrow><mo id="idp22385168">+</mo><mrow id="idp22385424"><msub id="idp22385552"><mi id="idp22385680">d</mi><mn id="idp22385936">2</mn></msub><mo id="idp22386192">⁢</mo><mrow id="idp22386480"><mstyle id="idp22386608" displaystyle="true"><msub id="idp22387008"><mo id="idp22387136">∫</mo><msub id="idp22387424"><mover id="idp22387552" accent="true"><mi id="idp22387952" mathvariant="normal">Γ</mi><mo id="idp22388512">~</mo></mover><mi id="idp22388768">k</mi></msub></msub></mstyle><mrow id="idp22389024"><msup id="idp22389152"><mrow id="idp22389280"><mo id="idp22389408">(</mo><mrow id="idp22389664"><mo id="idp22389792">-</mo><mi id="idp22390048">u</mi></mrow><mo id="idp22390304">)</mo></mrow><mrow id="idp22390560"><msub id="idp22390688"><mi id="idp22390816">q</mi><mn id="idp22391072">1</mn></msub><mo id="idp22391328">⁢</mo><mrow id="idp22391616"><mo id="idp22391744">(</mo><mi id="idp22392000">x</mi><mo id="idp22392256">)</mo></mrow></mrow></msup><mo id="idp22392512">⁢</mo><mi id="idp22392800">d</mi><mo id="idp22393056">⁢</mo><mi id="idp22393344">σ</mi></mrow></mrow></mrow></mrow></mrow><mo id="idp22393632">,</mo></mrow><annotation-xml id="idp22393888" encoding="MathML-Content"><apply id="idp22394288"><leq id="idp22394416"/><apply id="idp22394544"><apply id="idp22394672"><csymbol id="idp22394800" cd="ambiguous">subscript</csymbol><int id="idp22395360"/><apply id="idp22395488"><csymbol id="idp22395616" cd="ambiguous">subscript</csymbol><apply id="idp22396176"><ci id="idp22396304">~</ci><ci id="idp22396560">A</ci></apply><ci id="idp22396816">k</ci></apply></apply><apply id="idp22397072"><times id="idp22397200"/><apply id="idp22397328"><csymbol id="idp22397456" cd="ambiguous">superscript</csymbol><apply id="idp22398016"><abs id="idp22398144"/><apply id="idp22398272"><ci id="idp22398400">∇</ci><ci id="idp22398688">u</ci></apply></apply><apply id="idp22398944"><times id="idp22399072"/><ci id="idp22399200">p</ci><ci id="idp22399456">x</ci></apply></apply><ci id="idp22399712">d</ci><ci id="idp22399968">x</ci></apply></apply><apply id="idp22400224"><plus id="idp22400352"/><apply id="idp22400480"><times id="idp22400608"/><apply id="idp22400736"><csymbol id="idp22400864" cd="ambiguous">subscript</csymbol><ci id="idp22401424">d</ci><cn id="idp22401680" type="integer">1</cn></apply><apply id="idp22402208"><apply id="idp22402336"><csymbol id="idp22402464" cd="ambiguous">subscript</csymbol><int id="idp22403024"/><apply id="idp22403152"><csymbol id="idp22403280" cd="ambiguous">subscript</csymbol><apply id="idp22403840"><ci id="idp22403968">~</ci><ci id="idp22404224">A</ci></apply><ci id="idp22404480">k</ci></apply></apply><apply id="idp22404736"><times id="idp22404864"/><apply id="idp22404992"><csymbol id="idp22405120" cd="ambiguous">superscript</csymbol><apply id="idp22405680"><minus id="idp22405808"/><ci id="idp22405936">u</ci></apply><apply id="idp22406192"><times id="idp22406320"/><apply id="idp22406448"><csymbol id="idp22406576" cd="ambiguous">subscript</csymbol><ci id="idp22407136">q</ci><cn id="idp22407392" type="integer">0</cn></apply><ci id="idp22407920">x</ci></apply></apply><ci id="idp22408176">d</ci><ci id="idp22408432">x</ci></apply></apply></apply><apply id="idp22408688"><times id="idp22408816"/><apply id="idp22408944"><csymbol id="idp22409072" cd="ambiguous">subscript</csymbol><ci id="idp22409632">d</ci><cn id="idp22409888" type="integer">2</cn></apply><apply id="idp22410416"><apply id="idp22410544"><csymbol id="idp22410672" cd="ambiguous">subscript</csymbol><int id="idp22411232"/><apply id="idp22411360"><csymbol id="idp22411488" cd="ambiguous">subscript</csymbol><apply id="idp22412048"><ci id="idp22412176">~</ci><ci id="idp22412432">Γ</ci></apply><ci id="idp22412720">k</ci></apply></apply><apply id="idp22412976"><times id="idp22413104"/><apply id="idp22413232"><csymbol id="idp22413360" cd="ambiguous">superscript</csymbol><apply id="idp22413920"><minus id="idp22414048"/><ci id="idp22414176">u</ci></apply><apply id="idp22414432"><times id="idp22414560"/><apply id="idp22414688"><csymbol id="idp22414816" cd="ambiguous">subscript</csymbol><ci id="idp22415376">q</ci><cn id="idp22415632" type="integer">1</cn></apply><ci id="idp22416160">x</ci></apply></apply><ci id="idp22416416">d</ci><ci id="idp22416672">σ</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp22416960" encoding="application/x-tex">\displaystyle\int _{{\tilde{A}_{k}}}|\nabla u|^{{p(x)}}dx\leq d_{1}\int _{{\tilde{A}_{k}}}(-u)^{{q_{0}(x)}}dx+d_{2}\int _{{\tilde{\Gamma}_{k}}}(-u)^{{q_{1}(x)}}d\sigma,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp8107968"><h4>Hit idp8107968</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 11</li> <li>Formulasearchengine score: 12016</li> <li>Reference to collection: _PREFIX_/62/f024686.xhtml#idp8107968</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\delta\sum _{{i=1}}^{d}\left(\int _{\Omega}|\nabla\phi _{i}|^{2}\, dx+\int _{\Omega}\beta(x)|\phi _{i}|^{2}\, dx\right)\geq\delta\lambda _{0}\sum _{{i=1}}^{d}\int _{{\Omega}}|\nabla\phi _{i}|^{2}\, dx.$ at pos:971952(70%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.75 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.0 * TOKEN_SCORE[leq] + 1.5 * TOKEN_SCORE[+] + 1.75 * TOKEN_SCORE[(] + 1.75 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.5 * TOKEN_SCORE[0] + 1.75 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999998807907104 * TOKEN_SCORE[\] + 1.998046875 * TOKEN_SCORE[_] + 1.984375 * TOKEN_SCORE[|] + 1.96875 * TOKEN_SCORE[^] =+100.0+0.0+1.75*0.158568544552516+1.875*0.279351653691737+1.0*2.71610004241772+1.5*0.0160883895861106+1.75*0.00418257496311516+1.75*0.00417601612706465+1.0*4.28403503219485+1.5*0.0483458611105983+1.75*6.39416349760091+1.0*0.855340292115138+1.9999998807907104*5.92879328325965E-4+1.998046875*0.00257082788077282+1.984375*0.0975909302497933+1.96875*0.00338742677192689 = 12016.446809349207' final score ~ 12016 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp8107968" alttext="\delta\sum _{{i=1}}^{d}\left(\int _{\Omega}|\nabla\phi _{i}|^{2}\, dx+\int _{\Omega}\beta(x)|\phi _{i}|^{2}\, dx\right)\geq\delta\lambda _{0}\sum _{{i=1}}^{d}\int _{{\Omega}}|\nabla\phi _{i}|^{2}\, dx." display="block"><semantics id="idp8108912"><mrow id="idp8109040"><mrow id="idp8109168"><mrow id="idp8109296"><mi id="idp8109424">δ</mi><mo id="idp8109680">⁢</mo><mrow id="idp8109936"><mover id="idp8110064"><munder id="idp8110192"><mo id="idp8110320" movablelimits="false">∑</mo><mrow id="idp8110880"><mi id="idp8111008">i</mi><mo id="idp8111264" movablelimits="false">=</mo><mn id="idp8111792">1</mn></mrow></munder><mi id="idp8112048">d</mi></mover><mrow id="idp8112304"><mo id="idp8112432">(</mo><mrow id="idp8112688"><mrow id="idp8112816"><msub id="idp8112944"><mo id="idp8113072">∫</mo><mi id="idp8113360" mathvariant="normal">Ω</mi></msub><mrow id="idp8113920"><msup id="idp8114048"><mrow id="idp8114176"><mo id="idp8114304" fence="true">|</mo><mrow id="idp8114832"><mo id="idp8114960">∇</mo><mo id="idp8115248">⁡</mo><msub id="idp8115536"><mi id="idp8115664">ϕ</mi><mi id="idp8115952">i</mi></msub></mrow><mo id="idp8116208" fence="true">|</mo></mrow><mn id="idp8116736">2</mn></msup><mo id="idp8116992">⁢</mo><mi id="idp8117280">d</mi><mo id="idp8117536">⁢</mo><mi id="idp8117824">x</mi></mrow></mrow><mo id="idp8118080">+</mo><mrow id="idp8118336"><msub id="idp8118464"><mo id="idp8118592">∫</mo><mi id="idp8118880" mathvariant="normal">Ω</mi></msub><mrow id="idp8119440"><mi id="idp8119568">β</mi><mo id="idp8119856">⁢</mo><mrow id="idp8120144"><mo id="idp8120272">(</mo><mi id="idp8120528">x</mi><mo id="idp8120784">)</mo></mrow><mo id="idp8121040">⁢</mo><msup id="idp8121328"><mrow id="idp8121456"><mo id="idp8121584" fence="true">|</mo><msub id="idp8122112"><mi id="idp8122240">ϕ</mi><mi id="idp8122528">i</mi></msub><mo id="idp8122784" fence="true">|</mo></mrow><mn id="idp8123312">2</mn></msup><mo id="idp8123568">⁢</mo><mi id="idp8123856">d</mi><mo id="idp8124112">⁢</mo><mi id="idp8124400">x</mi></mrow></mrow></mrow><mo id="idp8124656">)</mo></mrow></mrow></mrow><mo id="idp8124912">≥</mo><mrow id="idp8125200"><mi id="idp8125328">δ</mi><mo id="idp8125616">⁢</mo><msub id="idp8125904"><mi id="idp8126032">λ</mi><mn id="idp8126320">0</mn></msub><mo id="idp8126576">⁢</mo><mrow id="idp8126864"><mover id="idp8126992"><munder id="idp8127120"><mo id="idp8127248" movablelimits="false">∑</mo><mrow id="idp8127808"><mi id="idp8127936">i</mi><mo id="idp8128192" movablelimits="false">=</mo><mn id="idp8128720">1</mn></mrow></munder><mi id="idp8128976">d</mi></mover><mrow id="idp8129232"><msub id="idp8129360"><mo id="idp8129488">∫</mo><mi id="idp8129776" mathvariant="normal">Ω</mi></msub><mrow id="idp8130336"><msup id="idp8130464"><mrow id="idp8130592"><mo id="idp8130720" fence="true">|</mo><mrow id="idp8131248"><mo id="idp8131376">∇</mo><mo id="idp8131664">⁡</mo><msub id="idp8131952"><mi id="idp8132080">ϕ</mi><mi id="idp8132368">i</mi></msub></mrow><mo id="idp8132624" fence="true">|</mo></mrow><mn id="idp8133152">2</mn></msup><mo id="idp8133408">⁢</mo><mi id="idp8133696">d</mi><mo id="idp8133952">⁢</mo><mi id="idp8134240">x</mi></mrow></mrow></mrow></mrow></mrow><mo id="idp8134496">.</mo></mrow><annotation-xml id="idp8134752" encoding="MathML-Content"><apply id="idp8135152"><geq id="idp8135280"/><apply id="idp8135408"><times id="idp8135536"/><ci id="idp8135664">δ</ci><apply id="idp8135952"><apply id="idp8136080"><csymbol id="idp8136208" cd="ambiguous">superscript</csymbol><apply id="idp8136768"><csymbol id="idp8136896" cd="ambiguous">subscript</csymbol><sum id="idp8137456"/><apply id="idp8137584"><eq id="idp8137712"/><ci id="idp8137840">i</ci><cn id="idp8138096" type="integer">1</cn></apply></apply><ci id="idp8138624">d</ci></apply><apply id="idp8138880"><plus id="idp8139008"/><apply id="idp8139136"><apply id="idp8139264"><csymbol id="idp8139392" cd="ambiguous">subscript</csymbol><int id="idp8139952"/><ci id="idp8140080">Ω</ci></apply><apply id="idp8140368"><times id="idp8140496"/><apply id="idp8140624"><csymbol id="idp8140752" cd="ambiguous">superscript</csymbol><apply id="idp8141312"><abs id="idp8141440"/><apply id="idp8141568"><ci id="idp8141696">∇</ci><apply id="idp8141984"><csymbol id="idp8142112" cd="ambiguous">subscript</csymbol><ci id="idp8142672">ϕ</ci><ci id="idp8142960">i</ci></apply></apply></apply><cn id="idp8143216" type="integer">2</cn></apply><ci id="idp8143744">d</ci><ci id="idp8144000">x</ci></apply></apply><apply id="idp8144256"><apply id="idp8144384"><csymbol id="idp8144512" cd="ambiguous">subscript</csymbol><int id="idp8145072"/><ci id="idp8145200">Ω</ci></apply><apply id="idp8145488"><times id="idp8145616"/><ci id="idp8145744">β</ci><ci id="idp8146032">x</ci><apply id="idp8146288"><csymbol id="idp8146416" cd="ambiguous">superscript</csymbol><apply id="idp8146976"><abs id="idp8147104"/><apply id="idp8147232"><csymbol id="idp8147360" cd="ambiguous">subscript</csymbol><ci id="idp8147920">ϕ</ci><ci id="idp8148208">i</ci></apply></apply><cn id="idp8148464" type="integer">2</cn></apply><ci id="idp8148992">d</ci><ci id="idp8149248">x</ci></apply></apply></apply></apply></apply><apply id="idp8149504"><times id="idp8149632"/><ci id="idp8149760">δ</ci><apply id="idp8150048"><csymbol id="idp8150176" cd="ambiguous">subscript</csymbol><ci id="idp8150736">λ</ci><cn id="idp8151024" type="integer">0</cn></apply><apply id="idp8151552"><apply id="idp8151680"><csymbol id="idp8151808" cd="ambiguous">superscript</csymbol><apply id="idp8152368"><csymbol id="idp8152496" cd="ambiguous">subscript</csymbol><sum id="idp8153056"/><apply id="idp8153184"><eq id="idp8153312"/><ci id="idp8153440">i</ci><cn id="idp8153696" type="integer">1</cn></apply></apply><ci id="idp8154224">d</ci></apply><apply id="idp8154480"><apply id="idp8154608"><csymbol id="idp8154736" cd="ambiguous">subscript</csymbol><int id="idp8155296"/><ci id="idp8155424">Ω</ci></apply><apply id="idp8155712"><times id="idp8155840"/><apply id="idp8155968"><csymbol id="idp8156096" cd="ambiguous">superscript</csymbol><apply id="idp8156656"><abs id="idp8156784"/><apply id="idp8156912"><ci id="idp8157040">∇</ci><apply id="idp8157328"><csymbol id="idp8157456" cd="ambiguous">subscript</csymbol><ci id="idp8158016">ϕ</ci><ci id="idp8158304">i</ci></apply></apply></apply><cn id="idp8158560" type="integer">2</cn></apply><ci id="idp8159088">d</ci><ci id="idp8159344">x</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp8159600" encoding="application/x-tex">\delta\sum _{{i=1}}^{d}\left(\int _{\Omega}|\nabla\phi _{i}|^{2}\, dx+\int _{\Omega}\beta(x)|\phi _{i}|^{2}\, dx\right)\geq\delta\lambda _{0}\sum _{{i=1}}^{d}\int _{{\Omega}}|\nabla\phi _{i}|^{2}\, dx.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp22985904"><h4>Hit idp22985904</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 12</li> <li>Formulasearchengine score: 11983</li> <li>Reference to collection: _PREFIX_/17/f006529.xhtml#idp22985904</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\Phi(u)=\frac{1}{p_{0}}\int _{\Omega}\lvert\nabla u\rvert^{{p_{0}}}\,\textup{d}x\leq\frac{1}{p_{0}}\int _{{\mathbbm{R}^{d}}}\lvert\textup{D}u\rvert^{{p_{0}}}\,\textup{d}x<+\infty.$ at pos:435307(71%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.75 * TOKEN_SCORE[int] + 1.5 * TOKEN_SCORE[leq] + 1.5 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.9375 * TOKEN_SCORE[0] + 1.5 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999980926513672 * TOKEN_SCORE[\] + 1.984375 * TOKEN_SCORE[_] + 1.0 * TOKEN_SCORE[|] + 1.875 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.75*0.279351653691737+1.5*2.71610004241772+1.5*0.0160883895861106+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*4.28403503219485+1.9375*0.0483458611105983+1.5*6.39416349760091+1.0*0.855340292115138+1.9999980926513672*5.92879328325965E-4+1.984375*0.00257082788077282+1.0*0.0975909302497933+1.875*0.00338742677192689 = 11983.152222579953' final score ~ 11983 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp22985904" alttext="\Phi(u)=\frac{1}{p_{0}}\int _{\Omega}\lvert\nabla u\rvert^{{p_{0}}}\,\textup{d}x\leq\frac{1}{p_{0}}\int _{{\mathbbm{R}^{d}}}\lvert\textup{D}u\rvert^{{p_{0}}}\,\textup{d}x<+\infty." display="block"><semantics id="idp22985680"><mrow id="idp22986816"><mrow id="idp22986944"><mrow id="idp22987072"><mi id="idp22987200" mathvariant="normal">Φ</mi><mo id="idp22987696">⁢</mo><mrow id="idp22987952"><mo id="idp22988080">(</mo><mi id="idp22988336">u</mi><mo id="idp22988592">)</mo></mrow></mrow><mo id="idp22988848">=</mo><mrow id="idp22989104"><mfrac id="idp22989232"><mn id="idp22989360">1</mn><msub id="idp22989616"><mi id="idp22989744">p</mi><mn id="idp22990000">0</mn></msub></mfrac><mo id="idp22990256">⁢</mo><mrow id="idp22990512"><msub id="idp22990640"><mo id="idp22990768">∫</mo><mi id="idp22991024" mathvariant="normal">Ω</mi></msub><mrow id="idp22991584"><msup id="idp22991712"><mrow id="idp22991840"><mo id="idp22991968" fence="true">|</mo><mrow id="idp22992496"><mo id="idp22992624">∇</mo><mo id="idp22992912">⁡</mo><mi id="idp22993200">u</mi></mrow><mo id="idp22993456" fence="true">|</mo></mrow><msub id="idp22993984"><mi id="idp22994112">p</mi><mn id="idp22994368">0</mn></msub></msup><mo id="idp22994624">⁢</mo><mtext id="idp22994912">d</mtext><mo id="idp22995168">⁢</mo><mi id="idp22995456">x</mi></mrow></mrow></mrow><mo id="idp22995712">≤</mo><mrow id="idp22996000"><mfrac id="idp22996128"><mn id="idp22996256">1</mn><msub id="idp22996512"><mi id="idp22996640">p</mi><mn id="idp22996896">0</mn></msub></mfrac><mo id="idp22997152">⁢</mo><mrow id="idp22997440"><msub id="idp22997568"><mo id="idp22997696">∫</mo><msup id="idp22997984"><mi id="idp22998112" mathvariant="double-struck">R</mi><mi id="idp22998640">d</mi></msup></msub><mrow id="idp22998896"><msup id="idp22999024"><mrow id="idp22999152"><mo id="idp22999280" fence="true">|</mo><mrow id="idp22999808"><mtext id="idp22999936">D</mtext><mo id="idp23000192">⁢</mo><mi id="idp23000480">u</mi></mrow><mo id="idp23000736" fence="true">|</mo></mrow><msub id="idp23001264"><mi id="idp23001392">p</mi><mn id="idp23001648">0</mn></msub></msup><mo id="idp23001904">⁢</mo><mtext id="idp23002192">d</mtext><mo id="idp23002448">⁢</mo><mi id="idp23002736">x</mi></mrow></mrow></mrow><mo id="idp23002992"><</mo><mrow id="idp23003280"><mo id="idp23003408">+</mo><mi id="idp23003664" mathvariant="normal">∞</mi></mrow></mrow><mo id="idp23004224">.</mo></mrow><annotation-xml id="idp23004480" encoding="MathML-Content"><apply id="idp23004880"><and id="idp23005008"/><apply id="idp23005136"><eq id="idp23005264"/><apply id="idp23005392"><times id="idp23005520"/><ci id="idp23005648">Φ</ci><ci id="idp23005936">u</ci></apply><apply id="S4.Ex11.m1.sh1ab.cmml"><times id="S4.Ex11.m1.sh1.cmml"/><apply id="S4.Ex11.m1.sh1g.cmml"><divide id="S4.Ex11.m1.sh1a.cmml"/><cn type="integer" id="S4.Ex11.m1.sh1b.cmml">1</cn><apply id="S4.Ex11.m1.sh1f.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh1c.cmml">subscript</csymbol><ci id="S4.Ex11.m1.sh1d.cmml">p</ci><cn type="integer" id="S4.Ex11.m1.sh1e.cmml">0</cn></apply></apply><apply id="S4.Ex11.m1.sh1aa.cmml"><apply id="S4.Ex11.m1.sh1k.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh1h.cmml">subscript</csymbol><int id="S4.Ex11.m1.sh1i.cmml"/><ci id="S4.Ex11.m1.sh1j.cmml">Ω</ci></apply><apply id="S4.Ex11.m1.sh1z.cmml"><times id="S4.Ex11.m1.sh1l.cmml"/><apply id="S4.Ex11.m1.sh1w.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh1m.cmml">superscript</csymbol><apply id="S4.Ex11.m1.sh1r.cmml"><abs id="S4.Ex11.m1.sh1n.cmml"/><apply id="S4.Ex11.m1.sh1q.cmml"><ci id="S4.Ex11.m1.sh1o.cmml">∇</ci><ci id="S4.Ex11.m1.sh1p.cmml">u</ci></apply></apply><apply id="S4.Ex11.m1.sh1v.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh1s.cmml">subscript</csymbol><ci id="S4.Ex11.m1.sh1t.cmml">p</ci><cn type="integer" id="S4.Ex11.m1.sh1u.cmml">0</cn></apply></apply><mtext id="S4.Ex11.m1.sh1x.cmml">d</mtext><ci id="S4.Ex11.m1.sh1y.cmml">x</ci></apply></apply></apply></apply><apply id="idp23021680"><leq id="idp23021808"/><share id="idp23021936" href="#S4.Ex11.m1.sh1.cmml"/><apply id="S4.Ex11.m1.sh2af.cmml"><times id="S4.Ex11.m1.sh2.cmml"/><apply id="S4.Ex11.m1.sh2g.cmml"><divide id="S4.Ex11.m1.sh2a.cmml"/><cn type="integer" id="S4.Ex11.m1.sh2b.cmml">1</cn><apply id="S4.Ex11.m1.sh2f.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh2c.cmml">subscript</csymbol><ci id="S4.Ex11.m1.sh2d.cmml">p</ci><cn type="integer" id="S4.Ex11.m1.sh2e.cmml">0</cn></apply></apply><apply id="S4.Ex11.m1.sh2ae.cmml"><apply id="S4.Ex11.m1.sh2n.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh2h.cmml">subscript</csymbol><int id="S4.Ex11.m1.sh2i.cmml"/><apply id="S4.Ex11.m1.sh2m.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh2j.cmml">superscript</csymbol><ci id="S4.Ex11.m1.sh2k.cmml">R</ci><ci id="S4.Ex11.m1.sh2l.cmml">d</ci></apply></apply><apply id="S4.Ex11.m1.sh2ad.cmml"><times id="S4.Ex11.m1.sh2o.cmml"/><apply id="S4.Ex11.m1.sh2aa.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh2p.cmml">superscript</csymbol><apply id="S4.Ex11.m1.sh2v.cmml"><abs id="S4.Ex11.m1.sh2q.cmml"/><apply id="S4.Ex11.m1.sh2u.cmml"><times id="S4.Ex11.m1.sh2r.cmml"/><mtext id="S4.Ex11.m1.sh2s.cmml">D</mtext><ci id="S4.Ex11.m1.sh2t.cmml">u</ci></apply></apply><apply id="S4.Ex11.m1.sh2z.cmml"><csymbol cd="ambiguous" id="S4.Ex11.m1.sh2w.cmml">subscript</csymbol><ci id="S4.Ex11.m1.sh2x.cmml">p</ci><cn type="integer" id="S4.Ex11.m1.sh2y.cmml">0</cn></apply></apply><mtext id="S4.Ex11.m1.sh2ab.cmml">d</mtext><ci id="S4.Ex11.m1.sh2ac.cmml">x</ci></apply></apply></apply></apply><apply id="idp23039920"><lt id="idp23040048"/><share id="idp23040176" href="#S4.Ex11.m1.sh2.cmml"/><apply id="S4.Ex11.m1.sh3b.cmml"><plus id="S4.Ex11.m1.sh3.cmml"/><infinity id="S4.Ex11.m1.sh3a.cmml"/></apply></apply></apply></annotation-xml><annotation id="idp23041776" encoding="application/x-tex">\Phi(u)=\frac{1}{p_{0}}\int _{\Omega}\lvert\nabla u\rvert^{{p_{0}}}\,\textup{d}x\leq\frac{1}{p_{0}}\int _{{\mathbbm{R}^{d}}}\lvert\textup{D}u\rvert^{{p_{0}}}\,\textup{d}x<+\infty.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="id124859"><h4>Hit id124859</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 14</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/94/f037521.xhtml#id124859</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1059464(000058%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <m:math id="id124859" display="block"><m:semantics id="id124862"><m:mrow id="id124863"><m:mrow id="id124864"><m:msubsup id="id124866"><m:mfenced id="id124868" open="∥" close="∥"><m:mrow id="id124874"><m:mrow id="id124875"><m:mo id="id124876">∇</m:mo><m:mo id="id124879">⁡</m:mo><m:mi id="id124881" mathvariant="normal">Λ</m:mi></m:mrow><m:mo id="id124885">⁢</m:mo><m:mfenced id="id124887" open="(" close=")"><m:mi id="id124891">t</m:mi></m:mfenced></m:mrow></m:mfenced><m:msup id="id124893"><m:mi id="id124894">L</m:mi><m:mrow id="id124897"><m:mn id="id124898">2</m:mn><m:mo id="id124900">+</m:mo><m:mi id="id124902">q</m:mi></m:mrow></m:msup><m:mrow id="id124904"><m:mn id="id124905">2</m:mn><m:mo id="id124907">+</m:mo><m:mi id="id124909">q</m:mi></m:mrow></m:msubsup><m:mo id="id124912">≤</m:mo><m:mrow id="id124914"><m:msubsup id="id124915"><m:mfenced id="id124918" open="∥" close="∥"><m:mrow id="id124924"><m:mrow id="id124925"><m:mo id="id124926">∇</m:mo><m:mo id="id124928">⁡</m:mo><m:mi id="id124930" mathvariant="normal">Λ</m:mi></m:mrow><m:mo id="id124934">⁢</m:mo><m:mfenced id="id124937" open="(" close=")"><m:mn id="id124941">0</m:mn></m:mfenced></m:mrow></m:mfenced><m:msup id="id124943"><m:mi id="id124944">L</m:mi><m:mrow id="id124946"><m:mn id="id124947">2</m:mn><m:mo id="id124949">+</m:mo><m:mi id="id124951">q</m:mi></m:mrow></m:msup><m:mrow id="id124954"><m:mn id="id124955">2</m:mn><m:mo id="id124957">+</m:mo><m:mi id="id124959">q</m:mi></m:mrow></m:msubsup><m:mo id="id124961">+</m:mo><m:mrow id="id124963"><m:mi id="id124964">K</m:mi><m:mo id="id124966">⁢</m:mo><m:mrow id="id124969"><m:msubsup id="id124970"><m:mo id="id124971">∫</m:mo><m:mn id="id124973">0</m:mn><m:mi id="id124975">t</m:mi></m:msubsup><m:mfenced id="id124978" open="(" close=")"><m:mrow id="id124983"><m:msubsup id="id124984"><m:mfenced id="id124987" open="∥" close="∥"><m:mrow id="id124992"><m:mo id="id124993">∇</m:mo><m:mo id="id124996">⁡</m:mo><m:mi id="id124998" mathvariant="normal">Λ</m:mi></m:mrow></m:mfenced><m:msup id="id125002"><m:mi id="id125003">L</m:mi><m:mrow id="id125005"><m:mn id="id125006">2</m:mn><m:mo id="id125008">+</m:mo><m:mi id="id125010">q</m:mi></m:mrow></m:msup><m:mrow id="id125012"><m:mn id="id125014">2</m:mn><m:mo id="id125016">+</m:mo><m:mi id="id125018">q</m:mi></m:mrow></m:msubsup><m:mo id="id125020">+</m:mo><m:mrow id="id125022"><m:msub id="id125023"><m:mfenced id="id125025" open="∥" close="∥"><m:mrow id="id125031"><m:mo id="id125032">∇</m:mo><m:mo id="id125034">⁡</m:mo><m:mi id="id125037">F</m:mi></m:mrow></m:mfenced><m:msup id="id125039"><m:mi id="id125040">L</m:mi><m:mrow id="id125042"><m:mn id="id125043">2</m:mn><m:mo id="id125045">+</m:mo><m:mi id="id125047">q</m:mi></m:mrow></m:msup></m:msub><m:mo id="id125049">⁢</m:mo><m:msubsup id="id125052"><m:mfenced id="id125053" open="∥" close="∥"><m:mrow id="id125058"><m:mo id="id125060">∇</m:mo><m:mo id="id125062">⁡</m:mo><m:mi id="id125064" mathvariant="normal">Λ</m:mi></m:mrow></m:mfenced><m:msup id="id125068"><m:mi id="id125069">L</m:mi><m:mrow id="id125071"><m:mn id="id125072">2</m:mn><m:mo id="id125074">+</m:mo><m:mi id="id125077">q</m:mi></m:mrow></m:msup><m:mrow id="id125079"><m:mn id="id125080">1</m:mn><m:mo id="id125082">+</m:mo><m:mi id="id125084">q</m:mi></m:mrow></m:msubsup></m:mrow><m:mo id="id125086">+</m:mo><m:mrow id="id125088"><m:msub id="id125089"><m:mfenced id="id125091" open="∥" close="∥"><m:mrow id="id125097"><m:mo id="id125098">∇</m:mo><m:mo id="id125100">⁡</m:mo><m:mi id="id125103">u</m:mi></m:mrow></m:mfenced><m:msup id="id125105"><m:mi id="id125106">L</m:mi><m:mi id="id125108" mathvariant="normal">∞</m:mi></m:msup></m:msub><m:mo id="id125112">⁢</m:mo><m:msubsup id="id125114"><m:mfenced id="id125116" open="∥" close="∥"><m:mrow id="id125122"><m:mo id="id125123">∇</m:mo><m:mo id="id125125">⁡</m:mo><m:mi id="id125128" mathvariant="normal">Λ</m:mi></m:mrow></m:mfenced><m:msup id="id125132"><m:mi id="id125133">L</m:mi><m:mrow id="id125135"><m:mn id="id125136">2</m:mn><m:mo id="id125138">+</m:mo><m:mi id="id125140">q</m:mi></m:mrow></m:msup><m:mrow id="id125142"><m:mn id="id125143">2</m:mn><m:mo id="id125145">+</m:mo><m:mi id="id125148">q</m:mi></m:mrow></m:msubsup></m:mrow></m:mrow></m:mfenced><m:mo id="id125150">⁢</m:mo><m:mi id="id125152">d</m:mi><m:mo id="id125154">⁢</m:mo><m:mi id="id125157">s</m:mi></m:mrow></m:mrow></m:mrow></m:mrow><m:mo id="id125159">.</m:mo></m:mrow><m:annotation-xml id="id125161" encoding="MathML-Content"><m:apply id="id125163"><m:leq id="id125164"/><m:apply id="id125165"><m:csymbol id="id125166" cd="ambiguous">superscript</m:csymbol><m:apply id="id125171"><m:csymbol id="id125172" cd="ambiguous">subscript</m:csymbol><m:apply id="id125177"><m:ci id="id125178"/><m:apply id="id125179"><m:times id="id125180"/><m:apply id="id125181"><m:ci id="id125182">∇</m:ci><m:ci id="id125185">Λ</m:ci></m:apply><m:ci id="id125187">t</m:ci></m:apply></m:apply><m:apply id="id125189"><m:csymbol id="id125190" cd="ambiguous">superscript</m:csymbol><m:ci id="id125195">L</m:ci><m:apply id="id125197"><m:plus id="id125198"/><m:cn id="id125199">2</m:cn><m:ci id="id125201">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125203"><m:plus id="id125204"/><m:cn id="id125206">2</m:cn><m:ci id="id125208">q</m:ci></m:apply></m:apply><m:apply id="id125210"><m:plus id="id125211"/><m:apply id="id125212"><m:csymbol id="id125213" cd="ambiguous">superscript</m:csymbol><m:apply id="id125218"><m:csymbol id="id125219" cd="ambiguous">subscript</m:csymbol><m:apply id="id125223"><m:ci id="id125224"/><m:apply id="id125226"><m:times id="id125227"/><m:apply id="id125228"><m:ci id="id125229">∇</m:ci><m:ci id="id125231">Λ</m:ci></m:apply><m:cn id="id125234">0</m:cn></m:apply></m:apply><m:apply id="id125236"><m:csymbol id="id125237" cd="ambiguous">superscript</m:csymbol><m:ci id="id125241">L</m:ci><m:apply id="id125244"><m:plus id="id125245"/><m:cn id="id125246">2</m:cn><m:ci id="id125248">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125250"><m:plus id="id125251"/><m:cn id="id125252">2</m:cn><m:ci id="id125254">q</m:ci></m:apply></m:apply><m:apply id="id125256"><m:times id="id125257"/><m:ci id="id125258">K</m:ci><m:apply id="id125261"><m:apply id="id125262"><m:csymbol id="id125263" cd="ambiguous">subscript</m:csymbol><m:apply id="id125267"><m:csymbol id="id125268" cd="ambiguous">superscript</m:csymbol><m:int id="id125273"/><m:ci id="id125274">t</m:ci></m:apply><m:cn id="id125276">0</m:cn></m:apply><m:apply id="id125278"><m:times id="id125280"/><m:apply id="id125281"><m:plus id="id125282"/><m:apply id="id125283"><m:csymbol id="id125284" cd="ambiguous">superscript</m:csymbol><m:apply id="id125288"><m:csymbol id="id125290" cd="ambiguous">subscript</m:csymbol><m:apply id="id125294"><m:ci id="id125295"/><m:apply id="id125296"><m:ci id="id125297">∇</m:ci><m:ci id="id125300">Λ</m:ci></m:apply></m:apply><m:apply id="id125302"><m:csymbol id="id125303" cd="ambiguous">superscript</m:csymbol><m:ci id="id125308">L</m:ci><m:apply id="id125310"><m:plus id="id125311"/><m:cn id="id125312">2</m:cn><m:ci id="id125314">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125316"><m:plus id="id125318"/><m:cn id="id125319">2</m:cn><m:ci id="id125321">q</m:ci></m:apply></m:apply><m:apply id="id125323"><m:times id="id125324"/><m:apply id="id125325"><m:csymbol id="id125326" cd="ambiguous">subscript</m:csymbol><m:apply id="id125331"><m:ci id="id125332"/><m:apply id="id125333"><m:ci id="id125334">∇</m:ci><m:ci id="id125336">F</m:ci></m:apply></m:apply><m:apply id="id125338"><m:csymbol id="id125340" cd="ambiguous">superscript</m:csymbol><m:ci id="id125344">L</m:ci><m:apply id="id125346"><m:plus id="id125347"/><m:cn id="id125348">2</m:cn><m:ci id="id125351">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125353"><m:csymbol id="id125354" cd="ambiguous">superscript</m:csymbol><m:apply id="id125358"><m:csymbol id="id125360" cd="ambiguous">subscript</m:csymbol><m:apply id="id125364"><m:ci id="id125365"/><m:apply id="id125366"><m:ci id="id125367">∇</m:ci><m:ci id="id125370">Λ</m:ci></m:apply></m:apply><m:apply id="id125372"><m:csymbol id="id125373" cd="ambiguous">superscript</m:csymbol><m:ci id="id125378">L</m:ci><m:apply id="id125380"><m:plus id="id125381"/><m:cn id="id125382">2</m:cn><m:ci id="id125384">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125386"><m:plus id="id125388"/><m:cn id="id125389">1</m:cn><m:ci id="id125391">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125393"><m:times id="id125394"/><m:apply id="id125395"><m:csymbol id="id125396" cd="ambiguous">subscript</m:csymbol><m:apply id="id125401"><m:ci id="id125402"/><m:apply id="id125403"><m:ci id="id125404">∇</m:ci><m:ci id="id125406">u</m:ci></m:apply></m:apply><m:apply id="id125408"><m:csymbol id="id125410" cd="ambiguous">superscript</m:csymbol><m:ci id="id125414">L</m:ci><m:infinity id="id125416"/></m:apply></m:apply><m:apply id="id125417"><m:csymbol id="id125418" cd="ambiguous">superscript</m:csymbol><m:apply id="id125423"><m:csymbol id="id125424" cd="ambiguous">subscript</m:csymbol><m:apply id="id125429"><m:ci id="id125430"/><m:apply id="id125431"><m:ci id="id125432">∇</m:ci><m:ci id="id125434">Λ</m:ci></m:apply></m:apply><m:apply id="id125437"><m:csymbol id="id125438" cd="ambiguous">superscript</m:csymbol><m:ci id="id125443">L</m:ci><m:apply id="id125445"><m:plus id="id125446"/><m:cn id="id125447">2</m:cn><m:ci id="id125449">q</m:ci></m:apply></m:apply></m:apply><m:apply id="id125451"><m:plus id="id125452"/><m:cn id="id125453">2</m:cn><m:ci id="id125455">q</m:ci></m:apply></m:apply></m:apply></m:apply><m:ci id="id125458">d</m:ci><m:ci id="id125460">s</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id67365"><h4>Hit id67365</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 15</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/97/f038444.xhtml#id67365</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:201994(000033%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <m:math id="id67365" display="block"><m:semantics id="id67368"><m:mrow id="id67369"><m:mrow id="id67370"><m:mrow id="id67372"><m:munder id="id67373"><m:mo id="id67374" movablelimits="false">lim sup</m:mo><m:mrow id="id67378"><m:msub id="id67379"><m:mi id="id67380">ϵ</m:mi><m:mi id="id67383">i</m:mi></m:msub><m:mo id="id67385">→</m:mo><m:mn id="id67387">0</m:mn></m:mrow></m:munder><m:mo id="id67390">⁡</m:mo><m:mrow id="id67392"><m:msub id="id67393"><m:mo id="id67394">∫</m:mo><m:msub id="id67396"><m:mi id="id67398">B</m:mi><m:mn id="id67400">1</m:mn></m:msub></m:msub><m:mi id="id67402">η</m:mi><m:mo id="id67404">⁢</m:mo><m:msup id="id67407"><m:mfenced id="id67408" open="|" close="|"><m:mrow id="id67413"><m:mo id="id67414">∇</m:mo><m:mo id="id67416">⁡</m:mo><m:msub id="id67419"><m:mi id="id67420">v</m:mi><m:msub id="id67422"><m:mi id="id67423">ϵ</m:mi><m:mi id="id67425">i</m:mi></m:msub></m:msub></m:mrow></m:mfenced><m:mn id="id67427">2</m:mn></m:msup><m:mo id="id67430">⁢</m:mo><m:mi id="id67432">d</m:mi><m:mo id="id67434">⁢</m:mo><m:mi id="id67436">x</m:mi></m:mrow></m:mrow><m:mo id="id67439">≤</m:mo><m:mrow id="id67441"><m:mo id="id67442">-</m:mo><m:mrow id="id67444"><m:msub id="id67445"><m:mo id="id67446">∫</m:mo><m:msub id="id67449"><m:mi id="id67450">B</m:mi><m:mn id="id67452">1</m:mn></m:msub></m:msub><m:mrow id="id67454"><m:msub id="id67455"><m:mi id="id67456">v</m:mi><m:mn id="id67458">0</m:mn></m:msub><m:mo id="id67460">⁢</m:mo><m:mrow id="id67463"><m:mo id="id67464">∇</m:mo><m:mo id="id67466">⁡</m:mo><m:mi id="id67469">η</m:mi></m:mrow></m:mrow><m:mo id="id67471">⋅</m:mo><m:mrow id="id67474"><m:mo id="id67475">∇</m:mo><m:mo id="id67477">⁡</m:mo><m:mrow id="id67479"><m:msub id="id67480"><m:mi id="id67482">v</m:mi><m:mn id="id67484">0</m:mn></m:msub><m:mo id="id67486">⁢</m:mo><m:mi id="id67488">d</m:mi><m:mo id="id67490">⁢</m:mo><m:mi id="id67493">x</m:mi></m:mrow></m:mrow></m:mrow></m:mrow></m:mrow><m:mo id="id67495">.</m:mo></m:mrow><m:annotation-xml id="id67497" encoding="MathML-Content"><m:apply id="id67500"><m:leq id="id67501"/><m:apply id="id67502"><m:apply id="id67504"><m:csymbol id="id67505" cd="ambiguous">subscript</m:csymbol><m:ci id="id67509">lim sup</m:ci><m:apply id="id67512"><m:ci id="id67513">→</m:ci><m:apply id="id67515"><m:csymbol id="id67516" cd="ambiguous">subscript</m:csymbol><m:ci id="id67521">ϵ</m:ci><m:ci id="id67523">i</m:ci></m:apply><m:cn id="id67525">0</m:cn></m:apply></m:apply><m:apply id="id67528"><m:apply id="id67529"><m:csymbol id="id67530" cd="ambiguous">subscript</m:csymbol><m:int id="id67534"/><m:apply id="id67535"><m:csymbol id="id67536" cd="ambiguous">subscript</m:csymbol><m:ci id="id67541">B</m:ci><m:cn id="id67543">1</m:cn></m:apply></m:apply><m:apply id="id67545"><m:times id="id67546"/><m:ci id="id67548">η</m:ci><m:apply id="id67550"><m:csymbol id="id67551" cd="ambiguous">superscript</m:csymbol><m:apply id="id67556"><m:abs id="id67557"/><m:apply id="id67558"><m:ci id="id67559">∇</m:ci><m:apply id="id67561"><m:csymbol id="id67562" cd="ambiguous">subscript</m:csymbol><m:ci id="id67567">v</m:ci><m:apply id="id67569"><m:csymbol id="id67570" cd="ambiguous">subscript</m:csymbol><m:ci id="id67575">ϵ</m:ci><m:ci id="id67577">i</m:ci></m:apply></m:apply></m:apply></m:apply><m:cn id="id67579">2</m:cn></m:apply><m:ci id="id67582">d</m:ci><m:ci id="id67584">x</m:ci></m:apply></m:apply></m:apply><m:apply id="id67586"><m:minus id="id67587"/><m:apply id="id67588"><m:apply id="id67589"><m:csymbol id="id67590" cd="ambiguous">subscript</m:csymbol><m:int id="id67595"/><m:apply id="id67596"><m:csymbol id="id67597" cd="ambiguous">subscript</m:csymbol><m:ci id="id67602">B</m:ci><m:cn id="id67604">1</m:cn></m:apply></m:apply><m:apply id="id67606"><m:ci id="id67607">⋅</m:ci><m:apply id="id67609"><m:times id="id67610"/><m:apply id="id67611"><m:csymbol id="id67612" cd="ambiguous">subscript</m:csymbol><m:ci id="id67617">v</m:ci><m:cn id="id67619">0</m:cn></m:apply><m:apply id="id67621"><m:ci id="id67622">∇</m:ci><m:ci id="id67625">η</m:ci></m:apply></m:apply><m:apply id="id67627"><m:ci id="id67628">∇</m:ci><m:apply id="id67631"><m:times id="id67632"/><m:apply id="id67633"><m:csymbol id="id67634" cd="ambiguous">subscript</m:csymbol><m:ci id="id67639">v</m:ci><m:cn id="id67641">0</m:cn></m:apply><m:ci id="id67643">d</m:ci><m:ci id="id67645">x</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id70843"><h4>Hit id70843</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 16</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/151/f060175.xhtml#id70843</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:252295(000018%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <m:math id="id70843" display="block"><m:semantics id="id70847"><m:mrow id="id70848"><m:mrow id="id70849"><m:mrow id="id70850"><m:mo id="id70851">+</m:mo><m:mrow id="id70853"><m:msubsup id="id70854"><m:mo id="id70855">∫</m:mo><m:mn id="id70858">0</m:mn><m:mi id="id70860">b</m:mi></m:msubsup><m:mfenced id="id70862" open="(" close=")"><m:mrow id="id70867"><m:msup id="id70868"><m:mfenced id="id70871" open="∥" close="∥"><m:mrow id="id70877"><m:mo id="id70878">∇</m:mo><m:mo id="id70880">⁡</m:mo><m:mi id="id70883">θ</m:mi></m:mrow></m:mfenced><m:mn id="id70885">2</m:mn></m:msup><m:mo id="id70887">+</m:mo><m:msup id="id70890"><m:mfenced id="id70891" open="∥" close="∥"><m:mrow id="id70896"><m:mo id="id70897">∇</m:mo><m:mo id="id70900">⁡</m:mo><m:mi id="id70902">q</m:mi></m:mrow></m:mfenced><m:mn id="id70904">2</m:mn></m:msup><m:mo id="id70906">+</m:mo><m:msup id="id70908"><m:mfenced id="id70910" open="∥" close="∥"><m:mrow id="id70915"><m:mo id="id70916">∇</m:mo><m:mo id="id70919">⁡</m:mo><m:mi id="id70921">T</m:mi></m:mrow></m:mfenced><m:mn id="id70923">2</m:mn></m:msup><m:mo id="id70925">+</m:mo><m:msup id="id70927"><m:mfenced id="id70928" open="∥" close="∥"><m:mrow id="id70934"><m:mo id="id70935">∇</m:mo><m:mo id="id70938">⁡</m:mo><m:mi id="id70940">S</m:mi></m:mrow></m:mfenced><m:mn id="id70942">2</m:mn></m:msup></m:mrow></m:mfenced><m:mo id="id70944">⁢</m:mo><m:mi id="id70947">d</m:mi><m:mo id="id70949">⁢</m:mo><m:mi id="id70951">t</m:mi></m:mrow></m:mrow><m:mo id="id70953">≤</m:mo><m:mrow id="id70956"><m:msub id="id70957"><m:mi id="id70958">C</m:mi><m:mn id="id70960">1</m:mn></m:msub><m:mo id="id70962">⁢</m:mo><m:mfenced id="id70964" open="(" close=")"><m:mi id="id70968">b</m:mi></m:mfenced></m:mrow></m:mrow><m:mo id="id70970">,</m:mo></m:mrow><m:annotation-xml id="id70972" encoding="MathML-Content"><m:apply id="id70975"><m:leq id="id70976"/><m:apply id="id70977"><m:plus id="id70978"/><m:apply id="id70980"><m:apply id="id70981"><m:csymbol id="id70982" cd="ambiguous">superscript</m:csymbol><m:apply id="id70986"><m:csymbol id="id70987" cd="ambiguous">subscript</m:csymbol><m:int id="id70992"/><m:cn id="id70993">0</m:cn></m:apply><m:ci id="id70995">b</m:ci></m:apply><m:apply id="id70997"><m:times id="id70998"/><m:apply id="id71000"><m:plus id="id71001"/><m:apply id="id71002"><m:csymbol id="id71003" cd="ambiguous">superscript</m:csymbol><m:apply id="id71007"><m:ci id="id71008"/><m:apply id="id71010"><m:ci id="id71011">∇</m:ci><m:ci id="id71013">θ</m:ci></m:apply></m:apply><m:cn id="id71015">2</m:cn></m:apply><m:apply id="id71018"><m:csymbol id="id71019" cd="ambiguous">superscript</m:csymbol><m:apply id="id71023"><m:ci id="id71024"/><m:apply id="id71025"><m:ci id="id71026">∇</m:ci><m:ci id="id71029">q</m:ci></m:apply></m:apply><m:cn id="id71031">2</m:cn></m:apply><m:apply id="id71033"><m:csymbol id="id71034" cd="ambiguous">superscript</m:csymbol><m:apply id="id71039"><m:ci id="id71040"/><m:apply id="id71041"><m:ci id="id71042">∇</m:ci><m:ci id="id71044">T</m:ci></m:apply></m:apply><m:cn id="id71047">2</m:cn></m:apply><m:apply id="id71049"><m:csymbol id="id71050" cd="ambiguous">superscript</m:csymbol><m:apply id="id71054"><m:ci id="id71056"/><m:apply id="id71057"><m:ci id="id71058">∇</m:ci><m:ci id="id71060">S</m:ci></m:apply></m:apply><m:cn id="id71062">2</m:cn></m:apply></m:apply><m:ci id="id71064">d</m:ci><m:ci id="id71066">t</m:ci></m:apply></m:apply></m:apply><m:apply id="id71069"><m:times id="id71070"/><m:apply id="id71071"><m:csymbol id="id71072" cd="ambiguous">subscript</m:csymbol><m:ci id="id71076">C</m:ci><m:cn id="id71079">1</m:cn></m:apply><m:ci id="id71081">b</m:ci></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id91042"><h4>Hit id91042</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 17</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/233/f093179.xhtml#id91042</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:557274(000054%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <m:math id="id91042" display="block"><m:semantics id="id91045"><m:mrow id="id91046"><m:mrow id="id91047"><m:mrow id="id91048"><m:mrow id="id91050"><m:msub id="id91051"><m:mo id="id91052">∫</m:mo><m:msub id="id91054"><m:mi id="id91055">X</m:mi><m:mi id="id91057">k</m:mi></m:msub></m:msub><m:msup id="id91059"><m:mfenced id="id91060" open="|" close="|"><m:mrow id="id91066"><m:mo id="id91067">∇</m:mo><m:mo id="id91069">⁡</m:mo><m:msub id="id91071"><m:mi id="id91072">η</m:mi><m:mi id="id91075">k</m:mi></m:msub></m:mrow></m:mfenced><m:mn id="id91077">2</m:mn></m:msup><m:mo id="id91079">⁢</m:mo><m:mi id="id91082">d</m:mi><m:mo id="id91084">⁢</m:mo><m:msub id="id91086"><m:mi id="id91087">V</m:mi><m:mrow id="id91089"><m:mi id="id91090">k</m:mi><m:mo id="id91092">,</m:mo><m:mrow id="id91095"><m:mi id="id91096">A</m:mi><m:mo id="id91098">⁢</m:mo><m:mi id="id91100">F</m:mi></m:mrow></m:mrow></m:msub></m:mrow><m:mo id="id91102">≤</m:mo><m:mi id="id91105">ε</m:mi></m:mrow><m:mo id="id91107">,</m:mo><m:mrow id="id91109"><m:mrow id="id91110"><m:msub id="id91111"><m:mi id="id91112">Vol</m:mi><m:mrow id="id91115"><m:mi id="id91116">k</m:mi><m:mo id="id91118">,</m:mo><m:mrow id="id91120"><m:mi id="id91121">A</m:mi><m:mo id="id91123">⁢</m:mo><m:mi id="id91126">F</m:mi></m:mrow></m:mrow></m:msub><m:mo id="id91128">⁢</m:mo><m:mfenced id="id91130" open="(" close=")"><m:mfenced id="id91135" open="{" close="}"><m:mrow id="id91140"><m:mrow id="id91141"><m:mi id="id91142">x</m:mi><m:mo id="id91144">∈</m:mo><m:msub id="id91147"><m:mi id="id91148">X</m:mi><m:mi id="id91150">k</m:mi></m:msub></m:mrow><m:mo id="id91152">|</m:mo><m:mrow id="id91154"><m:mrow id="id91155"><m:mo id="id91156">∇</m:mo><m:mo id="id91159">⁡</m:mo><m:msub id="id91161"><m:mi id="id91162">η</m:mi><m:mi id="id91165">k</m:mi></m:msub></m:mrow><m:mo id="id91167">≠</m:mo><m:mn id="id91169">0</m:mn></m:mrow></m:mrow></m:mfenced></m:mfenced></m:mrow><m:mo id="id91171">≤</m:mo><m:mi id="id91174">ε</m:mi></m:mrow></m:mrow><m:mo id="id91176">.</m:mo></m:mrow><m:annotation-xml id="id91178" encoding="MathML-Content"><m:apply id="id91182"><m:ci id="id91183"/><m:apply id="id91184"><m:leq id="id91185"/><m:apply id="id91186"><m:apply id="id91187"><m:csymbol id="id91188" cd="ambiguous">subscript</m:csymbol><m:int id="id91193"/><m:apply id="id91194"><m:csymbol id="id91195" cd="ambiguous">subscript</m:csymbol><m:ci id="id91200">X</m:ci><m:ci id="id91202">k</m:ci></m:apply></m:apply><m:apply id="id91204"><m:times id="id91205"/><m:apply id="id91206"><m:csymbol id="id91207" cd="ambiguous">superscript</m:csymbol><m:apply id="id91212"><m:abs id="id91213"/><m:apply id="id91214"><m:ci id="id91215">∇</m:ci><m:apply id="id91217"><m:csymbol id="id91218" cd="ambiguous">subscript</m:csymbol><m:ci id="id91223">η</m:ci><m:ci id="id91225">k</m:ci></m:apply></m:apply></m:apply><m:cn id="id91228">2</m:cn></m:apply><m:ci id="id91230">d</m:ci><m:apply id="id91232"><m:csymbol id="id91233" cd="ambiguous">subscript</m:csymbol><m:ci id="id91238">V</m:ci><m:apply id="id91240"><m:list id="id91241"/><m:ci id="id91242">k</m:ci><m:apply id="id91244"><m:times id="id91245"/><m:ci id="id91246">A</m:ci><m:ci id="id91248">F</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply><m:ci id="id91250">ε</m:ci></m:apply><m:apply id="id91253"><m:leq id="id91254"/><m:apply id="id91255"><m:times id="id91256"/><m:apply id="id91257"><m:csymbol id="id91258" cd="ambiguous">subscript</m:csymbol><m:ci id="id91263">Vol</m:ci><m:apply id="id91265"><m:list id="id91266"/><m:ci id="id91267">k</m:ci><m:apply id="id91269"><m:times id="id91270"/><m:ci id="id91271">A</m:ci><m:ci id="id91273">F</m:ci></m:apply></m:apply></m:apply><m:apply id="id91276"><m:ci id="id91277"/><m:apply id="id91278"><m:ci id="id91279">∈</m:ci><m:ci id="id91281">x</m:ci><m:apply id="id91283"><m:csymbol id="id91284" cd="ambiguous">subscript</m:csymbol><m:ci id="id91289">X</m:ci><m:ci id="id91291">k</m:ci></m:apply></m:apply><m:apply id="id91293"><m:neq id="id91294"/><m:apply id="id91295"><m:ci id="id91296">∇</m:ci><m:apply id="id91299"><m:csymbol id="id91300" cd="ambiguous">subscript</m:csymbol><m:ci id="id91305">η</m:ci><m:ci id="id91307">k</m:ci></m:apply></m:apply><m:cn id="id91309">0</m:cn></m:apply></m:apply></m:apply><m:ci id="id91311">ε</m:ci></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="idp13677424"><h4>Hit idp13677424</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 18</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/116/f046110.xhtml#idp13677424</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1730695(000065%) VariableMap:[dx x 2, mathbb x 3, C, N x 3, sup, T x 5, nabla, \ x 12, _ x 10, ^ x 7, int x 4, leq x 3, +, (, ), ,, w x 2, 2 x 3, u, 1 x 2, dxdt, t x 2, 0 x 5, | x 6, x] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp13677424" alttext="\sup _{{0\leq t\leq T_{{0}}}}\int _{{\mathbb{T}^{{N}}}}|w_{{1}}(t,x)|^{{2}}dx+\int^{{T_{{0}}}}_{{0}}\int _{{\mathbb{T}^{{N}}}}|\nabla w_{{1}}|^{{2}}dxdt\leq C\int _{{\mathbb{T}^{{N}}}}|u_{{0}}|^{{2}}dx" display="block"><semantics id="idp13678368"><mrow id="idp13678496"><mrow id="idp13678624"><mrow id="idp13678752"><munder id="idp13678880"><mo id="idp13679008" movablelimits="false">sup</mo><mrow id="idp13679504"><mn id="idp13679632">0</mn><mo id="idp13679888">≤</mo><mi id="idp13680144">t</mi><mo id="idp13680400">≤</mo><msub id="idp13680688"><mi id="idp13680816">T</mi><mn id="idp13681072">0</mn></msub></mrow></munder><mo id="idp13681328">⁡</mo><mrow id="idp13681616"><msub id="idp13681744"><mo id="idp13681872">∫</mo><msup id="idp13682160"><mi id="idp13682288" mathvariant="double-struck">T</mi><mi id="idp13682816">N</mi></msup></msub><mrow id="idp13683072"><msup id="idp13683200"><mrow id="idp13683328"><mo id="idp13683456" fence="true">|</mo><mrow id="idp13683984"><msub id="idp13684112"><mi id="idp13684240">w</mi><mn id="idp13684496">1</mn></msub><mo id="idp13684752">⁢</mo><mrow id="idp13685040"><mo id="idp13685168">(</mo><mrow id="idp13685424"><mi id="idp13685552">t</mi><mo id="idp13685808">,</mo><mi id="idp13686064">x</mi></mrow><mo id="idp13686320">)</mo></mrow></mrow><mo id="idp13686576" fence="true">|</mo></mrow><mn id="idp13687104">2</mn></msup><mo id="idp13687360">⁢</mo><mi id="idp13687648">d</mi><mo id="idp13687904">⁢</mo><mi id="idp13688192">x</mi></mrow></mrow></mrow><mo id="idp13688448">+</mo><mrow id="idp13688704"><msubsup id="idp13688832"><mo id="idp13688960">∫</mo><mn id="idp13689248">0</mn><msub id="idp13689504"><mi id="idp13689632">T</mi><mn id="idp13689888">0</mn></msub></msubsup><mrow id="idp13690144"><msub id="idp13690272"><mo id="idp13690400">∫</mo><msup id="idp13690688"><mi id="idp13690816" mathvariant="double-struck">T</mi><mi id="idp13691344">N</mi></msup></msub><mrow id="idp13691600"><msup id="idp13691728"><mrow id="idp13691856"><mo id="idp13691984" fence="true">|</mo><mrow id="idp13692512"><mo id="idp13692640">∇</mo><mo id="idp13692928">⁡</mo><msub id="idp13693216"><mi id="idp13693344">w</mi><mn id="idp13693600">1</mn></msub></mrow><mo id="idp13693856" fence="true">|</mo></mrow><mn id="idp13694384">2</mn></msup><mo id="idp13694640">⁢</mo><mi id="idp13694928">d</mi><mo id="idp13695184">⁢</mo><mi id="idp13695472">x</mi><mo id="idp13695728">⁢</mo><mi id="idp13696016">d</mi><mo id="idp13696272">⁢</mo><mi id="idp13696560">t</mi></mrow></mrow></mrow></mrow><mo id="idp13696816">≤</mo><mrow id="idp13697104"><mi id="idp13697232">C</mi><mo id="idp13697488">⁢</mo><mrow id="idp13697776"><msub id="idp13697904"><mo id="idp13698032">∫</mo><msup id="idp13698320"><mi id="idp13698448" mathvariant="double-struck">T</mi><mi id="idp13698976">N</mi></msup></msub><mrow id="idp13699232"><msup id="idp13699360"><mrow id="idp13699488"><mo id="idp13699616" fence="true">|</mo><msub id="idp13700144"><mi id="idp13700272">u</mi><mn id="idp13700528">0</mn></msub><mo id="idp13700784" fence="true">|</mo></mrow><mn id="idp13701312">2</mn></msup><mo id="idp13701568">⁢</mo><mi id="idp13701856">d</mi><mo id="idp13702112">⁢</mo><mi id="idp13702400">x</mi></mrow></mrow></mrow></mrow><annotation-xml id="idp13702656" encoding="MathML-Content"><apply id="idp13703056"><leq id="idp13703184"/><apply id="idp13703312"><plus id="idp13703440"/><apply id="idp13703568"><apply id="idp13703696"><csymbol id="idp13703824" cd="ambiguous">subscript</csymbol><csymbol id="idp13704384" cd="latexml">supremum</csymbol><apply id="idp13704944"><and id="idp13705072"/><apply id="idp13705200"><leq id="idp13705328"/><cn id="idp13705456" type="integer">0</cn><ci id="S4.E64.m1.sh1.cmml">t</ci></apply><apply id="idp13706512"><leq id="idp13706640"/><share id="idp13706768" href="#S4.E64.m1.sh1.cmml"/><apply id="S4.E64.m1.sh2c.cmml"><csymbol cd="ambiguous" id="S4.E64.m1.sh2.cmml">subscript</csymbol><ci id="S4.E64.m1.sh2a.cmml">T</ci><cn type="integer" id="S4.E64.m1.sh2b.cmml">0</cn></apply></apply></apply></apply><apply id="idp13709728"><apply id="idp13709856"><csymbol id="idp13709984" cd="ambiguous">subscript</csymbol><int id="idp13710544"/><apply id="idp13710672"><csymbol id="idp13710800" cd="ambiguous">superscript</csymbol><ci id="idp13711360">T</ci><ci id="idp13711616">N</ci></apply></apply><apply id="idp13711872"><times id="idp13712000"/><apply id="idp13712128"><csymbol id="idp13712256" cd="ambiguous">superscript</csymbol><apply id="idp13712816"><abs id="idp13712944"/><apply id="idp13713072"><times id="idp13713200"/><apply id="idp13713328"><csymbol id="idp13713456" cd="ambiguous">subscript</csymbol><ci id="idp13714016">w</ci><cn id="idp13714272" type="integer">1</cn></apply><apply id="idp13714800"><interval id="idp13714928" closure="open"/><ci id="idp13715328">t</ci><ci id="idp13715584">x</ci></apply></apply></apply><cn id="idp13715840" type="integer">2</cn></apply><ci id="idp13716368">d</ci><ci id="idp13716624">x</ci></apply></apply></apply><apply id="idp13716880"><apply id="idp13717008"><csymbol id="idp13717136" cd="ambiguous">subscript</csymbol><apply id="idp13717696"><csymbol id="idp13717824" cd="ambiguous">superscript</csymbol><int id="idp13718384"/><apply id="idp13718512"><csymbol id="idp13718640" cd="ambiguous">subscript</csymbol><ci id="idp13719200">T</ci><cn id="idp13719456" type="integer">0</cn></apply></apply><cn id="idp13719984" type="integer">0</cn></apply><apply id="idp13720512"><apply id="idp13720640"><csymbol id="idp13720768" cd="ambiguous">subscript</csymbol><int id="idp13721328"/><apply id="idp13721456"><csymbol id="idp13721584" cd="ambiguous">superscript</csymbol><ci id="idp13722144">T</ci><ci id="idp13722400">N</ci></apply></apply><apply id="idp13722656"><times id="idp13722784"/><apply id="idp13722912"><csymbol id="idp13723040" cd="ambiguous">superscript</csymbol><apply id="idp13723600"><abs id="idp13723728"/><apply id="idp13723856"><ci id="idp13723984">∇</ci><apply id="idp13724272"><csymbol id="idp13724400" cd="ambiguous">subscript</csymbol><ci id="idp13724960">w</ci><cn id="idp13725216" type="integer">1</cn></apply></apply></apply><cn id="idp13725744" type="integer">2</cn></apply><ci id="idp13726272">d</ci><ci id="idp13726528">x</ci><ci id="idp13726784">d</ci><ci id="idp13727040">t</ci></apply></apply></apply></apply><apply id="idp13727296"><times id="idp13727424"/><ci id="idp13727552">C</ci><apply id="idp13727808"><apply id="idp13727936"><csymbol id="idp13728064" cd="ambiguous">subscript</csymbol><int id="idp13728624"/><apply id="idp13728752"><csymbol id="idp13728880" cd="ambiguous">superscript</csymbol><ci id="idp13729440">T</ci><ci id="idp13729696">N</ci></apply></apply><apply id="idp13729952"><times id="idp13730080"/><apply id="idp13730208"><csymbol id="idp13730336" cd="ambiguous">superscript</csymbol><apply id="idp13730896"><abs id="idp13731024"/><apply id="idp13731152"><csymbol id="idp13731280" cd="ambiguous">subscript</csymbol><ci id="idp13731840">u</ci><cn id="idp13732096" type="integer">0</cn></apply></apply><cn id="idp13732624" type="integer">2</cn></apply><ci id="idp13733152">d</ci><ci id="idp13733408">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp13733664" encoding="application/x-tex">\sup _{{0\leq t\leq T_{{0}}}}\int _{{\mathbb{T}^{{N}}}}|w_{{1}}(t,x)|^{{2}}dx+\int^{{T_{{0}}}}_{{0}}\int _{{\mathbb{T}^{{N}}}}|\nabla w_{{1}}|^{{2}}dxdt\leq C\int _{{\mathbb{T}^{{N}}}}|u_{{0}}|^{{2}}dx</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp13993328"><h4>Hit idp13993328</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 19</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/116/f046110.xhtml#idp13993328</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1770602(000067%) VariableMap:[dxd x 2, mathbb x 2, int x 4, +, mu, N x 2, k x 3, ,, -, frac, w x 2, T x 2, 2 x 3, u, 1 x 4, 0 x 2, t x 2, displaystyle, nabla x 3, tau x 4, \ x 16, _ x 6, | x 6, ^ x 8] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp13993328" alttext="\displaystyle\frac{1}{2}\mu k\int^{{t}}_{{0}}\int _{{\mathbb{T}^{{N}}}}\tau^{{k-1}}|\nabla w_{{1}}|^{{2}}dxd\tau+\int^{{t}}_{{0}}\int _{{\mathbb{T}^{{N}}}}\tau^{{k}}|\nabla w_{{1}}|^{{2}}|\nabla u|dxd\tau," display="inline"><semantics id="idp13994272"><mrow id="idp13994400"><mrow id="idp13994528"><mrow id="idp13994656"><mstyle id="idp13994784" displaystyle="true"><mfrac id="idp13995152"><mn id="idp13995280">1</mn><mn id="idp13995536">2</mn></mfrac></mstyle><mo id="idp13995792">⁢</mo><mi id="idp13996048">μ</mi><mo id="idp13996336">⁢</mo><mi id="idp13996624">k</mi><mo id="idp13996880">⁢</mo><mrow id="idp13997168"><mstyle id="idp13997296" displaystyle="true"><msubsup id="idp13997696"><mo id="idp13997824">∫</mo><mn id="idp13998112">0</mn><mi id="idp13998368">t</mi></msubsup></mstyle><mrow id="idp13998624"><mstyle id="idp13998752" displaystyle="true"><msub id="idp13999152"><mo id="idp13999280">∫</mo><msup id="idp13999568"><mi id="idp13999696" mathvariant="double-struck">T</mi><mi id="idp14000224">N</mi></msup></msub></mstyle><mrow id="idp14000480"><msup id="idp14000608"><mi id="idp14000736">τ</mi><mrow id="idp14001024"><mi id="idp14001152">k</mi><mo id="idp14001408">-</mo><mn id="idp14001664">1</mn></mrow></msup><mo id="idp14001920">⁢</mo><msup id="idp14002208"><mrow id="idp14002336"><mo id="idp14002464" fence="true">|</mo><mrow id="idp14002992"><mo id="idp14003120">∇</mo><mo id="idp14003408">⁡</mo><msub id="idp14003664"><mi id="idp14003792">w</mi><mn id="idp14004048">1</mn></msub></mrow><mo id="idp14004304" fence="true">|</mo></mrow><mn id="idp14004800">2</mn></msup><mo id="idp14005056">⁢</mo><mi id="idp14005312">d</mi><mo id="idp14005568">⁢</mo><mi id="idp14005856">x</mi><mo id="idp14006112">⁢</mo><mi id="idp14006400">d</mi><mo id="idp14006656">⁢</mo><mi id="idp14006944">τ</mi></mrow></mrow></mrow></mrow><mo id="idp14007232">+</mo><mrow id="idp14007488"><mstyle id="idp14007616" displaystyle="true"><msubsup id="idp14008016"><mo id="idp14008144">∫</mo><mn id="idp14008432">0</mn><mi id="idp14008688">t</mi></msubsup></mstyle><mrow id="idp14008944"><mstyle id="idp14009072" displaystyle="true"><msub id="idp14009472"><mo id="idp14009600">∫</mo><msup id="idp14009888"><mi id="idp14010016" mathvariant="double-struck">T</mi><mi id="idp14010544">N</mi></msup></msub></mstyle><mrow id="idp14010800"><msup id="idp14010928"><mi id="idp14011056">τ</mi><mi id="idp14011344">k</mi></msup><mo id="idp14011600">⁢</mo><msup id="idp14011888"><mrow id="idp14012016"><mo id="idp14012144" fence="true">|</mo><mrow id="idp14012672"><mo id="idp14012800">∇</mo><mo id="idp14013088">⁡</mo><msub id="idp14013376"><mi id="idp14013504">w</mi><mn id="idp14013760">1</mn></msub></mrow><mo id="idp14014016" fence="true">|</mo></mrow><mn id="idp14014544">2</mn></msup><mo id="idp14014800">⁢</mo><mrow id="idp14015088"><mo id="idp14015216" fence="true">|</mo><mrow id="idp14015744"><mo id="idp14015872">∇</mo><mo id="idp14016160">⁡</mo><mi id="idp14016448">u</mi></mrow><mo id="idp14016704" fence="true">|</mo></mrow><mo id="idp14017232">⁢</mo><mi id="idp14017520">d</mi><mo id="idp14017776">⁢</mo><mi id="idp14018064">x</mi><mo id="idp14018320">⁢</mo><mi id="idp14018608">d</mi><mo id="idp14018864">⁢</mo><mi id="idp14019152">τ</mi></mrow></mrow></mrow></mrow><mo id="idp14019440">,</mo></mrow><annotation-xml id="idp14019696" encoding="MathML-Content"><apply id="idp14020096"><plus id="idp14020224"/><apply id="idp14020352"><times id="idp14020480"/><apply id="idp14020608"><divide id="idp14020736"/><cn id="idp14020864" type="integer">1</cn><cn id="idp14021392" type="integer">2</cn></apply><ci id="idp14021920">μ</ci><ci id="idp14022208">k</ci><apply id="idp14022464"><apply id="idp14022592"><csymbol id="idp14022720" cd="ambiguous">subscript</csymbol><apply id="idp14023280"><csymbol id="idp14023408" cd="ambiguous">superscript</csymbol><int id="idp14023968"/><ci id="idp14024096">t</ci></apply><cn id="idp14024352" type="integer">0</cn></apply><apply id="idp14024880"><apply id="idp14025008"><csymbol id="idp14025136" cd="ambiguous">subscript</csymbol><int id="idp14025696"/><apply id="idp14025824"><csymbol id="idp14025952" cd="ambiguous">superscript</csymbol><ci id="idp14026512">T</ci><ci id="idp14026768">N</ci></apply></apply><apply id="idp14027024"><times id="idp14027152"/><apply id="idp14027280"><csymbol id="idp14027408" cd="ambiguous">superscript</csymbol><ci id="idp14027968">τ</ci><apply id="idp14028256"><minus id="idp14028384"/><ci id="idp14028512">k</ci><cn id="idp14028768" type="integer">1</cn></apply></apply><apply id="idp14029296"><csymbol id="idp14029424" cd="ambiguous">superscript</csymbol><apply id="idp14029984"><abs id="idp14030112"/><apply id="idp14030240"><ci id="idp14030368">∇</ci><apply id="idp14030656"><csymbol id="idp14030784" cd="ambiguous">subscript</csymbol><ci id="idp14031344">w</ci><cn id="idp14031600" type="integer">1</cn></apply></apply></apply><cn id="idp14032128" type="integer">2</cn></apply><ci id="idp14032656">d</ci><ci id="idp14032912">x</ci><ci id="idp14033168">d</ci><ci id="idp14033424">τ</ci></apply></apply></apply></apply><apply id="idp14033712"><apply id="idp14033840"><csymbol id="idp14033968" cd="ambiguous">subscript</csymbol><apply id="idp14034528"><csymbol id="idp14034656" cd="ambiguous">superscript</csymbol><int id="idp14035216"/><ci id="idp14035344">t</ci></apply><cn id="idp14035600" type="integer">0</cn></apply><apply id="idp14036128"><apply id="idp14036256"><csymbol id="idp14036384" cd="ambiguous">subscript</csymbol><int id="idp14036944"/><apply id="idp14037072"><csymbol id="idp14037200" cd="ambiguous">superscript</csymbol><ci id="idp14037760">T</ci><ci id="idp14038016">N</ci></apply></apply><apply id="idp14038272"><times id="idp14038400"/><apply id="idp14038528"><csymbol id="idp14038656" cd="ambiguous">superscript</csymbol><ci id="idp14039216">τ</ci><ci id="idp14039504">k</ci></apply><apply id="idp14039760"><csymbol id="idp14039888" cd="ambiguous">superscript</csymbol><apply id="idp14040448"><abs id="idp14040576"/><apply id="idp14040704"><ci id="idp14040832">∇</ci><apply id="idp14041120"><csymbol id="idp14041248" cd="ambiguous">subscript</csymbol><ci id="idp14041808">w</ci><cn id="idp14042064" type="integer">1</cn></apply></apply></apply><cn id="idp14042592" type="integer">2</cn></apply><apply id="idp14043120"><abs id="idp14043248"/><apply id="idp14043376"><ci id="idp14043504">∇</ci><ci id="idp14043792">u</ci></apply></apply><ci id="idp14044048">d</ci><ci id="idp14044304">x</ci><ci id="idp14044560">d</ci><ci id="idp14044816">τ</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp14045104" encoding="application/x-tex">\displaystyle\frac{1}{2}\mu k\int^{{t}}_{{0}}\int _{{\mathbb{T}^{{N}}}}\tau^{{k-1}}|\nabla w_{{1}}|^{{2}}dxd\tau+\int^{{t}}_{{0}}\int _{{\mathbb{T}^{{N}}}}\tau^{{k}}|\nabla w_{{1}}|^{{2}}|\nabla u|dxd\tau,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp15748240"><h4>Hit idp15748240</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 20</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/18/f007142.xhtml#idp15748240</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:2010895(000071%) VariableMap:[dv x 3, A x 2, B,  , sum, , Vol, infty, I x 2, backslash x 2, hbox, nabla x 3, alpha x 8, R x 2, \ x 37, left, _ x 19, ^ x 8, right, end, g x 4, & x 2, leq, int x 3, n, o, + x 2,   , ( x 2, ) x 2, Omega x 4, ., j x 2, k, in x 2, , x 4, frac, i x 4, begin, prime x 2, 2 x 5, 1, u x 2, bigcup x 2, split x 2, | x 6, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp15748240" alttext="\begin{split}&\int _{{\Omega _{\alpha}\backslash\bigcup _{{i\in I^{\prime}}}A_{{i,\alpha,R}}}}|\nabla u_{\alpha}|^{2}dv_{g}\leq 2\int _{{\Omega _{\alpha}}}|\nabla u_{\infty}|^{2}dv_{g}\\ &  +\sum _{{j=1}}^{k}\int _{{\Omega _{\alpha}\backslash\bigcup _{{i\in I^{\prime}}}A_{{i,\alpha,R}}}}|\nabla B_{\alpha}^{j}|^{2}dv_{g}+o\left(\hbox{Vol}_{g}(\Omega _{\alpha})^{{\frac{2}{n}}}\right) .\end{split}" display="block"><semantics id="idp15747792"><mrow id="idp15747920"><mrow id="idp15748048"><mrow id="idp15749376"><msub id="idp15749504"><mo id="idp15749632">∫</mo><mrow id="idp15749888"><msub id="idp15750016"><mi id="idp15750144" mathvariant="normal">Ω</mi><mi id="idp15750640">α</mi></msub><mo id="idp15750896">\</mo><mrow id="idp15751152"><msub id="idp15751280"><mo id="idp15751408">⋃</mo><mrow id="idp15751696"><mi id="idp15751824">i</mi><mo id="idp15752080">∈</mo><msup id="idp15752368"><mi id="idp15752496">I</mi><mo id="idp15752752">′</mo></msup></mrow></msub><msub id="idp15753040"><mi id="idp15753168">A</mi><mrow id="idp15753424"><mi id="idp15753552">i</mi><mo id="idp15753808">,</mo><mi id="idp15754064">α</mi><mo id="idp15754352">,</mo><mi id="idp15754608">R</mi></mrow></msub></mrow></mrow></msub><mrow id="idp15754864"><msup id="idp15754992"><mrow id="idp15755120"><mo id="idp15755248" fence="true">|</mo><mrow id="idp15755776"><mo id="idp15755904">∇</mo><mo id="idp15756192">⁡</mo><msub id="idp15756480"><mi id="idp15756608">u</mi><mi id="idp15756864">α</mi></msub></mrow><mo id="idp15757152" fence="true">|</mo></mrow><mn id="idp15757680">2</mn></msup><mo id="idp15757936">⁢</mo><mi id="idp15758224">d</mi><mo id="idp15758480">⁢</mo><msub id="idp15758768"><mi id="idp15758896">v</mi><mi id="idp15759152">g</mi></msub></mrow></mrow><mo id="idp15759408">≤</mo><mrow id="idp15759696"><mrow id="idp15759824"><mn id="idp15759952">2</mn><mo id="idp15760208">⁢</mo><mrow id="idp15760496"><msub id="idp15760624"><mo id="idp15760752">∫</mo><msub id="idp15761040"><mi id="idp15761168" mathvariant="normal">Ω</mi><mi id="idp15761728">α</mi></msub></msub><mrow id="idp15762016"><msup id="idp15762144"><mrow id="idp15762272"><mo id="idp15762400" fence="true">|</mo><mrow id="idp15762928"><mo id="idp15763056">∇</mo><mo id="idp15763344">⁡</mo><msub id="idp15763632"><mi id="idp15763760">u</mi><mi id="idp15764016" mathvariant="normal">∞</mi></msub></mrow><mo id="idp15764576" fence="true">|</mo></mrow><mn id="idp15765104">2</mn></msup><mo id="idp15765360">⁢</mo><mi id="idp15765648">d</mi><mo id="idp15765904">⁢</mo><msub id="idp15766192"><mi id="idp15766320">v</mi><mi id="idp15766576">g</mi></msub><mo id="idp15766832">⁢</mo><mi id="idp15767120">  </mi></mrow></mrow></mrow><mo id="idp15767408">+</mo><mrow id="idp15767664"><mover id="idp15767792"><munder id="idp15767920"><mo id="idp15768048" movablelimits="false">∑</mo><mrow id="idp15768608"><mi id="idp15768736">j</mi><mo id="idp15768992" movablelimits="false">=</mo><mn id="idp15769520">1</mn></mrow></munder><mi id="idp15769776">k</mi></mover><mrow id="idp15770032"><msub id="idp15770160"><mo id="idp15770288">∫</mo><mrow id="idp15770576"><msub id="idp15770704"><mi id="idp15770832" mathvariant="normal">Ω</mi><mi id="idp15771392">α</mi></msub><mo id="idp15771680">\</mo><mrow id="idp15771936"><msub id="idp15772064"><mo id="idp15772192">⋃</mo><mrow id="idp15772480"><mi id="idp15772608">i</mi><mo id="idp15772864">∈</mo><msup id="idp15773152"><mi id="idp15773280">I</mi><mo id="idp15773536">′</mo></msup></mrow></msub><msub id="idp15773824"><mi id="idp15773952">A</mi><mrow id="idp15774208"><mi id="idp15774336">i</mi><mo id="idp15774592">,</mo><mi id="idp15774848">α</mi><mo id="idp15775136">,</mo><mi id="idp15775392">R</mi></mrow></msub></mrow></mrow></msub><mrow id="idp15775648"><msup id="idp15775776"><mrow id="idp15775904"><mo id="idp15776032" fence="true">|</mo><mrow id="idp15776560"><mo id="idp15776688">∇</mo><mo id="idp15776976">⁡</mo><msubsup id="idp15777232"><mi id="idp15777360">B</mi><mi id="idp15777616">α</mi><mi id="idp15777872">j</mi></msubsup></mrow><mo id="idp15778128" fence="true">|</mo></mrow><mn id="idp15778624">2</mn></msup><mo id="idp15778880">⁢</mo><mi id="idp15779168">d</mi><mo id="idp15779424">⁢</mo><msub id="idp15779712"><mi id="idp15779840">v</mi><mi id="idp15780096">g</mi></msub></mrow></mrow></mrow><mo id="idp15780352">+</mo><mrow id="idp15780608"><mi id="idp15780736">o</mi><mo id="idp15780992">⁢</mo><mrow id="idp15781280"><mo id="idp15781408">(</mo><mrow id="idp15781664"><msub id="idp15781792"><mtext id="idp15781920">Vol</mtext><mi id="idp15782176">g</mi></msub><mo id="idp15782432">⁢</mo><msup id="idp15782720"><mrow id="idp15782848"><mo id="idp15782976">(</mo><msub id="idp15783232"><mi id="idp15783360" mathvariant="normal">Ω</mi><mi id="idp15783920">α</mi></msub><mo id="idp15784208">)</mo></mrow><mfrac id="idp15784464"><mn id="idp15784592">2</mn><mi id="idp15784848">n</mi></mfrac></msup></mrow><mo id="idp15785104">)</mo></mrow><mo id="idp15785360">⁢</mo><mi id="idp15785648" mathvariant="normal"> </mi></mrow></mrow></mrow><mo id="idp15786208">.</mo></mrow><annotation-xml id="idp15786464" encoding="MathML-Content"><apply id="idp15786864"><leq id="idp15786992"/><apply id="idp15787120"><apply id="idp15787248"><csymbol id="idp15787376" cd="ambiguous">subscript</csymbol><int id="idp15787936"/><apply id="idp15788064"><ci id="idp15788192">\</ci><apply id="idp15788448"><csymbol id="idp15788576" cd="ambiguous">subscript</csymbol><ci id="idp15789136">Ω</ci><ci id="idp15789424">α</ci></apply><apply id="idp15789712"><apply id="idp15789840"><csymbol id="idp15789968" cd="ambiguous">subscript</csymbol><union id="idp15790528"/><apply id="idp15790656"><in id="idp15790784"/><ci id="idp15790912">i</ci><apply id="idp15791168"><csymbol id="idp15791296" cd="ambiguous">superscript</csymbol><ci id="idp15791856">I</ci><ci id="idp15792112">′</ci></apply></apply></apply><apply id="idp15792400"><csymbol id="idp15792528" cd="ambiguous">subscript</csymbol><ci id="idp15793088">A</ci><apply id="idp15793344"><list id="idp15793472"/><ci id="idp15793600">i</ci><ci id="idp15793856">α</ci><ci id="idp15794144">R</ci></apply></apply></apply></apply></apply><apply id="idp15794400"><times id="idp15794528"/><apply id="idp15794656"><csymbol id="idp15794784" cd="ambiguous">superscript</csymbol><apply id="idp15795344"><abs id="idp15795472"/><apply id="idp15795600"><ci id="idp15795728">∇</ci><apply id="idp15796016"><csymbol id="idp15796144" cd="ambiguous">subscript</csymbol><ci id="idp15796704">u</ci><ci id="idp15796960">α</ci></apply></apply></apply><cn id="idp15797248" type="integer">2</cn></apply><ci id="idp15797776">d</ci><apply id="idp15798032"><csymbol id="idp15798160" cd="ambiguous">subscript</csymbol><ci id="idp15798720">v</ci><ci id="idp15798976">g</ci></apply></apply></apply><apply id="idp15799232"><plus id="idp15799360"/><apply id="idp15799488"><times id="idp15799616"/><cn id="idp15799744" type="integer">2</cn><apply id="idp15800272"><apply id="idp15800400"><csymbol id="idp15800528" cd="ambiguous">subscript</csymbol><int id="idp15801088"/><apply id="idp15801216"><csymbol id="idp15801344" cd="ambiguous">subscript</csymbol><ci id="idp15801904">Ω</ci><ci id="idp15802192">α</ci></apply></apply><apply id="idp15802480"><times id="idp15802608"/><apply id="idp15802736"><csymbol id="idp15802864" cd="ambiguous">superscript</csymbol><apply id="idp15803424"><abs id="idp15803552"/><apply id="idp15803680"><ci id="idp15803808">∇</ci><apply id="idp15804096"><csymbol id="idp15804224" cd="ambiguous">subscript</csymbol><ci id="idp15804784">u</ci><infinity id="idp15805040"/></apply></apply></apply><cn id="idp15805168" type="integer">2</cn></apply><ci id="idp15805696">d</ci><apply id="idp15805952"><csymbol id="idp15806080" cd="ambiguous">subscript</csymbol><ci id="idp15806640">v</ci><ci id="idp15806896">g</ci></apply><ci id="idp15807152">  </ci></apply></apply></apply><apply id="idp15807440"><apply id="idp15807568"><csymbol id="idp15807696" cd="ambiguous">superscript</csymbol><apply id="idp15808256"><csymbol id="idp15808384" cd="ambiguous">subscript</csymbol><sum id="idp15808944"/><apply id="idp15809072"><eq id="idp15809200"/><ci id="idp15809328">j</ci><cn id="idp15809584" type="integer">1</cn></apply></apply><ci id="idp15810112">k</ci></apply><apply id="idp15810368"><apply id="idp15810496"><csymbol id="idp15810624" cd="ambiguous">subscript</csymbol><int id="idp15811184"/><apply id="idp15811312"><ci id="idp15811440">\</ci><apply id="idp15811696"><csymbol id="idp15811824" cd="ambiguous">subscript</csymbol><ci id="idp15812384">Ω</ci><ci id="idp15812672">α</ci></apply><apply id="idp15812960"><apply id="idp15813088"><csymbol id="idp15813216" cd="ambiguous">subscript</csymbol><union id="idp15813776"/><apply id="idp15813904"><in id="idp15814032"/><ci id="idp15814160">i</ci><apply id="idp15814416"><csymbol id="idp15814544" cd="ambiguous">superscript</csymbol><ci id="idp15815104">I</ci><ci id="idp15815360">′</ci></apply></apply></apply><apply id="idp15815648"><csymbol id="idp15815776" cd="ambiguous">subscript</csymbol><ci id="idp15816336">A</ci><apply id="idp15816592"><list id="idp15816720"/><ci id="idp15816848">i</ci><ci id="idp15817104">α</ci><ci id="idp15817392">R</ci></apply></apply></apply></apply></apply><apply id="idp15817648"><times id="idp15817776"/><apply id="idp15817904"><csymbol id="idp15818032" cd="ambiguous">superscript</csymbol><apply id="idp15818592"><abs id="idp15818720"/><apply id="idp15818848"><ci id="idp15818976">∇</ci><apply id="idp15819264"><csymbol id="idp15819392" cd="ambiguous">superscript</csymbol><apply id="idp15819952"><csymbol id="idp15820080" cd="ambiguous">subscript</csymbol><ci id="idp15820640">B</ci><ci id="idp15820896">α</ci></apply><ci id="idp15821184">j</ci></apply></apply></apply><cn id="idp15821440" type="integer">2</cn></apply><ci id="idp15821968">d</ci><apply id="idp15822224"><csymbol id="idp15822352" cd="ambiguous">subscript</csymbol><ci id="idp15822912">v</ci><ci id="idp15823168">g</ci></apply></apply></apply></apply><apply id="idp15823424"><times id="idp15823552"/><ci id="idp15823680">o</ci><apply id="idp15823936"><times id="idp15824064"/><apply id="idp15824192"><csymbol id="idp15824320" cd="ambiguous">subscript</csymbol><mtext id="idp15824880">Vol</mtext><ci id="idp15825136">g</ci></apply><apply id="idp15825392"><csymbol id="idp15825520" cd="ambiguous">superscript</csymbol><apply id="idp15826080"><csymbol id="idp15826208" cd="ambiguous">subscript</csymbol><ci id="idp15826768">Ω</ci><ci id="idp15827056">α</ci></apply><apply id="idp15827344"><divide id="idp15827472"/><cn id="idp15827600" type="integer">2</cn><ci id="idp15828128">n</ci></apply></apply></apply><ci id="idp15828384"> </ci></apply></apply></apply></annotation-xml><annotation id="idp15828672" encoding="application/x-tex">\begin{split}&\int _{{\Omega _{\alpha}\backslash\bigcup _{{i\in I^{\prime}}}A_{{i,\alpha,R}}}}|\nabla u_{\alpha}|^{2}dv_{g}\leq 2\int _{{\Omega _{\alpha}}}|\nabla u_{\infty}|^{2}dv_{g}\\ &  +\sum _{{j=1}}^{k}\int _{{\Omega _{\alpha}\backslash\bigcup _{{i\in I^{\prime}}}A_{{i,\alpha,R}}}}|\nabla B_{\alpha}^{j}|^{2}dv_{g}+o\left(\hbox{Vol}_{g}(\Omega _{\alpha})^{{\frac{2}{n}}}\right) .\end{split}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp192576"><h4>Hit idp192576</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 21</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/205/f081941.xhtml#idp192576</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:16173(000003%) VariableMap:[dx x 2, mathbb x 3, nabla, R x 3, \ x 16, _ x 4, ^ x 7, limits x 4, leq, int x 4, a, +, (, ), ,, frac x 2, prime, 3 x 3, 2 x 4, v x 2, 1 x 2, dxdt, t x 2, 0, | x 6, x] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp192576" alttext="\frac{1}{2}\int\limits _{{\mathbb{R}^{3}}}|v(x,t)|dx+\int\limits^{t}_{0}\int\limits _{{\mathbb{R}^{3}}}|\nabla v|^{2}dxdt^{{\prime}}\leq\frac{1}{2}\int\limits _{{\mathbb{R}^{3}}}|a|^{2}dx" display="block"><semantics id="idp193504"><mrow id="idp193632"><mrow id="idp193760"><mrow id="idp193888"><mfrac id="idp194016"><mn id="idp194144">1</mn><mn id="idp194400">2</mn></mfrac><mo id="idp194656">⁢</mo><mrow id="idp194912"><munder id="idp195040"><mo id="idp195168" movablelimits="false">∫</mo><msup id="idp195696"><mi id="idp195824" mathvariant="double-struck">R</mi><mn id="idp196352">3</mn></msup></munder><mrow id="idp196608"><mrow id="idp196736"><mo id="idp196864" fence="true">|</mo><mrow id="idp197392"><mi id="idp197520">v</mi><mo id="idp197776">⁢</mo><mrow id="idp198064"><mo id="idp198192">(</mo><mrow id="idp198448"><mi id="idp198576">x</mi><mo id="idp198832">,</mo><mi id="idp199088">t</mi></mrow><mo id="idp199344">)</mo></mrow></mrow><mo id="idp199600" fence="true">|</mo></mrow><mo id="idp200128">⁢</mo><mi id="idp200416">d</mi><mo id="idp200672">⁢</mo><mi id="idp200960">x</mi></mrow></mrow></mrow><mo id="idp201216">+</mo><mrow id="idp201472"><munder id="idp201600"><mover id="idp201776"><mo id="idp201904" movablelimits="false">∫</mo><mi id="idp202464">t</mi></mover><mn id="idp202720">0</mn></munder><mrow id="idp202976"><munder id="idp203104"><mo id="idp203232" movablelimits="false">∫</mo><msup id="idp203792"><mi id="idp203920" mathvariant="double-struck">R</mi><mn id="idp204448">3</mn></msup></munder><mrow id="idp204704"><msup id="idp204832"><mrow id="idp204960"><mo id="idp205088" fence="true">|</mo><mrow id="idp205616"><mo id="idp205744">∇</mo><mo id="idp206032">⁡</mo><mi id="idp206320">v</mi></mrow><mo id="idp206576" fence="true">|</mo></mrow><mn id="idp207104">2</mn></msup><mo id="idp207360">⁢</mo><mi id="idp207648">d</mi><mo id="idp207904">⁢</mo><mi id="idp208192">x</mi><mo id="idp208448">⁢</mo><mi id="idp208736">d</mi><mo id="idp208992">⁢</mo><msup id="idp209280"><mi id="idp209408">t</mi><mo id="idp209664">′</mo></msup></mrow></mrow></mrow></mrow><mo id="idp209952">≤</mo><mrow id="idp210240"><mfrac id="idp210368"><mn id="idp210496">1</mn><mn id="idp210752">2</mn></mfrac><mo id="idp211008">⁢</mo><mrow id="idp211296"><munder id="idp211424"><mo id="idp211552" movablelimits="false">∫</mo><msup id="idp212112"><mi id="idp212240" mathvariant="double-struck">R</mi><mn id="idp212736">3</mn></msup></munder><mrow id="idp212992"><msup id="idp213120"><mrow id="idp213248"><mo id="idp213376" fence="true">|</mo><mi id="idp213872">a</mi><mo id="idp214128" fence="true">|</mo></mrow><mn id="idp214624">2</mn></msup><mo id="idp214880">⁢</mo><mi id="idp215168">d</mi><mo id="idp215424">⁢</mo><mi id="idp215712">x</mi></mrow></mrow></mrow></mrow><annotation-xml id="idp215968" encoding="MathML-Content"><apply id="idp216368"><leq id="idp216496"/><apply id="idp216624"><plus id="idp216752"/><apply id="idp216880"><times id="idp217008"/><apply id="idp217136"><divide id="idp217264"/><cn id="idp217392" type="integer">1</cn><cn id="idp217920" type="integer">2</cn></apply><apply id="idp218448"><apply id="idp218576"><csymbol id="idp218704" cd="ambiguous">subscript</csymbol><int id="idp219264"/><apply id="idp219392"><csymbol id="idp219520" cd="ambiguous">superscript</csymbol><ci id="idp220080">R</ci><cn id="idp220336" type="integer">3</cn></apply></apply><apply id="idp220864"><times id="idp220992"/><apply id="idp221120"><abs id="idp221248"/><apply id="idp221376"><times id="idp221504"/><ci id="idp221632">v</ci><apply id="idp221888"><interval id="idp222064" closure="open"/><ci id="idp222464">x</ci><ci id="idp222720">t</ci></apply></apply></apply><ci id="idp222976">d</ci><ci id="idp223232">x</ci></apply></apply></apply><apply id="idp223488"><apply id="idp223616"><csymbol id="idp223744" cd="ambiguous">subscript</csymbol><apply id="idp224304"><csymbol id="idp224432" cd="ambiguous">superscript</csymbol><int id="idp224992"/><ci id="idp225120">t</ci></apply><cn id="idp225376" type="integer">0</cn></apply><apply id="idp225904"><apply id="idp226032"><csymbol id="idp226160" cd="ambiguous">subscript</csymbol><int id="idp226720"/><apply id="idp226848"><csymbol id="idp226976" cd="ambiguous">superscript</csymbol><ci id="idp227536">R</ci><cn id="idp227792" type="integer">3</cn></apply></apply><apply id="idp228320"><times id="idp228448"/><apply id="idp228576"><csymbol id="idp228704" cd="ambiguous">superscript</csymbol><apply id="idp229264"><abs id="idp229392"/><apply id="idp229520"><ci id="idp229648">∇</ci><ci id="idp229936">v</ci></apply></apply><cn id="idp230192" type="integer">2</cn></apply><ci id="idp230720">d</ci><ci id="idp230976">x</ci><ci id="idp231232">d</ci><apply id="idp231488"><csymbol id="idp231616" cd="ambiguous">superscript</csymbol><ci id="idp232176">t</ci><ci id="idp232432">′</ci></apply></apply></apply></apply></apply><apply id="idp232720"><times id="idp232848"/><apply id="idp232976"><divide id="idp233104"/><cn id="idp233232" type="integer">1</cn><cn id="idp233760" type="integer">2</cn></apply><apply id="idp234288"><apply id="idp234416"><csymbol id="idp234544" cd="ambiguous">subscript</csymbol><int id="idp235104"/><apply id="idp235232"><csymbol id="idp235360" cd="ambiguous">superscript</csymbol><ci id="idp235920">R</ci><cn id="idp236176" type="integer">3</cn></apply></apply><apply id="idp236704"><times id="idp236832"/><apply id="idp236960"><csymbol id="idp237088" cd="ambiguous">superscript</csymbol><apply id="idp237648"><abs id="idp237776"/><ci id="idp237904">a</ci></apply><cn id="idp238160" type="integer">2</cn></apply><ci id="idp238688">d</ci><ci id="idp238944">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp239200" encoding="application/x-tex">\frac{1}{2}\int\limits _{{\mathbb{R}^{3}}}|v(x,t)|dx+\int\limits^{t}_{0}\int\limits _{{\mathbb{R}^{3}}}|\nabla v|^{2}dxdt^{{\prime}}\leq\frac{1}{2}\int\limits _{{\mathbb{R}^{3}}}|a|^{2}dx</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp20708592"><h4>Hit idp20708592</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 22</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/16/f006383.xhtml#idp20708592</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:206277(000042%) VariableMap:[g x 2, dv, A, leq, int, n x 2, + x 2, ., omega, ,, h, 2 x 3, 1, 0 x 2, displaystyle, nabla, \ x 6, _ x 5, ^ x 2, | x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 6 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp20708592" alttext="\displaystyle\int _{{2A}}|\nabla _{{g_{0}}}h|^{{n+1}}\, dv_{{g_{0}}}\leq 2^{{n+2}}\omega." display="inline"><semantics id="idp20709424"><mrow id="idp20709552"><mrow id="idp20709680"><mrow id="idp20709808"><mstyle id="idp20709936" displaystyle="true"><msub id="idp20710304"><mo id="idp20710432">∫</mo><mrow id="idp20710688"><mn id="idp20710816">2</mn><mo id="idp20711072">⁢</mo><mi id="idp20711360">A</mi></mrow></msub></mstyle><mrow id="idp20711616"><msup id="idp20711744"><mrow id="idp20711872"><mo id="idp20712000" fence="true">|</mo><mrow id="idp20712528"><msub id="idp20712656"><mo id="idp20712784">∇</mo><msub id="idp20713072"><mi id="idp20713200">g</mi><mn id="idp20713456">0</mn></msub></msub><mo id="idp20713712">⁡</mo><mi id="idp20714000">h</mi></mrow><mo id="idp20714256" fence="true">|</mo></mrow><mrow id="idp20714784"><mi id="idp20714912">n</mi><mo id="idp20715168">+</mo><mn id="idp20715424">1</mn></mrow></msup><mo id="idp20715680">⁢</mo><mi id="idp20715968">d</mi><mo id="idp20716224">⁢</mo><msub id="idp20716512"><mi id="idp20716640">v</mi><msub id="idp20716896"><mi id="idp20717024">g</mi><mn id="idp20717280">0</mn></msub></msub></mrow></mrow><mo id="idp20717536">≤</mo><mrow id="idp20717824"><msup id="idp20717952"><mn id="idp20718080">2</mn><mrow id="idp20718336"><mi id="idp20718464">n</mi><mo id="idp20718720">+</mo><mn id="idp20718976">2</mn></mrow></msup><mo id="idp20719232">⁢</mo><mi id="idp20719520">ω</mi></mrow></mrow><mo id="idp20719808">.</mo></mrow><annotation-xml id="idp20720064" encoding="MathML-Content"><apply id="idp20720464"><leq id="idp20720592"/><apply id="idp20720720"><apply id="idp20720848"><csymbol id="idp20720976" cd="ambiguous">subscript</csymbol><int id="idp20721536"/><apply id="idp20721664"><times id="idp20721792"/><cn id="idp20721920" type="integer">2</cn><ci id="idp20722448">A</ci></apply></apply><apply id="idp20722704"><times id="idp20722832"/><apply id="idp20722960"><csymbol id="idp20723088" cd="ambiguous">superscript</csymbol><apply id="idp20723648"><abs id="idp20723776"/><apply id="idp20723904"><apply id="idp20724032"><csymbol id="idp20724160" cd="ambiguous">subscript</csymbol><ci id="idp20724720">∇</ci><apply id="idp20725008"><csymbol id="idp20725136" cd="ambiguous">subscript</csymbol><ci id="idp20725696">g</ci><cn id="idp20725952" type="integer">0</cn></apply></apply><ci id="idp20726480">h</ci></apply></apply><apply id="idp20726736"><plus id="idp20726864"/><ci id="idp20726992">n</ci><cn id="idp20727248" type="integer">1</cn></apply></apply><ci id="idp20727776">d</ci><apply id="idp20728032"><csymbol id="idp20728160" cd="ambiguous">subscript</csymbol><ci id="idp20728720">v</ci><apply id="idp20728976"><csymbol id="idp20729104" cd="ambiguous">subscript</csymbol><ci id="idp20729664">g</ci><cn id="idp20729920" type="integer">0</cn></apply></apply></apply></apply><apply id="idp20730448"><times id="idp20730576"/><apply id="idp20730704"><csymbol id="idp20730832" cd="ambiguous">superscript</csymbol><cn id="idp20731392" type="integer">2</cn><apply id="idp20731920"><plus id="idp20732048"/><ci id="idp20732176">n</ci><cn id="idp20732432" type="integer">2</cn></apply></apply><ci id="idp20732960">ω</ci></apply></apply></annotation-xml><annotation id="idp20733248" encoding="application/x-tex">\displaystyle\int _{{2A}}|\nabla _{{g_{0}}}h|^{{n+1}}\, dv_{{g_{0}}}\leq 2^{{n+2}}\omega.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp21496224"><h4>Hit idp21496224</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 23</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/207/f082460.xhtml#idp21496224</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:238662(000077%) VariableMap:[f x 2, g x 2, leq x 2, int x 2, L, +, M x 2, , x 3, frac, v x 2, 2 x 3, 1, 0 x 2, nabla, \ x 9, _ x 4, | x 2, ^ x 2] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp21496224" alttext="0\leq\int _{M}L\, f^{2}\, v_{g}+\frac{1}{2}\int _{M}|\nabla f|^{2}\, v_{g}\leq 0" display="block"><semantics id="idp21496944"><mrow id="idp21497072"><mn id="idp21497200">0</mn><mo id="idp21497456">≤</mo><mrow id="idp21497712"><mrow id="idp21497840"><msub id="idp21497968"><mo id="idp21498096">∫</mo><mi id="idp21498352">M</mi></msub><mrow id="idp21498608"><mpadded id="idp21498736" width="+1.666667pt"><mi id="idp21499136">L</mi></mpadded><mo id="idp21499392">⁢</mo><msup id="idp21499680"><mi id="idp21499808">f</mi><mn id="idp21500064">2</mn></msup><mo id="idp21500320">⁢</mo><msub id="idp21500608"><mi id="idp21500736">v</mi><mi id="idp21500992">g</mi></msub></mrow></mrow><mo id="idp21501248">+</mo><mrow id="idp21501504"><mfrac id="idp21501632"><mn id="idp21501760">1</mn><mn id="idp21502016">2</mn></mfrac><mo id="idp21502272">⁢</mo><mrow id="idp21502560"><msub id="idp21502688"><mo id="idp21502816">∫</mo><mi id="idp21503104">M</mi></msub><mrow id="idp21503360"><msup id="idp21503488"><mrow id="idp21503616"><mo id="idp21503744" fence="true">|</mo><mrow id="idp21504272"><mo id="idp21504400">∇</mo><mo id="idp21504688">⁡</mo><mi id="idp21504976">f</mi></mrow><mo id="idp21505232" fence="true">|</mo></mrow><mn id="idp21505760">2</mn></msup><mo id="idp21506016">⁢</mo><msub id="idp21506304"><mi id="idp21506432">v</mi><mi id="idp21506688">g</mi></msub></mrow></mrow></mrow></mrow><mo id="idp21506944">≤</mo><mn id="idp21507232">0</mn></mrow><annotation-xml id="idp21507488" encoding="MathML-Content"><apply id="idp21507888"><and id="idp21508016"/><apply id="idp21508144"><leq id="idp21508272"/><cn id="idp21508400" type="integer">0</cn><apply id="S3.E13.m1.sh1ap.cmml"><plus id="S3.E13.m1.sh1.cmml"/><apply id="S3.E13.m1.sh1p.cmml"><apply id="S3.E13.m1.sh1d.cmml"><csymbol cd="ambiguous" id="S3.E13.m1.sh1a.cmml">subscript</csymbol><int id="S3.E13.m1.sh1b.cmml"/><ci id="S3.E13.m1.sh1c.cmml">M</ci></apply><apply id="S3.E13.m1.sh1o.cmml"><times id="S3.E13.m1.sh1e.cmml"/><ci id="S3.E13.m1.sh1f.cmml">L</ci><apply id="S3.E13.m1.sh1j.cmml"><csymbol cd="ambiguous" id="S3.E13.m1.sh1g.cmml">superscript</csymbol><ci id="S3.E13.m1.sh1h.cmml">f</ci><cn type="integer" id="S3.E13.m1.sh1i.cmml">2</cn></apply><apply id="S3.E13.m1.sh1n.cmml"><csymbol cd="ambiguous" id="S3.E13.m1.sh1k.cmml">subscript</csymbol><ci id="S3.E13.m1.sh1l.cmml">v</ci><ci id="S3.E13.m1.sh1m.cmml">g</ci></apply></apply></apply><apply id="S3.E13.m1.sh1ao.cmml"><times id="S3.E13.m1.sh1q.cmml"/><apply id="S3.E13.m1.sh1u.cmml"><divide id="S3.E13.m1.sh1r.cmml"/><cn type="integer" id="S3.E13.m1.sh1s.cmml">1</cn><cn type="integer" id="S3.E13.m1.sh1t.cmml">2</cn></apply><apply id="S3.E13.m1.sh1an.cmml"><apply id="S3.E13.m1.sh1y.cmml"><csymbol cd="ambiguous" id="S3.E13.m1.sh1v.cmml">subscript</csymbol><int id="S3.E13.m1.sh1w.cmml"/><ci id="S3.E13.m1.sh1x.cmml">M</ci></apply><apply id="S3.E13.m1.sh1am.cmml"><times id="S3.E13.m1.sh1z.cmml"/><apply id="S3.E13.m1.sh1ah.cmml"><csymbol cd="ambiguous" id="S3.E13.m1.sh1aa.cmml">superscript</csymbol><apply id="S3.E13.m1.sh1af.cmml"><abs id="S3.E13.m1.sh1ab.cmml"/><apply id="S3.E13.m1.sh1ae.cmml"><ci id="S3.E13.m1.sh1ac.cmml">∇</ci><ci id="S3.E13.m1.sh1ad.cmml">f</ci></apply></apply><cn type="integer" id="S3.E13.m1.sh1ag.cmml">2</cn></apply><apply id="S3.E13.m1.sh1al.cmml"><csymbol cd="ambiguous" id="S3.E13.m1.sh1ai.cmml">subscript</csymbol><ci id="S3.E13.m1.sh1aj.cmml">v</ci><ci id="S3.E13.m1.sh1ak.cmml">g</ci></apply></apply></apply></apply></apply></apply><apply id="idp21531632"><leq id="idp21531760"/><share id="idp21531888" href="#S3.E13.m1.sh1.cmml"/><cn type="integer" id="S3.E13.m1.sh2.cmml">0</cn></apply></apply></annotation-xml><annotation id="idp21533088" encoding="application/x-tex">0\leq\int _{M}L\, f^{2}\, v_{g}+\frac{1}{2}\int _{M}|\nabla f|^{2}\, v_{g}\leq 0</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp21648032"><h4>Hit idp21648032</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 24</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/63/f024901.xhtml#idp21648032</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:258862(000028%) VariableMap:[dx x 4, A x 7, x 3, nabla x 6, \ x 28, left, _ x 18, ^ x 4, right, end, geq x 2, & x 4, int x 5, a x 6, +, ( x 9, ) x 9, cdot x 2, k x 6, , x 5, begin, - x 4, udx, 3 x 2, u x 9, 0 x 2, mathcal x 2, displaystyle, 5 x 2, q x 2, 4 x 2, p x 2, split x 2, | x 8, =, x x 6] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp21648032" alttext="\displaystyle\begin{split}&\int _{{A_{k}}}\mathcal{A}(x,u,\nabla u)\cdot\nabla(u-k)dx\\ &=\int _{{A_{k}}}\mathcal{A}(x,u,\nabla u)\cdot\nabla udx\\ &\geq\int _{{A_{k}}}\left(a_{3}|\nabla u|^{{p(x)}}-a_{4}|u|^{{q_{0}(x)}}-a_{5}\right)dx\\ &\geq a_{3}\int _{{A_{k}}}|\nabla u|^{{p(x)}}dx-(a_{4}+a_{5})\int _{{A_{k}}}|u|^{{q_{0}(x)}}dx,\end{split}" display="inline"><semantics id="idp21647584"><mrow id="idp21647712"><mrow id="idp21647840"><mrow id="idp21649120"><mstyle id="idp21649248" displaystyle="true"><msub id="idp21649616"><mo id="idp21649744">∫</mo><msub id="idp21650000"><mi id="idp21650128">A</mi><mi id="idp21650384">k</mi></msub></msub></mstyle><mrow id="idp21650640"><mrow id="idp21650768"><mi id="idp21650896" mathvariant="script">A</mi><mo id="idp21651392">⁢</mo><mrow id="idp21651648"><mo id="idp21651776">(</mo><mrow id="idp21652032"><mi id="idp21652160">x</mi><mo id="idp21652416">,</mo><mi id="idp21652672">u</mi><mo id="idp21652928">,</mo><mrow id="idp21653184"><mo id="idp21653312">∇</mo><mo id="idp21653600">⁡</mo><mi id="idp21653888">u</mi></mrow></mrow><mo id="idp21654144">)</mo></mrow></mrow><mo id="idp21654400">⋅</mo><mrow id="idp21654688"><mrow id="idp21654816"><mo id="idp21654944">∇</mo><mo id="idp21655232">⁡</mo><mrow id="idp21655520"><mo id="idp21655648">(</mo><mrow id="idp21655904"><mi id="idp21656032">u</mi><mo id="idp21656288">-</mo><mi id="idp21656544">k</mi></mrow><mo id="idp21656800">)</mo></mrow></mrow><mo id="idp21657056">⁡</mo><mrow id="idp21657344"><mi id="idp21657472">d</mi><mo id="idp21657728">⁢</mo><mi id="idp21658016">x</mi></mrow></mrow></mrow></mrow><mo id="idp21658272">=</mo><mrow id="idp21658528"><mstyle id="idp21658656" displaystyle="true"><msub id="idp21659056"><mo id="idp21659184">∫</mo><msub id="idp21659472"><mi id="idp21659600">A</mi><mi id="idp21659856">k</mi></msub></msub></mstyle><mrow id="idp21660112"><mrow id="idp21660240"><mi id="idp21660368" mathvariant="script">A</mi><mo id="idp21660896">⁢</mo><mrow id="idp21661184"><mo id="idp21661312">(</mo><mrow id="idp21661568"><mi id="idp21661696">x</mi><mo id="idp21661952">,</mo><mi id="idp21662208">u</mi><mo id="idp21662464">,</mo><mrow id="idp21662720"><mo id="idp21662848">∇</mo><mo id="idp21663136">⁡</mo><mi id="idp21663424">u</mi></mrow></mrow><mo id="idp21663680">)</mo></mrow></mrow><mo id="idp21663936">⋅</mo><mrow id="idp21664224"><mo id="idp21664352">∇</mo><mo id="idp21664640">⁡</mo><mrow id="idp21664928"><mi id="idp21665056">u</mi><mo id="idp21665312">⁢</mo><mi id="idp21665600">d</mi><mo id="idp21665856">⁢</mo><mi id="idp21666144">x</mi></mrow></mrow></mrow></mrow><mo id="idp21666400">≥</mo><mrow id="idp21666688"><mstyle id="idp21666816" displaystyle="true"><msub id="idp21667216"><mo id="idp21667344">∫</mo><msub id="idp21667632"><mi id="idp21667760">A</mi><mi id="idp21668016">k</mi></msub></msub></mstyle><mrow id="idp21668272"><mrow id="idp21668400"><mo id="idp21668528">(</mo><mrow id="idp21668784"><mrow id="idp21668912"><msub id="idp21669040"><mi id="idp21669168">a</mi><mn id="idp21669424">3</mn></msub><mo id="idp21669680">⁢</mo><msup id="idp21669968"><mrow id="idp21670096"><mo id="idp21670224" fence="true">|</mo><mrow id="idp21670752"><mo id="idp21670880">∇</mo><mo id="idp21671168">⁡</mo><mi id="idp21671456">u</mi></mrow><mo id="idp21671712" fence="true">|</mo></mrow><mrow id="idp21672240"><mi id="idp21672368">p</mi><mo id="idp21672624">⁢</mo><mrow id="idp21672912"><mo id="idp21673040">(</mo><mi id="idp21673296">x</mi><mo id="idp21673552">)</mo></mrow></mrow></msup></mrow><mo id="idp21673808">-</mo><mrow id="idp21674064"><msub id="idp21674192"><mi id="idp21674320">a</mi><mn id="idp21674576">4</mn></msub><mo id="idp21674832">⁢</mo><msup id="idp21675120"><mrow id="idp21675248"><mo id="idp21675376" fence="true">|</mo><mi id="idp21675904">u</mi><mo id="idp21676160" fence="true">|</mo></mrow><mrow id="idp21676688"><msub id="idp21676816"><mi id="idp21676944">q</mi><mn id="idp21677200">0</mn></msub><mo id="idp21677456">⁢</mo><mrow id="idp21677744"><mo id="idp21677872">(</mo><mi id="idp21678128">x</mi><mo id="idp21678384">)</mo></mrow></mrow></msup></mrow><mo id="idp21678640">-</mo><msub id="idp21678896"><mi id="idp21679024">a</mi><mn id="idp21679280">5</mn></msub></mrow><mo id="idp21679536">)</mo></mrow><mo id="idp21679792">⁢</mo><mi id="idp21680080">d</mi><mo id="idp21680336">⁢</mo><mi id="idp21680624">x</mi></mrow></mrow><mo id="idp21680880">≥</mo><mrow id="idp21681168"><mrow id="idp21681296"><msub id="idp21681424"><mi id="idp21681552">a</mi><mn id="idp21681808">3</mn></msub><mo id="idp21682064">⁢</mo><mrow id="idp21682352"><mstyle id="idp21682480" displaystyle="true"><msub id="idp21682880"><mo 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id="S3.E2.m1.sh3ay.cmml">u</ci></apply><apply id="S3.E2.m1.sh3bg.cmml"><times id="S3.E2.m1.sh3ba.cmml"/><apply id="S3.E2.m1.sh3be.cmml"><csymbol cd="ambiguous" id="S3.E2.m1.sh3bb.cmml">subscript</csymbol><ci id="S3.E2.m1.sh3bc.cmml">q</ci><cn type="integer" id="S3.E2.m1.sh3bd.cmml">0</cn></apply><ci id="S3.E2.m1.sh3bf.cmml">x</ci></apply></apply><ci id="S3.E2.m1.sh3bi.cmml">d</ci><ci id="S3.E2.m1.sh3bj.cmml">x</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp21783792" encoding="application/x-tex">\displaystyle\begin{split}&\int _{{A_{k}}}\mathcal{A}(x,u,\nabla u)\cdot\nabla(u-k)dx\\ &=\int _{{A_{k}}}\mathcal{A}(x,u,\nabla u)\cdot\nabla udx\\ &\geq\int _{{A_{k}}}\left(a_{3}|\nabla u|^{{p(x)}}-a_{4}|u|^{{q_{0}(x)}}-a_{5}\right)dx\\ &\geq a_{3}\int _{{A_{k}}}|\nabla u|^{{p(x)}}dx-(a_{4}+a_{5})\int _{{A_{k}}}|u|^{{q_{0}(x)}}dx,\end{split}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp2190864"><h4>Hit idp2190864</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 25</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/15/f005696.xhtml#idp2190864</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:269680(000023%) VariableMap:[E, geq, ! x 2, dx x 2, int x 2, B, C, (, ), ., 2 x 2, u x 2, nabla x 2, \ x 10, _ x 4, ^ x 2, | x 4, bar, rho x 2, x] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp2190864" alttext="\int _{{B_{{\rho}}(\bar{x})}}\!|\nabla u|^{2}dx\geq C_{\rho}\int _{{E}}\!|\nabla u|^{2}dx." display="block"><semantics id="idp2191696"><mrow id="idp2191824"><mrow id="idp2191952"><mrow id="idp2192080"><msub id="idp2192208"><mo id="idp2192336">∫</mo><mrow id="idp2192592"><msub id="idp2192720"><mi id="idp2192848">B</mi><mi id="idp2193104">ρ</mi></msub><mo id="idp2193360">⁢</mo><mrow id="idp2193648"><mo id="idp2193776">(</mo><mover id="idp2194032" accent="true"><mi id="idp2194432">x</mi><mo id="idp2194688">¯</mo></mover><mo id="idp2194976">)</mo></mrow></mrow></msub><mrow id="idp2195232"><msup id="idp2195360"><mrow id="idp2195488"><mo id="idp2195616" fence="true">|</mo><mrow id="idp2196144"><mo id="idp2196272">∇</mo><mo id="idp2196560">⁡</mo><mi id="idp2196848">u</mi></mrow><mo id="idp2197104" fence="true">|</mo></mrow><mn id="idp2197632">2</mn></msup><mo id="idp2197888">⁢</mo><mi id="idp2198176">d</mi><mo id="idp2198432">⁢</mo><mi id="idp2198720">x</mi></mrow></mrow><mo id="idp2198976">≥</mo><mrow id="idp2199264"><msub id="idp2199392"><mi id="idp2199520">C</mi><mi 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id="idp2207696">B</ci><ci id="idp2207952">ρ</ci></apply><apply id="idp2208240"><ci id="idp2208368">¯</ci><ci id="idp2208656">x</ci></apply></apply></apply><apply id="idp2208912"><times id="idp2209040"/><apply id="idp2209168"><csymbol id="idp2209296" cd="ambiguous">superscript</csymbol><apply id="idp2209856"><abs id="idp2209984"/><apply id="idp2210112"><ci id="idp2210240">∇</ci><ci id="idp2210528">u</ci></apply></apply><cn id="idp2210784" type="integer">2</cn></apply><ci id="idp2211312">d</ci><ci id="idp2211568">x</ci></apply></apply><apply id="idp2211824"><times id="idp2211952"/><apply id="idp2212080"><csymbol id="idp2212208" cd="ambiguous">subscript</csymbol><ci id="idp2212768">C</ci><ci id="idp2213024">ρ</ci></apply><apply id="idp2213312"><apply id="idp2213440"><csymbol id="idp2213568" cd="ambiguous">subscript</csymbol><int id="idp2214128"/><ci id="idp2214256">E</ci></apply><apply id="idp2214512"><times id="idp2214640"/><apply id="idp2214768"><csymbol id="idp2214896" cd="ambiguous">superscript</csymbol><apply id="idp2215456"><abs id="idp2215584"/><apply id="idp2215712"><ci id="idp2215840">∇</ci><ci id="idp2216128">u</ci></apply></apply><cn id="idp2216384" type="integer">2</cn></apply><ci id="idp2216912">d</ci><ci id="idp2217168">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp2217424" encoding="application/x-tex">\int _{{B_{{\rho}}(\bar{x})}}\!|\nabla u|^{2}dx\geq C_{\rho}\int _{{E}}\!|\nabla u|^{2}dx.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp23618192"><h4>Hit idp23618192</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 26</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/113/f045003.xhtml#idp23618192</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:494167(000032%) VariableMap:[rm, mathbb, div, L x 5, , infty, W x 3, nabla x 4, R, \ x 49, _ x 12, left x 4, ^ x 12, right x 4, rho x 4, end, ds x 2, & x 2, leq x 2, int x 2, sqrt x 2, + x 2, ( x 6, ) x 6, ., ,, textrm x 2, begin, 3, 2, exp x 2, v x 4, t x 5, 0 x 4, mathcal x 2, q x 8, split x 2, | x 16] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp23618192" alttext="\begin{split}\|\nabla\rho(t)\|^{q}_{{L^{q}({\mathbb{R}}^{3})}}&\leq\left(\|\nabla\rho _{0}\|^{q}_{{L^{q}}}+\int _{0}^{t}\|\rho\| _{{L^{\infty}}}\|\nabla{\rm div}v\| _{{L^{q}}}ds\right)\textrm{exp}\left(\int _{0}^{t}\| v\| _{{W^{{2,q}}}}ds\right)\\ &\leq\left(\|\nabla\rho _{0}\|^{q}_{{L^{q}}}+\sqrt{t}\| v\| _{{\mathcal{W}}}\right)\textrm{exp}\left(\sqrt{t}\| v\| _{{\mathcal{W}}}\right).\end{split}" display="block"><semantics id="idp23617744"><mrow id="idp23617872"><mrow id="idp23618000"><msubsup id="idp23619328"><mrow id="idp23619456"><mo 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id="idp23627616">∇</mo><mo id="idp23627904">⁡</mo><msub id="idp23628192"><mi id="idp23628320">ρ</mi><mn id="idp23628608">0</mn></msub></mrow><mo id="idp23628864" fence="true">∥</mo></mrow><msup id="idp23629424"><mi id="idp23629552">L</mi><mi id="idp23629808">q</mi></msup><mi id="idp23630064">q</mi></msubsup><mo id="idp23630320">+</mo><mrow id="idp23630576"><msubsup id="idp23630704"><mo id="idp23630832">∫</mo><mn id="idp23631120">0</mn><mi id="idp23631376">t</mi></msubsup><mrow id="idp23631632"><msub id="idp23631760"><mrow id="idp23631888"><mo id="idp23632016" fence="true">∥</mo><mi id="idp23632576">ρ</mi><mo id="idp23632864" fence="true">∥</mo></mrow><msup id="idp23633424"><mi id="idp23633552">L</mi><mi id="idp23633808" mathvariant="normal">∞</mi></msup></msub><mo id="idp23634368">⁢</mo><msub id="idp23634656"><mrow id="idp23634784"><mo id="idp23634912" fence="true">∥</mo><mrow id="idp23635472"><mo id="idp23635600">∇</mo><mo id="idp23635888">⁡</mo><mrow id="idp23636176"><mi id="idp23636304">div</mi><mo id="idp23636560">⁢</mo><mi id="idp23636848">v</mi></mrow></mrow><mo id="idp23637104" fence="true">∥</mo></mrow><msup id="idp23637664"><mi id="idp23637792">L</mi><mi id="idp23638048">q</mi></msup></msub><mo id="idp23638304">⁢</mo><mi id="idp23638592">d</mi><mo id="idp23638848">⁢</mo><mi id="idp23639136">s</mi></mrow></mrow></mrow><mo id="idp23639392">)</mo></mrow><mo id="idp23639648">⁢</mo><mtext id="idp23639936">exp</mtext><mo id="idp23640192">⁢</mo><mrow id="idp23640480"><mo id="idp23640608">(</mo><mrow id="idp23640864"><msubsup id="idp23640992"><mo id="idp23641120">∫</mo><mn id="idp23641408">0</mn><mi id="idp23641664">t</mi></msubsup><mrow id="idp23641920"><msub id="idp23642048"><mrow id="idp23642176"><mo id="idp23642304" fence="true">∥</mo><mi id="idp23642864">v</mi><mo id="idp23643120" fence="true">∥</mo></mrow><msup id="idp23643680"><mi id="idp23643808">W</mi><mrow id="idp23644064"><mn id="idp23644192">2</mn><mo id="idp23644448">,</mo><mi 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id="S3.E4.m1.sh2ai.cmml"/><ci id="S3.E4.m1.sh2ag.cmml">t</ci></apply><apply id="S3.E4.m1.sh2ao.cmml"><csymbol cd="ambiguous" id="S3.E4.m1.sh2aj.cmml">subscript</csymbol><apply id="S3.E4.m1.sh2am.cmml"><csymbol cd="latexml" id="S3.E4.m1.sh2ak.cmml">norm</csymbol><ci id="S3.E4.m1.sh2al.cmml">v</ci></apply><ci id="S3.E4.m1.sh2an.cmml">W</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp23735216" encoding="application/x-tex">\begin{split}\|\nabla\rho(t)\|^{q}_{{L^{q}({\mathbb{R}}^{3})}}&\leq\left(\|\nabla\rho _{0}\|^{q}_{{L^{q}}}+\int _{0}^{t}\|\rho\| _{{L^{\infty}}}\|\nabla{\rm div}v\| _{{L^{q}}}ds\right)\textrm{exp}\left(\int _{0}^{t}\| v\| _{{W^{{2,q}}}}ds\right)\\ &\leq\left(\|\nabla\rho _{0}\|^{q}_{{L^{q}}}+\sqrt{t}\| v\| _{{\mathcal{W}}}\right)\textrm{exp}\left(\sqrt{t}\| v\| _{{\mathcal{W}}}\right).\end{split}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp24425744"><h4>Hit idp24425744</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 27</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/130/f051684.xhtml#idp24425744</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:629691(000060%) VariableMap:[M x 2, nabla x 2, \ x 20, left x 6, _ x 2, ^ x 8, right x 6, phi x 2, Rc, f x 2, c, leq, int x 2, a x 2, + x 2, Rm x 3, ( x 2, ) x 2, - x 4, 3, 2 x 2, 1 x 3, displaystyle, q x 2, p x 2, | x 8] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp24425744" alttext="\displaystyle\int _{M}\left|\nabla Rc\right|^{2}\left|Rm\right|^{{p-1}}\left(f+1\right)^{{-a}}\phi^{q}\leq c\int _{M}\left|\nabla Rm\right|^{2}\left|Rm\right|^{{p-3}}\left(f+1\right)^{{-a}}\phi^{q}" 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id="idp24434560">1</mn></mrow></msup><mo id="idp24434816">⁢</mo><msup id="idp24435104"><mrow id="idp24435232"><mo id="idp24435360">(</mo><mrow id="idp24435616"><mi id="idp24435744">f</mi><mo id="idp24436000">+</mo><mn id="idp24436256">1</mn></mrow><mo id="idp24436512">)</mo></mrow><mrow id="idp24436768"><mo id="idp24436896">-</mo><mi id="idp24437152">a</mi></mrow></msup><mo id="idp24437408">⁢</mo><msup id="idp24437696"><mi id="idp24437824">ϕ</mi><mi id="idp24438112">q</mi></msup></mrow></mrow><mo id="idp24438368">≤</mo><mrow id="idp24438656"><mi id="idp24438784">c</mi><mo id="idp24439040">⁢</mo><mrow id="idp24439328"><mstyle id="idp24439456" displaystyle="true"><msub id="idp24439856"><mo id="idp24439984">∫</mo><mi id="idp24440272">M</mi></msub></mstyle><mrow id="idp24440528"><msup id="idp24440656"><mrow id="idp24440784"><mo id="idp24440912" fence="true">|</mo><mrow id="idp24441440"><mo id="idp24441568">∇</mo><mo id="idp24441856">⁡</mo><mrow id="idp24442144"><mi id="idp24442272">R</mi><mo id="idp24442528">⁢</mo><mi id="idp24442816">m</mi></mrow></mrow><mo id="idp24443072" fence="true">|</mo></mrow><mn id="idp24443600">2</mn></msup><mo id="idp24443856">⁢</mo><msup id="idp24444144"><mrow id="idp24444272"><mo id="idp24444400" fence="true">|</mo><mrow id="idp24444928"><mi id="idp24445056">R</mi><mo id="idp24445312">⁢</mo><mi id="idp24445600">m</mi></mrow><mo id="idp24445856" fence="true">|</mo></mrow><mrow id="idp24446384"><mi id="idp24446512">p</mi><mo id="idp24446768">-</mo><mn id="idp24447024">3</mn></mrow></msup><mo id="idp24447280">⁢</mo><msup id="idp24447568"><mrow id="idp24447696"><mo id="idp24447824">(</mo><mrow id="idp24448080"><mi id="idp24448208">f</mi><mo id="idp24448464">+</mo><mn id="idp24448720">1</mn></mrow><mo id="idp24448976">)</mo></mrow><mrow id="idp24449232"><mo id="idp24449360">-</mo><mi id="idp24449616">a</mi></mrow></msup><mo id="idp24449872">⁢</mo><msup id="idp24450160"><mi id="idp24450288">ϕ</mi><mi id="idp24450576">q</mi></msup></mrow></mrow></mrow></mrow><annotation-xml id="idp24450832" encoding="MathML-Content"><apply id="idp24451232"><leq id="idp24451360"/><apply id="idp24451488"><apply id="idp24451616"><csymbol id="idp24451744" cd="ambiguous">subscript</csymbol><int id="idp24452304"/><ci id="idp24452432">M</ci></apply><apply id="idp24452688"><times id="idp24452816"/><apply id="idp24452944"><csymbol id="idp24453072" cd="ambiguous">superscript</csymbol><apply id="idp24453632"><abs id="idp24453760"/><apply id="idp24453888"><ci id="idp24454016">∇</ci><apply id="idp24454304"><times id="idp24454432"/><ci id="idp24454560">R</ci><ci id="idp24454816">c</ci></apply></apply></apply><cn id="idp24455072" type="integer">2</cn></apply><apply id="idp24455600"><csymbol id="idp24455728" cd="ambiguous">superscript</csymbol><apply id="idp24456288"><abs id="idp24456416"/><apply id="idp24456544"><times id="idp24456672"/><ci id="idp24456800">R</ci><ci id="idp24457056">m</ci></apply></apply><apply id="idp24457312"><minus id="idp24457440"/><ci id="idp24457568">p</ci><cn id="idp24457824" type="integer">1</cn></apply></apply><apply id="idp24458352"><csymbol id="idp24458480" cd="ambiguous">superscript</csymbol><apply id="idp24459040"><plus id="idp24459168"/><ci id="idp24459296">f</ci><cn id="idp24459552" type="integer">1</cn></apply><apply id="idp24460080"><minus id="idp24460208"/><ci id="idp24460336">a</ci></apply></apply><apply id="idp24460592"><csymbol id="idp24460720" cd="ambiguous">superscript</csymbol><ci id="idp24461280">ϕ</ci><ci id="idp24461568">q</ci></apply></apply></apply><apply id="idp24461824"><times id="idp24461952"/><ci id="idp24462080">c</ci><apply id="idp24462336"><apply id="idp24462464"><csymbol id="idp24462592" cd="ambiguous">subscript</csymbol><int id="idp24463152"/><ci id="idp24463280">M</ci></apply><apply id="idp24463536"><times id="idp24463664"/><apply id="idp24463792"><csymbol id="idp24463920" cd="ambiguous">superscript</csymbol><apply id="idp24464480"><abs id="idp24464608"/><apply id="idp24464736"><ci id="idp24464864">∇</ci><apply id="idp24465152"><times id="idp24465280"/><ci id="idp24465408">R</ci><ci id="idp24465664">m</ci></apply></apply></apply><cn id="idp24465920" type="integer">2</cn></apply><apply id="idp24466448"><csymbol id="idp24466576" cd="ambiguous">superscript</csymbol><apply id="idp24467136"><abs id="idp24467264"/><apply id="idp24467392"><times id="idp24467520"/><ci id="idp24467648">R</ci><ci id="idp24467904">m</ci></apply></apply><apply id="idp24468160"><minus id="idp24468288"/><ci id="idp24468416">p</ci><cn id="idp24468672" type="integer">3</cn></apply></apply><apply id="idp24469200"><csymbol id="idp24469328" cd="ambiguous">superscript</csymbol><apply id="idp24469888"><plus id="idp24470016"/><ci id="idp24470144">f</ci><cn id="idp24470400" type="integer">1</cn></apply><apply id="idp24470928"><minus id="idp24471056"/><ci id="idp24471184">a</ci></apply></apply><apply id="idp24471440"><csymbol id="idp24471568" cd="ambiguous">superscript</csymbol><ci id="idp24472128">ϕ</ci><ci id="idp24472416">q</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp24472672" encoding="application/x-tex">\displaystyle\int _{M}\left|\nabla Rc\right|^{2}\left|Rm\right|^{{p-1}}\left(f+1\right)^{{-a}}\phi^{q}\leq c\int _{M}\left|\nabla Rm\right|^{2}\left|Rm\right|^{{p-3}}\left(f+1\right)^{{-a}}\phi^{q}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp24527840"><h4>Hit idp24527840</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 28</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/205/f081718.xhtml#idp24527840</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:639576(000076%) VariableMap:[neq x 2, beta x 3, lambda x 2, psi x 8, nabla x 2, \ x 32, _ x 12, ^ x 5, limits x 2, g x 2, d, ! x 7, int x 2, +, mathrm x 2, (, cdot, ), ,, i x 8, - x 3, 3, 2 x 5, v x 2, 1, 0 x 2, displaystyle, | x 12, >, <] Expects 2 occurences for 'd' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp24527840" alttext="\displaystyle\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-2}}|\nabla^{\lambda}\psi _{i}|^{2}\mathrm{v}_{g}+\! 2(\beta-1)\!\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-3}}\!<d|\psi _{i}|\!\cdot\!\psi _{i},\nabla^{\lambda}\psi _{i}\!>\!\mathrm{v}_{g}" display="inline"><semantics id="idp24527392"><mrow id="idp24527520"><mrow id="idp24527648"><mrow id="idp24528848"><mrow id="idp24528976"><mstyle id="idp24529104" displaystyle="true"><munder id="idp24529472"><mo id="idp24529600" movablelimits="false">∫</mo><mrow id="idp24530096"><mrow id="idp24530224"><mo id="idp24530352" fence="true">|</mo><msub id="idp24530848"><mi id="idp24530976">ψ</mi><mi id="idp24531264">i</mi></msub><mo id="idp24531520" fence="true">|</mo></mrow><mo id="idp24532048">≠</mo><mn id="idp24532336">0</mn></mrow></munder></mstyle><mrow id="idp24532592"><msup id="idp24532720"><mrow id="idp24532848"><mo id="idp24532976" fence="true">|</mo><msub id="idp24533504"><mi id="idp24533632">ψ</mi><mi id="idp24533920">i</mi></msub><mo id="idp24534176" fence="true">|</mo></mrow><mrow id="idp24534704"><mrow id="idp24534832"><mn id="idp24534960">2</mn><mo id="idp24535216">⁢</mo><mi id="idp24535504">β</mi></mrow><mo id="idp24535792">-</mo><mn id="idp24536048">2</mn></mrow></msup><mo id="idp24536304">⁢</mo><msup id="idp24536592"><mrow id="idp24536720"><mo id="idp24536848" fence="true">|</mo><mrow id="idp24537376"><msup id="idp24537504"><mo id="idp24537632">∇</mo><mi id="idp24537920">λ</mi></msup><mo id="idp24538208">⁡</mo><msub id="idp24538496"><mi id="idp24538624">ψ</mi><mi id="idp24538912">i</mi></msub></mrow><mo id="idp24539168" fence="true">|</mo></mrow><mn id="idp24539696">2</mn></msup><mo id="idp24539952">⁢</mo><msub id="idp24540240"><mi id="idp24540368" mathvariant="normal">v</mi><mi id="idp24540896">g</mi></msub></mrow></mrow><mo id="idp24541152" rspace="-1.666667pt">+</mo><mrow id="idp24541680"><mn id="idp24541808">2</mn><mo id="idp24542064">⁢</mo><mrow id="idp24542352"><mo id="idp24542480">(</mo><mrow id="idp24542736"><mi id="idp24542864">β</mi><mo id="idp24543152">-</mo><mn id="idp24543408">1</mn></mrow><mo id="idp24543664">)</mo></mrow><mo id="idp24543920">⁢</mo><mrow id="idp24544208"><mstyle id="idp24544336" displaystyle="true"><munder id="idp24544736"><mo id="idp24544864" movablelimits="false">∫</mo><mrow id="idp24545424"><mrow id="idp24545552"><mo id="idp24545680" fence="true">|</mo><msub id="idp24546208"><mi id="idp24546336">ψ</mi><mi id="idp24546624">i</mi></msub><mo id="idp24546880" fence="true">|</mo></mrow><mo id="idp24547408">≠</mo><mn id="idp24547696">0</mn></mrow></munder></mstyle><msup id="idp24547952"><mrow id="idp24548080"><mo id="idp24548208" fence="true">|</mo><msub id="idp24548736"><mi id="idp24548864">ψ</mi><mi id="idp24549152">i</mi></msub><mo id="idp24549408" fence="true">|</mo></mrow><mrow id="idp24549936"><mrow id="idp24550064"><mn id="idp24550192">2</mn><mo id="idp24550448">⁢</mo><mi id="idp24550736">β</mi></mrow><mo id="idp24551024">-</mo><mn id="idp24551280">3</mn></mrow></msup></mrow></mrow></mrow><mo id="idp24551536"><</mo><mrow id="idp24551824"><mrow id="idp24551952"><mi id="idp24552080">d</mi><mo id="idp24552336">⁢</mo><mrow id="idp24552624"><mo id="idp24552752" fence="true">|</mo><msub id="idp24553280"><mi id="idp24553408">ψ</mi><mi id="idp24553696">i</mi></msub><mo id="idp24553952" fence="true">|</mo></mrow></mrow><mo id="idp24554480" rspace="-1.666667pt">⋅</mo><msub id="idp24555040"><mi id="idp24555168">ψ</mi><mi id="idp24555456">i</mi></msub></mrow></mrow><mo id="idp24555712">,</mo><mrow id="idp24555968"><mrow id="idp24556096"><msup id="idp24556224"><mo id="idp24556352">∇</mo><mi id="idp24556640">λ</mi></msup><mo id="idp24556928">⁡</mo><msub id="idp24557216"><mi id="idp24557344">ψ</mi><mi id="idp24557632">i</mi></msub></mrow><mo id="idp24557888" rspace="-1.666667pt">></mo><msub id="idp24558448"><mi id="idp24558576" mathvariant="normal">v</mi><mi id="idp24559104">g</mi></msub></mrow></mrow><annotation-xml id="idp24559360" encoding="MathML-Content"><apply id="idp24559760"><csymbol id="idp24559888" cd="ambiguous" name="formulae-sequence"/><apply id="idp24560560"><lt id="idp24560688"/><apply id="idp24560816"><plus id="idp24560944"/><apply id="idp24561072"><apply id="idp24561200"><csymbol id="idp24561328" cd="ambiguous">subscript</csymbol><int id="idp24561888"/><apply id="idp24562016"><neq id="idp24562144"/><apply id="idp24562272"><abs id="idp24562400"/><apply id="idp24562528"><csymbol id="idp24562656" cd="ambiguous">subscript</csymbol><ci id="idp24563216">ψ</ci><ci id="idp24563504">i</ci></apply></apply><cn id="idp24563760" type="integer">0</cn></apply></apply><apply id="idp24564288"><times id="idp24564416"/><apply id="idp24564544"><csymbol id="idp24564672" cd="ambiguous">superscript</csymbol><apply id="idp24565232"><abs id="idp24565360"/><apply id="idp24565488"><csymbol id="idp24565616" cd="ambiguous">subscript</csymbol><ci id="idp24566176">ψ</ci><ci id="idp24566464">i</ci></apply></apply><apply id="idp24566720"><minus id="idp24566848"/><apply id="idp24566976"><times id="idp24567104"/><cn id="idp24567232" type="integer">2</cn><ci id="idp24567760">β</ci></apply><cn id="idp24568048" type="integer">2</cn></apply></apply><apply id="idp24568576"><csymbol id="idp24568704" cd="ambiguous">superscript</csymbol><apply id="idp24569264"><abs id="idp24569392"/><apply id="idp24569520"><apply id="idp24569648"><csymbol id="idp24569776" cd="ambiguous">superscript</csymbol><ci id="idp24570336">∇</ci><ci id="idp24570624">λ</ci></apply><apply id="idp24570912"><csymbol id="idp24571040" cd="ambiguous">subscript</csymbol><ci id="idp24571600">ψ</ci><ci id="idp24571888">i</ci></apply></apply></apply><cn id="idp24572144" type="integer">2</cn></apply><apply id="idp24572672"><csymbol id="idp24572800" cd="ambiguous">subscript</csymbol><ci id="idp24573360">v</ci><ci id="idp24573616">g</ci></apply></apply></apply><apply id="idp24573872"><times id="idp24574000"/><cn id="idp24574128" type="integer">2</cn><apply id="idp24574656"><minus id="idp24574784"/><ci id="idp24574912">β</ci><cn id="idp24575200" type="integer">1</cn></apply><apply id="idp24575728"><apply id="idp24575856"><csymbol id="idp24575984" cd="ambiguous">subscript</csymbol><int id="idp24576544"/><apply id="idp24576672"><neq id="idp24576800"/><apply id="idp24576928"><abs id="idp24577056"/><apply id="idp24577184"><csymbol id="idp24577312" cd="ambiguous">subscript</csymbol><ci id="idp24577872">ψ</ci><ci id="idp24578160">i</ci></apply></apply><cn id="idp24578416" type="integer">0</cn></apply></apply><apply id="idp24578944"><csymbol id="idp24579072" cd="ambiguous">superscript</csymbol><apply id="idp24579632"><abs id="idp24579760"/><apply id="idp24579888"><csymbol id="idp24580016" cd="ambiguous">subscript</csymbol><ci id="idp24580576">ψ</ci><ci id="idp24580864">i</ci></apply></apply><apply id="idp24581120"><minus id="idp24581248"/><apply id="idp24581376"><times id="idp24581504"/><cn id="idp24581632" type="integer">2</cn><ci id="idp24582160">β</ci></apply><cn id="idp24582448" type="integer">3</cn></apply></apply></apply></apply></apply><apply id="idp24582976"><ci id="idp24583104">⋅</ci><apply id="idp24583392"><times id="idp24583520"/><ci id="idp24583648">d</ci><apply id="idp24583904"><abs id="idp24584032"/><apply id="idp24584160"><csymbol id="idp24584288" cd="ambiguous">subscript</csymbol><ci id="idp24584848">ψ</ci><ci id="idp24585136">i</ci></apply></apply></apply><apply id="idp24585392"><csymbol id="idp24585520" cd="ambiguous">subscript</csymbol><ci id="idp24586080">ψ</ci><ci id="idp24586368">i</ci></apply></apply></apply><apply id="idp24586624"><gt id="idp24586752"/><apply id="idp24586880"><apply id="idp24587008"><csymbol id="idp24587136" cd="ambiguous">superscript</csymbol><ci id="idp24587696">∇</ci><ci id="idp24587984">λ</ci></apply><apply id="idp24588272"><csymbol id="idp24588400" cd="ambiguous">subscript</csymbol><ci id="idp24588960">ψ</ci><ci id="idp24589248">i</ci></apply></apply><apply id="idp24589504"><csymbol id="idp24589632" cd="ambiguous">subscript</csymbol><ci id="idp24590192">v</ci><ci id="idp24590448">g</ci></apply></apply></apply></annotation-xml><annotation id="idp24590704" encoding="application/x-tex">\displaystyle\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-2}}|\nabla^{\lambda}\psi _{i}|^{2}\mathrm{v}_{g}+\! 2(\beta-1)\!\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-3}}\!<d|\psi _{i}|\!\cdot\!\psi _{i},\nabla^{\lambda}\psi _{i}\!>\!\mathrm{v}_{g}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp24672480"><h4>Hit idp24672480</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 29</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/205/f081718.xhtml#idp24672480</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:658364(000079%) VariableMap:[neq x 2, beta x 3, lambda x 2, psi x 8, nabla x 2, \ x 32, _ x 12, ^ x 5, limits x 2, g x 2, d, ! x 7, int x 2, +, mathrm x 2, (, cdot, ), ,, i x 8, - x 3, 3, 2 x 5, v x 2, 1, 0 x 2, displaystyle, | x 12, >, <] Expects 2 occurences for 'd' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp24672480" alttext="\displaystyle\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-2}}|\nabla^{\lambda}\psi _{i}|^{2}\mathrm{v}_{g}+\! 2(\beta-1)\!\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-3}}\!<d|\psi _{i}|\!\cdot\!\psi _{i},\nabla^{\lambda}\psi _{i}\!>\!\mathrm{v}_{g}" display="inline"><semantics id="idp24672032"><mrow id="idp24672160"><mrow id="idp24672288"><mrow id="idp24673488"><mrow id="idp24673616"><mstyle id="idp24673744" displaystyle="true"><munder id="idp24674112"><mo id="idp24674240" movablelimits="false">∫</mo><mrow id="idp24674736"><mrow id="idp24674864"><mo id="idp24674992" fence="true">|</mo><msub id="idp24675488"><mi id="idp24675616">ψ</mi><mi id="idp24675904">i</mi></msub><mo id="idp24676160" fence="true">|</mo></mrow><mo id="idp24676688">≠</mo><mn id="idp24676976">0</mn></mrow></munder></mstyle><mrow id="idp24677232"><msup id="idp24677360"><mrow id="idp24677488"><mo id="idp24677616" fence="true">|</mo><msub id="idp24678144"><mi id="idp24678272">ψ</mi><mi id="idp24678560">i</mi></msub><mo id="idp24678816" fence="true">|</mo></mrow><mrow id="idp24679344"><mrow id="idp24679472"><mn id="idp24679600">2</mn><mo id="idp24679856">⁢</mo><mi id="idp24680144">β</mi></mrow><mo id="idp24680432">-</mo><mn id="idp24680688">2</mn></mrow></msup><mo id="idp24680944">⁢</mo><msup id="idp24681232"><mrow id="idp24681360"><mo id="idp24681488" fence="true">|</mo><mrow id="idp24682016"><msup id="idp24682144"><mo id="idp24682272">∇</mo><mi id="idp24682560">λ</mi></msup><mo id="idp24682848">⁡</mo><msub id="idp24683136"><mi id="idp24683264">ψ</mi><mi id="idp24683552">i</mi></msub></mrow><mo id="idp24683808" fence="true">|</mo></mrow><mn id="idp24684336">2</mn></msup><mo id="idp24684592">⁢</mo><msub id="idp24684880"><mi id="idp24685008" mathvariant="normal">v</mi><mi id="idp24685536">g</mi></msub></mrow></mrow><mo id="idp24685792" rspace="-1.666667pt">+</mo><mrow id="idp24686320"><mn id="idp24686448">2</mn><mo id="idp24686704">⁢</mo><mrow id="idp24686992"><mo id="idp24687120">(</mo><mrow id="idp24687376"><mi id="idp24687504">β</mi><mo id="idp24687792">-</mo><mn id="idp24688048">1</mn></mrow><mo id="idp24688304">)</mo></mrow><mo id="idp24688560">⁢</mo><mrow id="idp24688848"><mstyle id="idp24688976" displaystyle="true"><munder id="idp24689376"><mo id="idp24689504" movablelimits="false">∫</mo><mrow id="idp24690064"><mrow id="idp24690192"><mo id="idp24690320" fence="true">|</mo><msub id="idp24690848"><mi id="idp24690976">ψ</mi><mi id="idp24691264">i</mi></msub><mo id="idp24691520" fence="true">|</mo></mrow><mo id="idp24692048">≠</mo><mn id="idp24692336">0</mn></mrow></munder></mstyle><msup id="idp24692592"><mrow id="idp24692720"><mo id="idp24692848" fence="true">|</mo><msub id="idp24693376"><mi id="idp24693504">ψ</mi><mi id="idp24693792">i</mi></msub><mo id="idp24694048" fence="true">|</mo></mrow><mrow id="idp24694576"><mrow id="idp24694704"><mn id="idp24694832">2</mn><mo id="idp24695088">⁢</mo><mi id="idp24695376">β</mi></mrow><mo id="idp24695664">-</mo><mn id="idp24695920">3</mn></mrow></msup></mrow></mrow></mrow><mo id="idp24696176"><</mo><mrow id="idp24696464"><mrow id="idp24696592"><mi id="idp24696720">d</mi><mo id="idp24696976">⁢</mo><mrow id="idp24697264"><mo id="idp24697392" fence="true">|</mo><msub id="idp24697920"><mi id="idp24698048">ψ</mi><mi id="idp24698336">i</mi></msub><mo id="idp24698592" fence="true">|</mo></mrow></mrow><mo id="idp24699120" rspace="-1.666667pt">⋅</mo><msub id="idp24699680"><mi id="idp24699808">ψ</mi><mi id="idp24700096">i</mi></msub></mrow></mrow><mo id="idp24700352">,</mo><mrow id="idp24700608"><mrow id="idp24700736"><msup id="idp24700864"><mo id="idp24700992">∇</mo><mi id="idp24701280">λ</mi></msup><mo id="idp24701568">⁡</mo><msub id="idp24701856"><mi id="idp24701984">ψ</mi><mi id="idp24702272">i</mi></msub></mrow><mo id="idp24702528" rspace="-1.666667pt">></mo><msub id="idp24703088"><mi id="idp24703216" mathvariant="normal">v</mi><mi id="idp24703744">g</mi></msub></mrow></mrow><annotation-xml id="idp24704000" encoding="MathML-Content"><apply id="idp24704400"><csymbol id="idp24704528" cd="ambiguous" name="formulae-sequence"/><apply id="idp24705200"><lt id="idp24705328"/><apply id="idp24705456"><plus id="idp24705584"/><apply id="idp24705712"><apply id="idp24705840"><csymbol id="idp24705968" cd="ambiguous">subscript</csymbol><int id="idp24706528"/><apply id="idp24706656"><neq id="idp24706784"/><apply id="idp24706912"><abs id="idp24707040"/><apply id="idp24707168"><csymbol id="idp24707296" cd="ambiguous">subscript</csymbol><ci id="idp24707856">ψ</ci><ci id="idp24708144">i</ci></apply></apply><cn id="idp24708400" type="integer">0</cn></apply></apply><apply id="idp24708928"><times id="idp24709056"/><apply id="idp24709184"><csymbol id="idp24709312" cd="ambiguous">superscript</csymbol><apply id="idp24709872"><abs id="idp24710000"/><apply id="idp24710128"><csymbol id="idp24710256" cd="ambiguous">subscript</csymbol><ci id="idp24710816">ψ</ci><ci id="idp24711104">i</ci></apply></apply><apply id="idp24711360"><minus id="idp24711488"/><apply id="idp24711616"><times id="idp24711744"/><cn id="idp24711872" type="integer">2</cn><ci id="idp24712400">β</ci></apply><cn id="idp24712688" type="integer">2</cn></apply></apply><apply id="idp24713216"><csymbol id="idp24713344" cd="ambiguous">superscript</csymbol><apply id="idp24713904"><abs id="idp24714032"/><apply id="idp24714160"><apply id="idp24714288"><csymbol id="idp24714416" cd="ambiguous">superscript</csymbol><ci id="idp24714976">∇</ci><ci id="idp24715264">λ</ci></apply><apply id="idp24715552"><csymbol id="idp24715680" cd="ambiguous">subscript</csymbol><ci id="idp24716240">ψ</ci><ci id="idp24716528">i</ci></apply></apply></apply><cn id="idp24716784" type="integer">2</cn></apply><apply id="idp24717312"><csymbol id="idp24717440" cd="ambiguous">subscript</csymbol><ci id="idp24718000">v</ci><ci id="idp24718256">g</ci></apply></apply></apply><apply id="idp24718512"><times id="idp24718640"/><cn id="idp24718768" type="integer">2</cn><apply id="idp24719296"><minus id="idp24719424"/><ci id="idp24719552">β</ci><cn id="idp24719840" type="integer">1</cn></apply><apply id="idp24720368"><apply id="idp24720496"><csymbol id="idp24720624" cd="ambiguous">subscript</csymbol><int id="idp24721184"/><apply id="idp24721312"><neq id="idp24721440"/><apply id="idp24721568"><abs id="idp24721696"/><apply id="idp24721824"><csymbol id="idp24721952" cd="ambiguous">subscript</csymbol><ci id="idp24722512">ψ</ci><ci id="idp24722800">i</ci></apply></apply><cn id="idp24723056" type="integer">0</cn></apply></apply><apply id="idp24723584"><csymbol id="idp24723712" cd="ambiguous">superscript</csymbol><apply id="idp24724272"><abs id="idp24724400"/><apply id="idp24724528"><csymbol id="idp24724656" cd="ambiguous">subscript</csymbol><ci id="idp24725216">ψ</ci><ci id="idp24725504">i</ci></apply></apply><apply id="idp24725760"><minus id="idp24725888"/><apply id="idp24726016"><times id="idp24726144"/><cn id="idp24726272" type="integer">2</cn><ci id="idp24726800">β</ci></apply><cn id="idp24727088" type="integer">3</cn></apply></apply></apply></apply></apply><apply id="idp24727616"><ci id="idp24727744">⋅</ci><apply id="idp24728032"><times id="idp24728160"/><ci id="idp24728288">d</ci><apply id="idp24728544"><abs id="idp24728672"/><apply id="idp24728800"><csymbol id="idp24728928" cd="ambiguous">subscript</csymbol><ci id="idp24729488">ψ</ci><ci id="idp24729776">i</ci></apply></apply></apply><apply id="idp24730032"><csymbol id="idp24730160" cd="ambiguous">subscript</csymbol><ci id="idp24730720">ψ</ci><ci id="idp24731008">i</ci></apply></apply></apply><apply id="idp24731264"><gt id="idp24731392"/><apply id="idp24731520"><apply id="idp24731648"><csymbol id="idp24731776" cd="ambiguous">superscript</csymbol><ci id="idp24732336">∇</ci><ci id="idp24732624">λ</ci></apply><apply id="idp24732912"><csymbol id="idp24733040" cd="ambiguous">subscript</csymbol><ci id="idp24733600">ψ</ci><ci id="idp24733888">i</ci></apply></apply><apply id="idp24734144"><csymbol id="idp24734272" cd="ambiguous">subscript</csymbol><ci id="idp24734832">v</ci><ci id="idp24735088">g</ci></apply></apply></apply></annotation-xml><annotation id="idp24735344" encoding="application/x-tex">\displaystyle\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-2}}|\nabla^{\lambda}\psi _{i}|^{2}\mathrm{v}_{g}+\! 2(\beta-1)\!\int\limits _{{|\psi _{i}|\neq 0}}|\psi _{i}|^{{2\beta-3}}\!<d|\psi _{i}|\!\cdot\!\psi _{i},\nabla^{\lambda}\psi _{i}\!>\!\mathrm{v}_{g}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp24959520"><h4>Hit idp24959520</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 30</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/15/f005875.xhtml#idp24959520</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:699264(000036%) VariableMap:[dt, dx x 2, B, C, iint, varepsilon x 2, mbox, lvert x 2, Q, nabla, \ x 21, left, _ x 8, ^ x 4, right, rho x 2, f, int, + x 2, rvert x 2, ( x 3, ) x 3, , x 4, frac, 2 x 8, u, t, 0 x 2, displaystyle, zeta x 2, x x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp24959520" alttext="\displaystyle\mbox{}+\frac{C}{\varepsilon _{{2}}}\iint _{{Q_{{2\rho}}}}\lvert f\rvert^{{2}}\zeta^{{2}}\, dx\, dt+\varepsilon _{{2}}\int _{{B_{{2\rho}}(x_{{0}})}}\left(\lvert\nabla u\rvert^{{2}}\zeta^{{2}}\right)(x,t_{{0}})\, dx" display="inline"><semantics id="idp24960480"><mrow id="idp24960608"><mrow id="idp24960736"/><mo id="idp24960864">+</mo><mrow id="idp24961120"><mstyle id="idp24961248" displaystyle="true"><mfrac id="idp24961616"><mi id="idp24961744">C</mi><msub id="idp24962000"><mi id="idp24962128">ε</mi><mn id="idp24962384">2</mn></msub></mfrac></mstyle><mo id="idp24962640">⁢</mo><mrow id="idp24962928"><mstyle id="idp24963056" displaystyle="true"><msub id="idp24963456"><mo id="idp24963584">∬</mo><msub id="idp24963872"><mi id="idp24964000">Q</mi><mrow id="idp24964256"><mn id="idp24964384">2</mn><mo id="idp24964640">⁢</mo><mi id="idp24964928">ρ</mi></mrow></msub></msub></mstyle><mrow id="idp24965216"><msup id="idp24965344"><mrow id="idp24965472"><mo id="idp24965600" fence="true">|</mo><mi id="idp24966128">f</mi><mo id="idp24966384" fence="true">|</mo></mrow><mn id="idp24966912">2</mn></msup><mo id="idp24967168">⁢</mo><msup id="idp24967456"><mi id="idp24967584">ζ</mi><mn id="idp24967872">2</mn></msup><mo id="idp24968128">⁢</mo><mi id="idp24968416">d</mi><mo id="idp24968672">⁢</mo><mpadded id="idp24968960" width="+1.666667pt"><mi id="idp24969360">x</mi></mpadded><mo id="idp24969616">⁢</mo><mi id="idp24969904">d</mi><mo id="idp24970160">⁢</mo><mi id="idp24970448">t</mi></mrow></mrow></mrow><mo id="idp24970704">+</mo><mrow id="idp24970960"><msub id="idp24971088"><mi id="idp24971216">ε</mi><mn id="idp24971504">2</mn></msub><mo id="idp24971760">⁢</mo><mrow id="idp24972048"><mstyle id="idp24972176" displaystyle="true"><msub id="idp24972576"><mo id="idp24972704">∫</mo><mrow id="idp24972992"><msub id="idp24973120"><mi id="idp24973248">B</mi><mrow id="idp24973504"><mn id="idp24973632">2</mn><mo id="idp24973888">⁢</mo><mi id="idp24974176">ρ</mi></mrow></msub><mo id="idp24974464">⁢</mo><mrow id="idp24974752"><mo id="idp24974880">(</mo><msub id="idp24975136"><mi id="idp24975264">x</mi><mn id="idp24975520">0</mn></msub><mo id="idp24975776">)</mo></mrow></mrow></msub></mstyle><mrow id="idp24976032"><mrow id="idp24976160"><mo id="idp24976288">(</mo><mrow id="idp24976544"><msup id="idp24976672"><mrow id="idp24976800"><mo id="idp24976928" fence="true">|</mo><mrow id="idp24977456"><mo id="idp24977584">∇</mo><mo id="idp24977872">⁡</mo><mi id="idp24978160">u</mi></mrow><mo id="idp24978416" fence="true">|</mo></mrow><mn id="idp24978944">2</mn></msup><mo id="idp24979200">⁢</mo><msup id="idp24979488"><mi id="idp24979616">ζ</mi><mn id="idp24979904">2</mn></msup></mrow><mo id="idp24980160">)</mo></mrow><mo id="idp24980416">⁢</mo><mrow id="idp24980704"><mo id="idp24980832">(</mo><mrow id="idp24981088"><mi id="idp24981216">x</mi><mo id="idp24981472">,</mo><msub id="idp24981728"><mi id="idp24981856">t</mi><mn id="idp24982112">0</mn></msub></mrow><mo id="idp24982368">)</mo></mrow><mo id="idp24982624">⁢</mo><mi id="idp24982912">d</mi><mo id="idp24983168">⁢</mo><mi id="idp24983456">x</mi></mrow></mrow></mrow></mrow><annotation-xml id="idp24983712" encoding="MathML-Content"><apply id="idp24984112"><plus id="idp24984240"/><mtext id="idp24984368"/><apply id="idp24984496"><times id="idp24984624"/><apply id="idp24984752"><divide id="idp24984880"/><ci id="idp24985008">C</ci><apply id="idp24985264"><csymbol id="idp24985392" cd="ambiguous">subscript</csymbol><ci id="idp24985952">ε</ci><cn id="idp24986240" type="integer">2</cn></apply></apply><apply id="idp24986768"><apply id="idp24986896"><csymbol id="idp24987024" cd="ambiguous">subscript</csymbol><csymbol id="idp24987584" cd="latexml">double-integral</csymbol><apply id="idp24988144"><csymbol id="idp24988272" cd="ambiguous">subscript</csymbol><ci id="idp24988832">Q</ci><apply id="idp24989088"><times id="idp24989216"/><cn id="idp24989344" type="integer">2</cn><ci id="idp24989872">ρ</ci></apply></apply></apply><apply id="idp24990160"><times id="idp24990288"/><apply id="idp24990416"><csymbol id="idp24990544" cd="ambiguous">superscript</csymbol><apply id="idp24991104"><abs id="idp24991232"/><ci id="idp24991360">f</ci></apply><cn id="idp24991616" type="integer">2</cn></apply><apply id="idp24992144"><csymbol id="idp24992272" cd="ambiguous">superscript</csymbol><ci id="idp24992832">ζ</ci><cn id="idp24993120" type="integer">2</cn></apply><ci id="idp24993648">d</ci><ci id="idp24993904">x</ci><ci id="idp24994160">d</ci><ci id="idp24994416">t</ci></apply></apply></apply><apply id="idp24994672"><times id="idp24994800"/><apply id="idp24994928"><csymbol id="idp24995056" cd="ambiguous">subscript</csymbol><ci id="idp24995616">ε</ci><cn id="idp24995904" type="integer">2</cn></apply><apply id="idp24996432"><apply id="idp24996560"><csymbol id="idp24996688" cd="ambiguous">subscript</csymbol><int id="idp24997248"/><apply id="idp24997376"><times id="idp24997504"/><apply id="idp24997632"><csymbol id="idp24997760" cd="ambiguous">subscript</csymbol><ci id="idp24998320">B</ci><apply id="idp24998576"><times id="idp24998704"/><cn id="idp24998832" type="integer">2</cn><ci id="idp24999360">ρ</ci></apply></apply><apply id="idp24999648"><csymbol id="idp24999776" cd="ambiguous">subscript</csymbol><ci id="idp25000336">x</ci><cn id="idp25000592" type="integer">0</cn></apply></apply></apply><apply id="idp25001120"><times id="idp25001248"/><apply id="idp25001376"><times id="idp25001504"/><apply id="idp25001632"><csymbol id="idp25001760" cd="ambiguous">superscript</csymbol><apply id="idp25002320"><abs id="idp25002448"/><apply id="idp25002576"><ci id="idp25002704">∇</ci><ci id="idp25002992">u</ci></apply></apply><cn id="idp25003248" type="integer">2</cn></apply><apply id="idp25003776"><csymbol id="idp25003904" cd="ambiguous">superscript</csymbol><ci id="idp25004464">ζ</ci><cn id="idp25004752" type="integer">2</cn></apply></apply><apply id="idp25005280"><interval id="idp25005408" closure="open"/><ci id="idp25005808">x</ci><apply id="idp25006064"><csymbol id="idp25006192" cd="ambiguous">subscript</csymbol><ci id="idp25006752">t</ci><cn id="idp25007008" type="integer">0</cn></apply></apply><ci id="idp25007536">d</ci><ci id="idp25007792">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp25008048" encoding="application/x-tex">\displaystyle\mbox{}+\frac{C}{\varepsilon _{{2}}}\iint _{{Q_{{2\rho}}}}\lvert f\rvert^{{2}}\zeta^{{2}}\, dx\, dt+\varepsilon _{{2}}\int _{{B_{{2\rho}}(x_{{0}})}}\left(\lvert\nabla u\rvert^{{2}}\zeta^{{2}}\right)(x,t_{{0}})\, dx</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp25578864"><h4>Hit idp25578864</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 31</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/114/f045477.xhtml#idp25578864</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:742733(000023%) VariableMap:[G x 3, dx x 3, mathbb x 3, L x 8, x 3, infty x 3, times, nabla x 8, R x 3, \ x 66, _ x 27, left x 5, ^ x 19, right x 5, end, ds x 4, d, & x 4, int x 8, leq x 2, n x 11, + x 8, ( x 12, ) x 12, ., textrm x 3, -, begin, 3 x 3, qquad, exp x 3, v x 8, 1 x 3, 0 x 7, t x 5, q x 13, tau, split x 2, | x 22] Expects 2 occurences for 'd' but has only 1 Expects 2 occurences for 'neq' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp25578864" alttext="\begin{split}&\int _{{{\mathbb{R}}^{3}}}|G_{n}|^{q}dx\\ &\leq\left\{\int _{{{\mathbb{R}}^{3}}}|G_{n}(0)|^{q}dx+q\int _{0}^{t}\|\nabla v_{n}\| _{{L^{q}}}\textrm{exp}\left(-\int _{0}^{t}(q+1)(\|\nabla v_{n}\| _{{L^{\infty}}}+\|\nabla v_{n}\| _{{L^{q}}})d\tau\right)ds\right\}\\ &\qquad\times\textrm{exp}\left(\int _{0}^{t}(q+1)(\|\nabla v_{n}\| _{{L^{\infty}}}+\|\nabla v_{n}\| _{{L^{q}}})ds\right)\\ &\leq\left(\int _{{{\mathbb{R}}^{3}}}|G_{n}(0)|^{q}dx+q\int _{0}^{t}\|\nabla v_{n}\| _{{L^{q}}}ds\right)\textrm{exp}\left(\int _{0}^{t}(q+1)(\|\nabla v_{n}\| _{{L^{\infty}}}+\|\nabla v_{n}\| _{{L^{q}}})ds\right).\end{split}" display="block"><semantics id="idp25577984"><mrow id="idp25578112"><mrow id="idp25578240"><mrow id="idp25578368"><msub id="idp25578496"><mo id="idp25578624">∫</mo><msup id="idp25580352"><mi id="idp25580480" mathvariant="double-struck">R</mi><mn id="idp25580864">3</mn></msup></msub><mrow id="idp25581120"><msup id="idp25581248"><mrow id="idp25581376"><mo id="idp25581504" fence="true">|</mo><msub id="idp25582032"><mi id="idp25582160">G</mi><mi id="idp25582416">n</mi></msub><mo id="idp25582672" fence="true">|</mo></mrow><mi id="idp25583200">q</mi></msup><mo id="idp25583456">⁢</mo><mi id="idp25583744">d</mi><mo id="idp25584000">⁢</mo><mi id="idp25584288">x</mi></mrow></mrow><mo id="idp25584544">≤</mo><mrow id="idp25584832"><mrow id="idp25584960"><mrow id="idp25585088"><mo id="idp25585216">{</mo><mrow id="idp25585472"><mrow id="idp25585600"><msub id="idp25585728"><mo id="idp25585856">∫</mo><msup id="idp25586144"><mi id="idp25586272" mathvariant="double-struck">R</mi><mn id="idp25586800">3</mn></msup></msub><mrow id="idp25587056"><msup id="idp25587184"><mrow id="idp25587312"><mo id="idp25587440" fence="true">|</mo><mrow id="idp25587968"><msub id="idp25588096"><mi id="idp25588224">G</mi><mi id="idp25588480">n</mi></msub><mo id="idp25588736">⁢</mo><mrow id="idp25589024"><mo id="idp25589152">(</mo><mn id="idp25589408">0</mn><mo id="idp25589664">)</mo></mrow></mrow><mo id="idp25589920" fence="true">|</mo></mrow><mi id="idp25590448">q</mi></msup><mo id="idp25590704">⁢</mo><mi id="idp25590992">d</mi><mo id="idp25591248">⁢</mo><mi id="idp25591536">x</mi></mrow></mrow><mo id="idp25591792">+</mo><mrow id="idp25592048"><mi id="idp25592176">q</mi><mo id="idp25592432">⁢</mo><mrow id="idp25592720"><msubsup id="idp25592848"><mo id="idp25592976">∫</mo><mn id="idp25593264">0</mn><mi id="idp25593520">t</mi></msubsup><mrow id="idp25593776"><msub id="idp25593904"><mrow id="idp25594032"><mo id="idp25594160" fence="true">∥</mo><mrow id="idp25594720"><mo 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id="S4.Ex15.m1.sh1cw.cmml">d</ci><ci id="S4.Ex15.m1.sh1cx.cmml">s</ci></apply></apply></apply></apply></apply><mtext id="S4.Ex15.m1.sh1dd.cmml">exp</mtext></apply><apply id="S4.Ex15.m1.sh1ey.cmml"><apply id="S4.Ex15.m1.sh1dl.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh1df.cmml">superscript</csymbol><apply id="S4.Ex15.m1.sh1dj.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh1dg.cmml">subscript</csymbol><int id="S4.Ex15.m1.sh1dh.cmml"/><cn type="integer" id="S4.Ex15.m1.sh1di.cmml">0</cn></apply><ci id="S4.Ex15.m1.sh1dk.cmml">t</ci></apply><apply id="S4.Ex15.m1.sh1ex.cmml"><times id="S4.Ex15.m1.sh1dm.cmml"/><apply id="S4.Ex15.m1.sh1dq.cmml"><plus id="S4.Ex15.m1.sh1dn.cmml"/><ci id="S4.Ex15.m1.sh1do.cmml">q</ci><cn type="integer" id="S4.Ex15.m1.sh1dp.cmml">1</cn></apply><apply id="S4.Ex15.m1.sh1eu.cmml"><plus id="S4.Ex15.m1.sh1dr.cmml"/><apply id="S4.Ex15.m1.sh1ef.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh1ds.cmml">subscript</csymbol><apply id="S4.Ex15.m1.sh1ea.cmml"><csymbol 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id="S4.Ex15.m1.sh2bs.cmml">norm</csymbol><apply id="S4.Ex15.m1.sh2by.cmml"><ci id="S4.Ex15.m1.sh2bt.cmml">∇</ci><apply id="S4.Ex15.m1.sh2bx.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh2bu.cmml">subscript</csymbol><ci id="S4.Ex15.m1.sh2bv.cmml">v</ci><ci id="S4.Ex15.m1.sh2bw.cmml">n</ci></apply></apply></apply><apply id="S4.Ex15.m1.sh2cd.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh2ca.cmml">superscript</csymbol><ci id="S4.Ex15.m1.sh2cb.cmml">L</ci><infinity id="S4.Ex15.m1.sh2cc.cmml"/></apply></apply><apply id="S4.Ex15.m1.sh2cs.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh2cf.cmml">subscript</csymbol><apply id="S4.Ex15.m1.sh2cn.cmml"><csymbol cd="latexml" id="S4.Ex15.m1.sh2cg.cmml">norm</csymbol><apply id="S4.Ex15.m1.sh2cm.cmml"><ci id="S4.Ex15.m1.sh2ch.cmml">∇</ci><apply id="S4.Ex15.m1.sh2cl.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh2ci.cmml">subscript</csymbol><ci id="S4.Ex15.m1.sh2cj.cmml">v</ci><ci id="S4.Ex15.m1.sh2ck.cmml">n</ci></apply></apply></apply><apply id="S4.Ex15.m1.sh2cr.cmml"><csymbol cd="ambiguous" id="S4.Ex15.m1.sh2co.cmml">superscript</csymbol><ci id="S4.Ex15.m1.sh2cp.cmml">L</ci><ci id="S4.Ex15.m1.sh2cq.cmml">q</ci></apply></apply></apply><ci id="S4.Ex15.m1.sh2cu.cmml">d</ci><ci id="S4.Ex15.m1.sh2cv.cmml">s</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp25801456" encoding="application/x-tex">\begin{split}&\int _{{{\mathbb{R}}^{3}}}|G_{n}|^{q}dx\\ &\leq\left\{\int _{{{\mathbb{R}}^{3}}}|G_{n}(0)|^{q}dx+q\int _{0}^{t}\|\nabla v_{n}\| _{{L^{q}}}\textrm{exp}\left(-\int _{0}^{t}(q+1)(\|\nabla v_{n}\| _{{L^{\infty}}}+\|\nabla v_{n}\| _{{L^{q}}})d\tau\right)ds\right\}\\ &\qquad\times\textrm{exp}\left(\int _{0}^{t}(q+1)(\|\nabla v_{n}\| _{{L^{\infty}}}+\|\nabla v_{n}\| _{{L^{q}}})ds\right)\\ &\leq\left(\int _{{{\mathbb{R}}^{3}}}|G_{n}(0)|^{q}dx+q\int _{0}^{t}\|\nabla v_{n}\| _{{L^{q}}}ds\right)\textrm{exp}\left(\int _{0}^{t}(q+1)(\|\nabla v_{n}\| _{{L^{\infty}}}+\|\nabla v_{n}\| _{{L^{q}}})ds\right).\end{split}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp26606096"><h4>Hit idp26606096</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 32</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/202/f080482.xhtml#idp26606096</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:895606(000091%) VariableMap:[D, E, dx x 2, C x 2, nabla x 2, ], \ x 17, epsilon, _ x 6, ^ x 5, lll, end, [, & x 2, int x 3, leq, + x 3, ( x 2, Omega x 3, Psi x 3, ) x 2, ., begin, 2 x 5, 1 x 3, mathcal x 2, | x 10, array x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp26606096" alttext="\begin{array}[]{lll}\int _{{\Omega _{1}}}|\nabla\Psi|^{2}dx&\leq&C\epsilon\int _{{\Omega _{1}}}(|\Psi|^{2}+|\nabla\Psi|^{2})+C\int _{{\Omega _{1}}}(|\mathcal{D}|^{2}+|\mathcal{E}|^{2})dx.\end{array}" display="block"><semantics id="idp26605872"><mtable id="idp26607024" rowspacing="0.2ex" columnspacing="0.4em"><mtr id="idp26607632"><mtd id="idp26607760" columnalign="left"><mrow id="idp26608128"><msub id="idp26608256"><mo id="idp26608384">∫</mo><msub id="idp26608640"><mi id="idp26608768" mathvariant="normal">Ω</mi><mn id="idp26609296">1</mn></msub></msub><mrow id="idp26609552"><msup id="idp26609680"><mrow id="idp26609808"><mo id="idp26609936" fence="true">|</mo><mrow id="idp26610464"><mo id="idp26610592">∇</mo><mo id="idp26610880">⁡</mo><mi id="idp26611168" mathvariant="normal">Ψ</mi></mrow><mo id="idp26611728" fence="true">|</mo></mrow><mn id="idp26612256">2</mn></msup><mo id="idp26612512">⁢</mo><mi id="idp26612800">d</mi><mo id="idp26613056">⁢</mo><mi id="idp26613344">x</mi></mrow></mrow></mtd><mtd id="idp26613600" columnalign="left"><mo id="idp26614000">≤</mo></mtd><mtd id="idp26614288" columnalign="left"><mrow id="idp26614688"><mrow id="idp26614816"><mrow id="idp26614944"><mi id="idp26615072">C</mi><mo id="idp26615328">⁢</mo><mi id="idp26615616">ϵ</mi><mo id="idp26615904">⁢</mo><mrow id="idp26616192"><msub id="idp26616320"><mo id="idp26616448">∫</mo><msub id="idp26616736"><mi id="idp26616864" mathvariant="normal">Ω</mi><mn id="idp26617424">1</mn></msub></msub><mrow id="idp26617680"><mo id="idp26617808">(</mo><mrow id="idp26618064"><msup id="idp26618192"><mrow id="idp26618320"><mo id="idp26618448" fence="true">|</mo><mi id="idp26618976" mathvariant="normal">Ψ</mi><mo id="idp26619536" fence="true">|</mo></mrow><mn id="idp26620064">2</mn></msup><mo id="idp26620320">+</mo><msup id="idp26620576"><mrow id="idp26620704"><mo id="idp26620832" fence="true">|</mo><mrow id="idp26621360"><mo id="idp26621488">∇</mo><mo id="idp26621776">⁡</mo><mi id="idp26622064" mathvariant="normal">Ψ</mi></mrow><mo id="idp26622624" fence="true">|</mo></mrow><mn id="idp26623152">2</mn></msup></mrow><mo id="idp26623408">)</mo></mrow></mrow></mrow><mo id="idp26623664">+</mo><mrow id="idp26623920"><mi id="idp26624048">C</mi><mo id="idp26624304">⁢</mo><mrow id="idp26624592"><msub id="idp26624720"><mo id="idp26624848">∫</mo><msub id="idp26625136"><mi id="idp26625264" mathvariant="normal">Ω</mi><mn id="idp26625824">1</mn></msub></msub><mrow id="idp26626080"><mrow id="idp26626208"><mo id="idp26626336">(</mo><mrow id="idp26626592"><msup id="idp26626720"><mrow id="idp26626848"><mo id="idp26626976" fence="true">|</mo><mi id="idp26627504" mathvariant="script">D</mi><mo id="idp26628032" fence="true">|</mo></mrow><mn id="idp26628560">2</mn></msup><mo id="idp26628816">+</mo><msup id="idp26629072"><mrow id="idp26629200"><mo id="idp26629328" fence="true">|</mo><mi id="idp26629856" mathvariant="script">E</mi><mo id="idp26630384" fence="true">|</mo></mrow><mn id="idp26630912">2</mn></msup></mrow><mo id="idp26631168">)</mo></mrow><mo id="idp26631424">⁢</mo><mi id="idp26631712">d</mi><mo id="idp26631968">⁢</mo><mi id="idp26632256">x</mi></mrow></mrow></mrow></mrow><mo id="idp26632512">.</mo></mrow></mtd></mtr></mtable><annotation-xml id="idp26632768" encoding="MathML-Content"><mtext id="idp26633168">∫Ω1⁢∇Ψ2dx≤+⁢Cϵ∫Ω1+Ψ2∇Ψ2⁢C∫Ω1⁢+D2E2dx</mtext></annotation-xml><annotation id="idp26633504" encoding="application/x-tex">\begin{array}[]{lll}\int _{{\Omega _{1}}}|\nabla\Psi|^{2}dx&\leq&C\epsilon\int _{{\Omega _{1}}}(|\Psi|^{2}+|\nabla\Psi|^{2})+C\int _{{\Omega _{1}}}(|\mathcal{D}|^{2}+|\mathcal{E}|^{2})dx.\end{array}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp26662016"><h4>Hit idp26662016</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 33</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/202/f080482.xhtml#idp26662016</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:902778(000092%) VariableMap:[dx x 2, int x 2, leq, C, Omega x 2, Psi x 2, ., 2 x 2, 1 x 2, nabla, \ x 8, _ x 4, | x 4, ^ x 2] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp26662016" alttext="\int _{{\Omega _{1}}}|\Psi|^{2}dx\leq C\int _{{\Omega _{1}}}|\nabla\Psi|^{2}dx." display="block"><semantics id="idp26662736"><mrow id="idp26662864"><mrow id="idp26662992"><mrow id="idp26663120"><msub id="idp26663248"><mo id="idp26663376">∫</mo><msub id="idp26663632"><mi id="idp26663760" mathvariant="normal">Ω</mi><mn id="idp26664288">1</mn></msub></msub><mrow id="idp26664544"><msup id="idp26664672"><mrow id="idp26664800"><mo id="idp26664928" fence="true">|</mo><mi id="idp26665456" mathvariant="normal">Ψ</mi><mo id="idp26666016" fence="true">|</mo></mrow><mn id="idp26666544">2</mn></msup><mo id="idp26666800">⁢</mo><mi id="idp26667088">d</mi><mo id="idp26667344">⁢</mo><mi id="idp26667632">x</mi></mrow></mrow><mo id="idp26667888">≤</mo><mrow id="idp26668176"><mi id="idp26668304">C</mi><mo id="idp26668560">⁢</mo><mrow id="idp26668848"><msub id="idp26668976"><mo id="idp26669104">∫</mo><msub id="idp26669392"><mi id="idp26669520" mathvariant="normal">Ω</mi><mn id="idp26670080">1</mn></msub></msub><mrow id="idp26670336"><msup id="idp26670464"><mrow id="idp26670592"><mo id="idp26670720" fence="true">|</mo><mrow id="idp26671248"><mo id="idp26671376">∇</mo><mo id="idp26671664">⁡</mo><mi id="idp26671952" mathvariant="normal">Ψ</mi></mrow><mo id="idp26672512" fence="true">|</mo></mrow><mn id="idp26673040">2</mn></msup><mo id="idp26673296">⁢</mo><mi id="idp26673584">d</mi><mo id="idp26673840">⁢</mo><mi id="idp26674128">x</mi></mrow></mrow></mrow></mrow><mo id="idp26674384">.</mo></mrow><annotation-xml id="idp26674640" encoding="MathML-Content"><apply id="idp26675040"><leq id="idp26675168"/><apply id="idp26675296"><apply id="idp26675424"><csymbol id="idp26675552" cd="ambiguous">subscript</csymbol><int id="idp26676112"/><apply id="idp26676240"><csymbol id="idp26676368" cd="ambiguous">subscript</csymbol><ci id="idp26676928">Ω</ci><cn id="idp26677216" type="integer">1</cn></apply></apply><apply id="idp26677744"><times id="idp26677872"/><apply id="idp26678000"><csymbol id="idp26678128" cd="ambiguous">superscript</csymbol><apply id="idp26678688"><abs id="idp26678816"/><ci id="idp26678944">Ψ</ci></apply><cn id="idp26679232" type="integer">2</cn></apply><ci id="idp26679760">d</ci><ci id="idp26680016">x</ci></apply></apply><apply id="idp26680272"><times id="idp26680400"/><ci id="idp26680528">C</ci><apply id="idp26680784"><apply id="idp26680912"><csymbol id="idp26681040" cd="ambiguous">subscript</csymbol><int id="idp26681600"/><apply id="idp26681728"><csymbol id="idp26681856" cd="ambiguous">subscript</csymbol><ci id="idp26682416">Ω</ci><cn id="idp26682704" type="integer">1</cn></apply></apply><apply id="idp26683232"><times id="idp26683360"/><apply id="idp26683488"><csymbol id="idp26683616" cd="ambiguous">superscript</csymbol><apply id="idp26684176"><abs id="idp26684304"/><apply id="idp26684432"><ci id="idp26684560">∇</ci><ci id="idp26684848">Ψ</ci></apply></apply><cn id="idp26685136" type="integer">2</cn></apply><ci id="idp26685664">d</ci><ci id="idp26685920">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp26686176" encoding="application/x-tex">\int _{{\Omega _{1}}}|\Psi|^{2}dx\leq C\int _{{\Omega _{1}}}|\nabla\Psi|^{2}dx.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp26815008"><h4>Hit idp26815008</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 34</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/60/f023879.xhtml#idp26815008</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:928119(000091%) VariableMap:[geq, g x 3, int x 3, C, delta, n x 2, M x 3, dV x 3, ,, - x 2, frac, 2 x 4, 0 x 2, psi x 3, nabla, \ x 10, _ x 8, | x 2, ^ x 3] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp26815008" alttext="\int _{M}|\nabla\psi|^{2}dV_{g}\geq\delta _{0}\int _{M}\psi^{{\frac{2n}{n-2}}}dV_{g}-C_{0}\int _{M}\psi^{2}dV_{g}," display="block"><semantics id="idp26815856"><mrow id="idp26815984"><mrow id="idp26816112"><mrow id="idp26816240"><msub id="idp26816368"><mo id="idp26816496">∫</mo><mi id="idp26816752">M</mi></msub><mrow id="idp26817008"><msup id="idp26817136"><mrow id="idp26817264"><mo id="idp26817392" fence="true">|</mo><mrow id="idp26817888"><mo id="idp26818016">∇</mo><mo id="idp26818304">⁡</mo><mi id="idp26818592">ψ</mi></mrow><mo id="idp26818880" fence="true">|</mo></mrow><mn id="idp26819408">2</mn></msup><mo id="idp26819664">⁢</mo><mi id="idp26819952">d</mi><mo id="idp26820208">⁢</mo><msub id="idp26820496"><mi id="idp26820624">V</mi><mi id="idp26820880">g</mi></msub></mrow></mrow><mo id="idp26821136">≥</mo><mrow id="idp26821424"><mrow id="idp26821552"><msub id="idp26821680"><mi id="idp26821808">δ</mi><mn id="idp26822096">0</mn></msub><mo id="idp26822352">⁢</mo><mrow id="idp26822640"><msub id="idp26822768"><mo id="idp26822896">∫</mo><mi id="idp26823184">M</mi></msub><mrow id="idp26823440"><msup id="idp26823568"><mi id="idp26823696">ψ</mi><mfrac id="idp26823984"><mrow id="idp26824112"><mn id="idp26824240">2</mn><mo id="idp26824496">⁢</mo><mi id="idp26824784">n</mi></mrow><mrow id="idp26825040"><mi id="idp26825168">n</mi><mo id="idp26825424">-</mo><mn id="idp26825680">2</mn></mrow></mfrac></msup><mo id="idp26825936">⁢</mo><mi id="idp26826224">d</mi><mo id="idp26826480">⁢</mo><msub id="idp26826768"><mi id="idp26826896">V</mi><mi id="idp26827152">g</mi></msub></mrow></mrow></mrow><mo id="idp26827408">-</mo><mrow id="idp26827664"><msub id="idp26827792"><mi id="idp26827920">C</mi><mn id="idp26828176">0</mn></msub><mo id="idp26828432">⁢</mo><mrow id="idp26828720"><msub id="idp26828848"><mo id="idp26828976">∫</mo><mi id="idp26829264">M</mi></msub><mrow id="idp26829520"><msup id="idp26829648"><mi id="idp26829776">ψ</mi><mn id="idp26830064">2</mn></msup><mo id="idp26830320">⁢</mo><mi id="idp26830608">d</mi><mo id="idp26830864">⁢</mo><msub id="idp26831152"><mi id="idp26831280">V</mi><mi id="idp26831536">g</mi></msub></mrow></mrow></mrow></mrow></mrow><mo id="idp26831792">,</mo></mrow><annotation-xml id="idp26832048" encoding="MathML-Content"><apply id="idp26832448"><geq id="idp26832576"/><apply id="idp26832704"><apply id="idp26832832"><csymbol id="idp26832960" cd="ambiguous">subscript</csymbol><int id="idp26833520"/><ci id="idp26833648">M</ci></apply><apply id="idp26833904"><times id="idp26834032"/><apply id="idp26834160"><csymbol id="idp26834288" cd="ambiguous">superscript</csymbol><apply id="idp26834848"><abs id="idp26834976"/><apply id="idp26835104"><ci id="idp26835232">∇</ci><ci id="idp26835520">ψ</ci></apply></apply><cn id="idp26835808" type="integer">2</cn></apply><ci id="idp26836336">d</ci><apply id="idp26836592"><csymbol id="idp26836720" cd="ambiguous">subscript</csymbol><ci id="idp26837280">V</ci><ci id="idp26837536">g</ci></apply></apply></apply><apply id="idp26837792"><minus id="idp26837920"/><apply id="idp26838048"><times id="idp26838176"/><apply id="idp26838304"><csymbol id="idp26838432" cd="ambiguous">subscript</csymbol><ci id="idp26838992">δ</ci><cn id="idp26839280" type="integer">0</cn></apply><apply id="idp26839808"><apply id="idp26839936"><csymbol id="idp26840064" cd="ambiguous">subscript</csymbol><int id="idp26840624"/><ci id="idp26840752">M</ci></apply><apply id="idp26841008"><times id="idp26841136"/><apply id="idp26841264"><csymbol id="idp26841392" cd="ambiguous">superscript</csymbol><ci id="idp26841952">ψ</ci><apply id="idp26842240"><divide id="idp26842368"/><apply id="idp26842496"><times id="idp26842624"/><cn id="idp26842752" type="integer">2</cn><ci id="idp26843280">n</ci></apply><apply id="idp26843536"><minus id="idp26843664"/><ci id="idp26843792">n</ci><cn id="idp26844048" type="integer">2</cn></apply></apply></apply><ci id="idp26844656">d</ci><apply id="idp26844912"><csymbol id="idp26845040" cd="ambiguous">subscript</csymbol><ci id="idp26845536">V</ci><ci id="idp26845792">g</ci></apply></apply></apply></apply><apply id="idp26846048"><times id="idp26846176"/><apply id="idp26846304"><csymbol id="idp26846432" cd="ambiguous">subscript</csymbol><ci id="idp26846960">C</ci><cn id="idp26847216" type="integer">0</cn></apply><apply id="idp26847744"><apply id="idp26847872"><csymbol id="idp26848000" cd="ambiguous">subscript</csymbol><int id="idp26848560"/><ci id="idp26848688">M</ci></apply><apply id="idp26848944"><times id="idp26849072"/><apply id="idp26849200"><csymbol id="idp26849328" cd="ambiguous">superscript</csymbol><ci id="idp26849888">ψ</ci><cn id="idp26850176" type="integer">2</cn></apply><ci id="idp26850704">d</ci><apply id="idp26850960"><csymbol id="idp26851088" cd="ambiguous">subscript</csymbol><ci id="idp26851648">V</ci><ci id="idp26851904">g</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp26852160" encoding="application/x-tex">\int _{M}|\nabla\psi|^{2}dV_{g}\geq\delta _{0}\int _{M}\psi^{{\frac{2n}{n-2}}}dV_{g}-C_{0}\int _{M}\psi^{2}dV_{g},</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp26879344"><h4>Hit idp26879344</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 35</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/60/f023879.xhtml#idp26879344</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:936737(000092%) VariableMap:[geq, g x 2, np, int x 2, C, delta, n x 3, L, M x 2, (, ), ., dV x 2, - x 3, frac x 3, prime, 2 x 4, u x 3, 0 x 2, nabla, p x 2, \ x 11, _ x 7, | x 4, ^ x 6] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp26879344" alttext="\int _{M}|\nabla u^{{\frac{p}{2}}}|^{2}dV_{g}\geq\delta _{0}(\| u\| _{{L^{{\frac{np}{n-2}}}}})^{{\frac{n-2}{n}}}-C_{0}^{{\prime}}\int _{M}u^{p}dV_{g}." display="block"><semantics id="idp26880224"><mrow id="idp26880352"><mrow id="idp26880480"><mrow id="idp26880608"><msub id="idp26880736"><mo id="idp26880864">∫</mo><mi id="idp26881120">M</mi></msub><mrow id="idp26881376"><msup id="idp26881504"><mrow id="idp26881632"><mo id="idp26881760" fence="true">|</mo><mrow id="idp26882256"><mo id="idp26882384">∇</mo><mo id="idp26882672">⁡</mo><msup id="idp26882960"><mi id="idp26883088">u</mi><mfrac id="idp26883344"><mi id="idp26883472">p</mi><mn id="idp26883728">2</mn></mfrac></msup></mrow><mo id="idp26883984" fence="true">|</mo></mrow><mn id="idp26884512">2</mn></msup><mo id="idp26884768">⁢</mo><mi id="idp26885056">d</mi><mo id="idp26885312">⁢</mo><msub id="idp26885600"><mi id="idp26885728">V</mi><mi id="idp26885984">g</mi></msub></mrow></mrow><mo id="idp26886240">≥</mo><mrow id="idp26886528"><mrow id="idp26886656"><msub id="idp26886784"><mi id="idp26886912">δ</mi><mn id="idp26887200">0</mn></msub><mo id="idp26887456">⁢</mo><msup id="idp26887744"><mrow id="idp26887872"><mo id="idp26888000">(</mo><msub id="idp26888256"><mrow id="idp26888384"><mo id="idp26888512" fence="true">∥</mo><mi id="idp26889072">u</mi><mo id="idp26889328" fence="true">∥</mo></mrow><msup id="idp26889888"><mi id="idp26890016">L</mi><mfrac id="idp26890272"><mrow id="idp26890400"><mi id="idp26890528">n</mi><mo id="idp26890784">⁢</mo><mi id="idp26891072">p</mi></mrow><mrow id="idp26891328"><mi id="idp26891456">n</mi><mo id="idp26891712">-</mo><mn id="idp26891968">2</mn></mrow></mfrac></msup></msub><mo id="idp26892224">)</mo></mrow><mfrac id="idp26892480"><mrow id="idp26892608"><mi id="idp26892736">n</mi><mo id="idp26892992">-</mo><mn id="idp26893248">2</mn></mrow><mi id="idp26893504">n</mi></mfrac></msup></mrow><mo id="idp26893760">-</mo><mrow id="idp26894016"><msubsup id="idp26894144"><mi id="idp26894272">C</mi><mn id="idp26894528">0</mn><mo id="idp26894784">′</mo></msubsup><mo id="idp26895072">⁢</mo><mrow id="idp26895360"><msub id="idp26895488"><mo id="idp26895616">∫</mo><mi id="idp26895904">M</mi></msub><mrow id="idp26896160"><msup id="idp26896288"><mi id="idp26896416">u</mi><mi id="idp26896672">p</mi></msup><mo id="idp26896928">⁢</mo><mi id="idp26897216">d</mi><mo id="idp26897472">⁢</mo><msub id="idp26897760"><mi id="idp26897888">V</mi><mi id="idp26898144">g</mi></msub></mrow></mrow></mrow></mrow></mrow><mo id="idp26898400">.</mo></mrow><annotation-xml id="idp26898656" encoding="MathML-Content"><apply id="idp26899056"><geq id="idp26899184"/><apply id="idp26899312"><apply id="idp26899440"><csymbol id="idp26899568" cd="ambiguous">subscript</csymbol><int id="idp26900128"/><ci id="idp26900256">M</ci></apply><apply id="idp26900512"><times id="idp26900640"/><apply id="idp26900768"><csymbol id="idp26900896" cd="ambiguous">superscript</csymbol><apply id="idp26901456"><abs id="idp26901584"/><apply id="idp26901712"><ci id="idp26901840">∇</ci><apply id="idp26902128"><csymbol id="idp26902256" cd="ambiguous">superscript</csymbol><ci id="idp26902816">u</ci><apply id="idp26903072"><divide id="idp26903200"/><ci id="idp26903328">p</ci><cn id="idp26903584" type="integer">2</cn></apply></apply></apply></apply><cn id="idp26904112" type="integer">2</cn></apply><ci id="idp26904640">d</ci><apply id="idp26904896"><csymbol id="idp26905024" cd="ambiguous">subscript</csymbol><ci id="idp26905584">V</ci><ci id="idp26905840">g</ci></apply></apply></apply><apply id="idp26906096"><minus id="idp26906224"/><apply id="idp26906352"><times id="idp26906480"/><apply id="idp26906608"><csymbol id="idp26906736" cd="ambiguous">subscript</csymbol><ci id="idp26907296">δ</ci><cn id="idp26907584" type="integer">0</cn></apply><apply id="idp26908112"><csymbol id="idp26908240" cd="ambiguous">superscript</csymbol><apply id="idp26908800"><csymbol id="idp26908928" cd="ambiguous">subscript</csymbol><apply id="idp26909488"><csymbol id="idp26909616" cd="latexml">norm</csymbol><ci id="idp26910176">u</ci></apply><apply id="idp26910432"><csymbol id="idp26910560" cd="ambiguous">superscript</csymbol><ci id="idp26911120">L</ci><apply id="idp26911376"><divide id="idp26911504"/><apply id="idp26911632"><times id="idp26911760"/><ci id="idp26911888">n</ci><ci id="idp26912144">p</ci></apply><apply id="idp26912400"><minus id="idp26912528"/><ci id="idp26912656">n</ci><cn id="idp26912912" type="integer">2</cn></apply></apply></apply></apply><apply id="idp26913440"><divide id="idp26913568"/><apply id="idp26913696"><minus id="idp26913824"/><ci id="idp26913952">n</ci><cn id="idp26914208" type="integer">2</cn></apply><ci id="idp26914736">n</ci></apply></apply></apply><apply id="idp26914992"><times id="idp26915120"/><apply id="idp26915248"><csymbol id="idp26915376" cd="ambiguous">superscript</csymbol><apply id="idp26915936"><csymbol id="idp26916064" cd="ambiguous">subscript</csymbol><ci id="idp26916624">C</ci><cn id="idp26916880" type="integer">0</cn></apply><ci id="idp26917408">′</ci></apply><apply id="idp26917696"><apply id="idp26917824"><csymbol id="idp26917952" cd="ambiguous">subscript</csymbol><int id="idp26918512"/><ci id="idp26918640">M</ci></apply><apply id="idp26918896"><times id="idp26919024"/><apply id="idp26919152"><csymbol id="idp26919280" cd="ambiguous">superscript</csymbol><ci id="idp26919840">u</ci><ci id="idp26920096">p</ci></apply><ci id="idp26920352">d</ci><apply id="idp26920608"><csymbol id="idp26920736" cd="ambiguous">subscript</csymbol><ci id="idp26921296">V</ci><ci id="idp26921552">g</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp26921808" encoding="application/x-tex">\int _{M}|\nabla u^{{\frac{p}{2}}}|^{2}dV_{g}\geq\delta _{0}(\| u\| _{{L^{{\frac{np}{n-2}}}}})^{{\frac{n-2}{n}}}-C_{0}^{{\prime}}\int _{M}u^{p}dV_{g}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp27231392"><h4>Hit idp27231392</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 36</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/60/f023879.xhtml#idp27231392</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:982338(000096%) VariableMap:[f, g x 2, fdV, leq, int x 2, C, +, M x 2, ., dV, prime x 2, 2, nabla, \ x 6, _ x 4, | x 2, ^ x 2] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 6 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp27231392" alttext="\int _{M}|\nabla f|^{2}dV_{g}\leq\int _{M}fdV_{g}+C^{{\prime\prime}}." display="block"><semantics id="idp27232192"><mrow id="idp27232320"><mrow id="idp27232448"><mrow id="idp27232576"><msub id="idp27232704"><mo id="idp27232832">∫</mo><mi id="idp27233088">M</mi></msub><mrow id="idp27233344"><msup id="idp27233472"><mrow id="idp27233600"><mo id="idp27233728" fence="true">|</mo><mrow id="idp27234224"><mo id="idp27234352">∇</mo><mo id="idp27234640">⁡</mo><mi id="idp27234928">f</mi></mrow><mo id="idp27235184" fence="true">|</mo></mrow><mn id="idp27235712">2</mn></msup><mo id="idp27235968">⁢</mo><mi id="idp27236256">d</mi><mo id="idp27236512">⁢</mo><msub id="idp27236800"><mi id="idp27236928">V</mi><mi id="idp27237184">g</mi></msub></mrow></mrow><mo id="idp27237440">≤</mo><mrow id="idp27237728"><mrow id="idp27237856"><msub id="idp27237984"><mo id="idp27238112">∫</mo><mi id="idp27238400">M</mi></msub><mrow id="idp27238656"><mi id="idp27238784">f</mi><mo id="idp27239040">⁢</mo><mi id="idp27239328">d</mi><mo id="idp27239584">⁢</mo><msub id="idp27239872"><mi id="idp27240000">V</mi><mi id="idp27240256">g</mi></msub></mrow></mrow><mo id="idp27240512">+</mo><msup id="idp27240768"><mi id="idp27240896">C</mi><mi id="idp27241152">′′</mi></msup></mrow></mrow><mo id="idp27241440">.</mo></mrow><annotation-xml id="idp27241696" encoding="MathML-Content"><apply id="idp27242096"><leq id="idp27242224"/><apply id="idp27242352"><apply id="idp27242480"><csymbol id="idp27242608" cd="ambiguous">subscript</csymbol><int id="idp27243168"/><ci id="idp27243296">M</ci></apply><apply id="idp27243552"><times id="idp27243680"/><apply id="idp27243808"><csymbol id="idp27243936" cd="ambiguous">superscript</csymbol><apply id="idp27244496"><abs id="idp27244624"/><apply id="idp27244752"><ci id="idp27244880">∇</ci><ci id="idp27245168">f</ci></apply></apply><cn id="idp27245424" type="integer">2</cn></apply><ci id="idp27245952">d</ci><apply id="idp27246208"><csymbol id="idp27246336" cd="ambiguous">subscript</csymbol><ci id="idp27246896">V</ci><ci id="idp27247152">g</ci></apply></apply></apply><apply id="idp27247408"><plus id="idp27247536"/><apply id="idp27247664"><apply id="idp27247792"><csymbol id="idp27247920" cd="ambiguous">subscript</csymbol><int id="idp27248480"/><ci id="idp27248608">M</ci></apply><apply id="idp27248864"><times id="idp27248992"/><ci id="idp27249120">f</ci><ci id="idp27249376">d</ci><apply id="idp27249632"><csymbol id="idp27249760" cd="ambiguous">subscript</csymbol><ci id="idp27250320">V</ci><ci id="idp27250576">g</ci></apply></apply></apply><apply id="idp27250832"><csymbol id="idp27250960" cd="ambiguous">superscript</csymbol><ci id="idp27251520">C</ci><ci id="idp27251776">′′</ci></apply></apply></apply></annotation-xml><annotation id="idp27252064" encoding="application/x-tex">\int _{M}|\nabla f|^{2}dV_{g}\leq\int _{M}fdV_{g}+C^{{\prime\prime}}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp27625952"><h4>Hit idp27625952</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 37</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/115/f045602.xhtml#idp27625952</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1039556(000078%) VariableMap:[dx, mathbb, leq, int, n, 2, v, 1, 0, nabla, R, \ x 4, _ x 2, ^ x 2, | x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 4 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp27625952" alttext="\int _{{{\mathbb{R}}^{n}}}|\nabla v_{0}|^{2}dx\leq 1" display="inline"><semantics id="idp27626736"><mrow id="idp27626864"><mrow id="idp27626992"><msub id="idp27627120"><mo id="idp27627248">∫</mo><msup id="idp27627504"><mi id="idp27627632" mathvariant="double-struck">R</mi><mi id="idp27628128">n</mi></msup></msub><mrow id="idp27628384"><msup id="idp27628512"><mrow id="idp27628640"><mo id="idp27628768" fence="true">|</mo><mrow id="idp27629296"><mo id="idp27629424">∇</mo><mo id="idp27629712">⁡</mo><msub id="idp27630000"><mi id="idp27630128">v</mi><mn id="idp27630384">0</mn></msub></mrow><mo id="idp27630640" fence="true">|</mo></mrow><mn id="idp27631168">2</mn></msup><mo id="idp27631424">⁢</mo><mi id="idp27631712">d</mi><mo id="idp27631968">⁢</mo><mi id="idp27632256">x</mi></mrow></mrow><mo id="idp27632512">≤</mo><mn id="idp27632800">1</mn></mrow><annotation-xml id="idp27633056" encoding="MathML-Content"><apply id="idp27633456"><leq id="idp27633584"/><apply id="idp27633712"><apply id="idp27633840"><csymbol id="idp27633968" cd="ambiguous">subscript</csymbol><int id="idp27634528"/><apply id="idp27634656"><csymbol id="idp27634784" cd="ambiguous">superscript</csymbol><ci id="idp27635344">R</ci><ci id="idp27635600">n</ci></apply></apply><apply id="idp27635856"><times id="idp27635984"/><apply id="idp27636112"><csymbol id="idp27636240" cd="ambiguous">superscript</csymbol><apply id="idp27636800"><abs id="idp27636928"/><apply id="idp27637056"><ci id="idp27637184">∇</ci><apply id="idp27637472"><csymbol id="idp27637600" cd="ambiguous">subscript</csymbol><ci id="idp27638160">v</ci><cn id="idp27638416" type="integer">0</cn></apply></apply></apply><cn id="idp27638944" type="integer">2</cn></apply><ci id="idp27639472">d</ci><ci id="idp27639728">x</ci></apply></apply><cn id="idp27639984" type="integer">1</cn></apply></annotation-xml><annotation id="idp27640512" encoding="application/x-tex">\int _{{{\mathbb{R}}^{n}}}|\nabla v_{0}|^{2}dx\leq 1</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp28303744"><h4>Hit idp28303744</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 38</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/14/f005428.xhtml#idp28303744</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1359228(000087%) VariableMap:[f x 2, e x 2, leq, int x 2, +, M x 2, ij, ., - x 2, 2 x 4, v x 2, displaystyle, nabla x 2, 4, \ x 14, _ x 3, left x 3, ^ x 6, | x 6, right x 3, phi x 2] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp28303744" alttext="\displaystyle\leq\int _{{M}}\left|v_{{ij}}\right|^{{2}}\phi^{{2}}e^{{-f}}+4\int _{{M}}\left|\nabla v\right|^{{2}}\left|\nabla\phi\right|^{{2}}e^{{-f}}." display="inline"><semantics id="idp28304624"><mrow id="idp28304752"><mrow id="idp28304880"><none id="idp28305008"/><mo id="idp28305136">≤</mo><mrow id="idp28305392"><mrow id="idp28305520"><mstyle id="idp28305648" displaystyle="true"><msub id="idp28306016"><mo id="idp28306144">∫</mo><mi id="idp28306432">M</mi></msub></mstyle><mrow id="idp28306688"><msup id="idp28306816"><mrow id="idp28306944"><mo id="idp28307072" fence="true">|</mo><msub id="idp28307600"><mi id="idp28307728">v</mi><mrow id="idp28307984"><mi id="idp28308112">i</mi><mo id="idp28308368">⁢</mo><mi id="idp28308656">j</mi></mrow></msub><mo id="idp28308912" fence="true">|</mo></mrow><mn id="idp28309440">2</mn></msup><mo id="idp28309696">⁢</mo><msup id="idp28309984"><mi id="idp28310112">ϕ</mi><mn id="idp28310400">2</mn></msup><mo id="idp28310656">⁢</mo><msup id="idp28310944"><mi id="idp28311072">e</mi><mrow id="idp28311328"><mo id="idp28311456">-</mo><mi id="idp28311712">f</mi></mrow></msup></mrow></mrow><mo id="idp28311968">+</mo><mrow id="idp28312224"><mn id="idp28312352">4</mn><mo id="idp28312608">⁢</mo><mrow id="idp28312896"><mstyle id="idp28313024" displaystyle="true"><msub id="idp28313424"><mo id="idp28313552">∫</mo><mi id="idp28313840">M</mi></msub></mstyle><mrow id="idp28314096"><msup id="idp28314224"><mrow id="idp28314352"><mo id="idp28314480" fence="true">|</mo><mrow id="idp28315008"><mo id="idp28315136">∇</mo><mo id="idp28315424">⁡</mo><mi id="idp28315712">v</mi></mrow><mo id="idp28315968" fence="true">|</mo></mrow><mn id="idp28316496">2</mn></msup><mo id="idp28316752">⁢</mo><msup id="idp28317040"><mrow id="idp28317168"><mo id="idp28317296" fence="true">|</mo><mrow id="idp28317824"><mo id="idp28317952">∇</mo><mo id="idp28318240">⁡</mo><mi id="idp28318528">ϕ</mi></mrow><mo id="idp28318816" fence="true">|</mo></mrow><mn id="idp28319344">2</mn></msup><mo id="idp28319600">⁢</mo><msup id="idp28319888"><mi id="idp28320016">e</mi><mrow id="idp28320272"><mo id="idp28320400">-</mo><mi id="idp28320656">f</mi></mrow></msup></mrow></mrow></mrow></mrow></mrow><mo id="idp28320912">.</mo></mrow><annotation-xml id="idp28321168" encoding="MathML-Content"><apply id="idp28321568"><leq id="idp28321696"/><csymbol id="idp28321824" cd="latexml">absent</csymbol><apply id="idp28322384"><plus id="idp28322512"/><apply id="idp28322640"><apply id="idp28322768"><csymbol id="idp28322896" cd="ambiguous">subscript</csymbol><int id="idp28323456"/><ci id="idp28323584">M</ci></apply><apply id="idp28323840"><times id="idp28323968"/><apply id="idp28324096"><csymbol id="idp28324224" cd="ambiguous">superscript</csymbol><apply id="idp28324784"><abs id="idp28324912"/><apply id="idp28325040"><csymbol id="idp28325168" cd="ambiguous">subscript</csymbol><ci id="idp28325728">v</ci><apply id="idp28325984"><times id="idp28326112"/><ci id="idp28326240">i</ci><ci id="idp28326496">j</ci></apply></apply></apply><cn id="idp28326752" type="integer">2</cn></apply><apply id="idp28327280"><csymbol id="idp28327408" cd="ambiguous">superscript</csymbol><ci id="idp28327968">ϕ</ci><cn id="idp28328256" type="integer">2</cn></apply><apply id="idp28328784"><csymbol id="idp28328912" cd="ambiguous">superscript</csymbol><ci id="idp28329472">e</ci><apply id="idp28329728"><minus id="idp28329856"/><ci id="idp28329984">f</ci></apply></apply></apply></apply><apply id="idp28330240"><times id="idp28330368"/><cn id="idp28330496" type="integer">4</cn><apply id="idp28331024"><apply id="idp28331152"><csymbol id="idp28331280" cd="ambiguous">subscript</csymbol><int id="idp28331840"/><ci id="idp28331968">M</ci></apply><apply id="idp28332224"><times id="idp28332352"/><apply id="idp28332480"><csymbol id="idp28332608" cd="ambiguous">superscript</csymbol><apply id="idp28333168"><abs id="idp28333296"/><apply id="idp28333424"><ci id="idp28333552">∇</ci><ci id="idp28333840">v</ci></apply></apply><cn id="idp28334096" type="integer">2</cn></apply><apply id="idp28334624"><csymbol id="idp28334752" cd="ambiguous">superscript</csymbol><apply id="idp28335312"><abs id="idp28335440"/><apply id="idp28335568"><ci id="idp28335696">∇</ci><ci id="idp28335984">ϕ</ci></apply></apply><cn id="idp28336272" type="integer">2</cn></apply><apply id="idp28336800"><csymbol id="idp28336928" cd="ambiguous">superscript</csymbol><ci id="idp28337488">e</ci><apply id="idp28337744"><minus id="idp28337872"/><ci id="idp28338000">f</ci></apply></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp28338256" encoding="application/x-tex">\displaystyle\leq\int _{{M}}\left|v_{{ij}}\right|^{{2}}\phi^{{2}}e^{{-f}}+4\int _{{M}}\left|\nabla v\right|^{{2}}\left|\nabla\phi\right|^{{2}}e^{{-f}}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp28342608"><h4>Hit idp28342608</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 39</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/14/f005428.xhtml#idp28342608</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1364402(000087%) VariableMap:[f x 2, e x 2, leq, int x 2, M x 2, ij, ., - x 2, v x 2, 2 x 4, nabla x 2, 4, \ x 13, _ x 3, left x 3, | x 6, ^ x 6, right x 3, phi x 2] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp28342608" alttext="\int _{{M}}\left|v_{{ij}}\right|^{{2}}e^{{-f}}\phi^{{2}}\leq 4\int _{{M}}\left|\nabla v\right|^{{2}}\left|\nabla\phi\right|^{{2}}e^{{-f}}." display="block"><semantics id="idp28343488"><mrow id="idp28343616"><mrow id="idp28343744"><mrow id="idp28343872"><msub id="idp28344000"><mo id="idp28344128">∫</mo><mi id="idp28344384">M</mi></msub><mrow id="idp28344640"><msup id="idp28344768"><mrow id="idp28344896"><mo id="idp28345024" fence="true">|</mo><msub id="idp28345520"><mi id="idp28345648">v</mi><mrow id="idp28345904"><mi id="idp28346032">i</mi><mo id="idp28346288">⁢</mo><mi id="idp28346576">j</mi></mrow></msub><mo id="idp28346832" fence="true">|</mo></mrow><mn id="idp28347360">2</mn></msup><mo id="idp28347616">⁢</mo><msup id="idp28347904"><mi id="idp28348032">e</mi><mrow id="idp28348288"><mo id="idp28348416">-</mo><mi id="idp28348672">f</mi></mrow></msup><mo id="idp28348928">⁢</mo><msup id="idp28349216"><mi id="idp28349344">ϕ</mi><mn id="idp28349632">2</mn></msup></mrow></mrow><mo id="idp28349888">≤</mo><mrow id="idp28350176"><mn id="idp28350304">4</mn><mo id="idp28350560">⁢</mo><mrow id="idp28350848"><msub id="idp28350976"><mo id="idp28351104">∫</mo><mi id="idp28351392">M</mi></msub><mrow id="idp28351648"><msup id="idp28351776"><mrow id="idp28351904"><mo id="idp28352032" fence="true">|</mo><mrow id="idp28352560"><mo id="idp28352688">∇</mo><mo id="idp28352976">⁡</mo><mi id="idp28353264">v</mi></mrow><mo id="idp28353520" fence="true">|</mo></mrow><mn id="idp28354048">2</mn></msup><mo id="idp28354304">⁢</mo><msup id="idp28354592"><mrow id="idp28354720"><mo id="idp28354848" fence="true">|</mo><mrow id="idp28355376"><mo id="idp28355504">∇</mo><mo id="idp28355792">⁡</mo><mi id="idp28356080">ϕ</mi></mrow><mo id="idp28356368" fence="true">|</mo></mrow><mn id="idp28356896">2</mn></msup><mo id="idp28357152">⁢</mo><msup id="idp28357440"><mi id="idp28357568">e</mi><mrow id="idp28357824"><mo id="idp28357952">-</mo><mi id="idp28358208">f</mi></mrow></msup></mrow></mrow></mrow></mrow><mo id="idp28358464">.</mo></mrow><annotation-xml id="idp28358720" encoding="MathML-Content"><apply id="idp28359120"><leq id="idp28359248"/><apply id="idp28359376"><apply id="idp28359504"><csymbol id="idp28359632" cd="ambiguous">subscript</csymbol><int id="idp28360192"/><ci id="idp28360320">M</ci></apply><apply id="idp28360576"><times id="idp28360704"/><apply id="idp28360832"><csymbol id="idp28360960" cd="ambiguous">superscript</csymbol><apply id="idp28361520"><abs id="idp28361648"/><apply id="idp28361776"><csymbol id="idp28361904" cd="ambiguous">subscript</csymbol><ci id="idp28362464">v</ci><apply id="idp28362720"><times id="idp28362848"/><ci id="idp28362976">i</ci><ci id="idp28363232">j</ci></apply></apply></apply><cn id="idp28363488" type="integer">2</cn></apply><apply id="idp28364016"><csymbol id="idp28364144" cd="ambiguous">superscript</csymbol><ci id="idp28364704">e</ci><apply id="idp28364960"><minus id="idp28365088"/><ci id="idp28365216">f</ci></apply></apply><apply id="idp28365472"><csymbol id="idp28365600" cd="ambiguous">superscript</csymbol><ci id="idp28366160">ϕ</ci><cn id="idp28366448" type="integer">2</cn></apply></apply></apply><apply id="idp28366976"><times id="idp28367104"/><cn id="idp28367232" type="integer">4</cn><apply id="idp28367760"><apply id="idp28367888"><csymbol id="idp28368016" cd="ambiguous">subscript</csymbol><int id="idp28368576"/><ci id="idp28368704">M</ci></apply><apply id="idp28368960"><times id="idp28369088"/><apply id="idp28369216"><csymbol id="idp28369344" cd="ambiguous">superscript</csymbol><apply id="idp28369904"><abs id="idp28370032"/><apply id="idp28370160"><ci id="idp28370288">∇</ci><ci id="idp28370576">v</ci></apply></apply><cn id="idp28370832" type="integer">2</cn></apply><apply id="idp28371360"><csymbol id="idp28371488" cd="ambiguous">superscript</csymbol><apply id="idp28372048"><abs id="idp28372176"/><apply id="idp28372304"><ci id="idp28372432">∇</ci><ci id="idp28372720">ϕ</ci></apply></apply><cn id="idp28373008" type="integer">2</cn></apply><apply id="idp28373536"><csymbol id="idp28373664" cd="ambiguous">superscript</csymbol><ci id="idp28374224">e</ci><apply id="idp28374480"><minus id="idp28374608"/><ci id="idp28374736">f</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp28374992" encoding="application/x-tex">\int _{{M}}\left|v_{{ij}}\right|^{{2}}e^{{-f}}\phi^{{2}}\leq 4\int _{{M}}\left|\nabla v\right|^{{2}}\left|\nabla\phi\right|^{{2}}e^{{-f}}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp28800976"><h4>Hit idp28800976</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 40</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/203/f080893.xhtml#idp28800976</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1167466(000082%) VariableMap:[f x 2, dx x 2, leq, int x 2, delta x 2, n x 2, +, (, ), ., , x 2, frac x 2, 2 x 4, 1, u x 2, nabla x 2, 4, R x 2, epsilon, \ x 16, left, _ x 4, ^ x 6, | x 6, right] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp28800976" alttext="\int _{{\R^{n}}}|\nabla u_{\delta}|^{2}\, dx\leq\left(\frac{1}{4}+\epsilon\right)\int _{{\R^{n}}}\frac{|\nabla f|^{2}}{f^{2}}|u_{\delta}|^{2}\, dx." display="block"><semantics id="idp28801856"><mrow id="idp28801984"><mrow id="idp28802112"><mrow id="idp28802240"><msub id="idp28802368"><mo id="idp28802496">∫</mo><msup id="idp28802752"><mi id="idp28802880">\mathbb{R}</mi><mi id="idp28803136">n</mi></msup></msub><mrow id="idp28803392"><msup id="idp28803520"><mrow id="idp28803648"><mo id="idp28803776" fence="true">|</mo><mrow id="idp28804304"><mo id="idp28804432">∇</mo><mo id="idp28804720">⁡</mo><msub id="idp28805008"><mi id="idp28805136">u</mi><mi id="idp28805392">δ</mi></msub></mrow><mo id="idp28805680" fence="true">|</mo></mrow><mn id="idp28806208">2</mn></msup><mo id="idp28806464">⁢</mo><mi id="idp28806752">d</mi><mo id="idp28807008">⁢</mo><mi id="idp28807296">x</mi></mrow></mrow><mo id="idp28807552">≤</mo><mrow id="idp28807840"><mrow id="idp28807968"><mo id="idp28808096">(</mo><mrow id="idp28808352"><mfrac id="idp28808480"><mn id="idp28808608">1</mn><mn id="idp28808864">4</mn></mfrac><mo id="idp28809120">+</mo><mi id="idp28809376">ϵ</mi></mrow><mo id="idp28809664">)</mo></mrow><mo id="idp28809920">⁢</mo><mrow id="idp28810208"><msub id="idp28810336"><mo id="idp28810464">∫</mo><msup id="idp28810752"><mi id="idp28810880">\mathbb{R}</mi><mi id="idp28811168">n</mi></msup></msub><mrow id="idp28811424"><mfrac id="idp28811552"><msup id="idp28811680"><mrow id="idp28811808"><mo id="idp28811936" fence="true">|</mo><mrow id="idp28812464"><mo id="idp28812592">∇</mo><mo id="idp28812880">⁡</mo><mi id="idp28813168">f</mi></mrow><mo id="idp28813424" fence="true">|</mo></mrow><mn id="idp28813952">2</mn></msup><msup id="idp28814208"><mi id="idp28814336">f</mi><mn id="idp28814592">2</mn></msup></mfrac><mo id="idp28814848">⁢</mo><msup id="idp28815136"><mrow id="idp28815264"><mo id="idp28815392" fence="true">|</mo><msub id="idp28815920"><mi id="idp28816048">u</mi><mi id="idp28816304">δ</mi></msub><mo id="idp28816592" fence="true">|</mo></mrow><mn id="idp28817120">2</mn></msup><mo id="idp28817376">⁢</mo><mi id="idp28817664">d</mi><mo id="idp28817920">⁢</mo><mi id="idp28818208">x</mi></mrow></mrow></mrow></mrow><mo id="idp28818464">.</mo></mrow><annotation-xml id="idp28818720" encoding="MathML-Content"><apply id="idp28819120"><leq id="idp28819248"/><apply id="idp28819376"><apply id="idp28819504"><csymbol id="idp28819632" cd="ambiguous">subscript</csymbol><int id="idp28820192"/><apply id="idp28820320"><csymbol id="idp28820448" cd="ambiguous">superscript</csymbol><ci id="idp28821008">\mathbb{R}</ci><ci id="idp28821296">n</ci></apply></apply><apply id="idp28821552"><times id="idp28821680"/><apply id="idp28821808"><csymbol id="idp28821936" cd="ambiguous">superscript</csymbol><apply id="idp28822496"><abs id="idp28822624"/><apply id="idp28822752"><ci id="idp28822880">∇</ci><apply id="idp28823168"><csymbol id="idp28823296" cd="ambiguous">subscript</csymbol><ci id="idp28823856">u</ci><ci id="idp28824112">δ</ci></apply></apply></apply><cn id="idp28824400" type="integer">2</cn></apply><ci id="idp28824928">d</ci><ci id="idp28825184">x</ci></apply></apply><apply id="idp28825440"><times id="idp28825568"/><apply id="idp28825696"><plus id="idp28825824"/><apply id="idp28825952"><divide id="idp28826080"/><cn id="idp28826208" type="integer">1</cn><cn id="idp28826736" type="integer">4</cn></apply><ci id="idp28827264">ϵ</ci></apply><apply id="idp28827552"><apply id="idp28827680"><csymbol id="idp28827808" cd="ambiguous">subscript</csymbol><int id="idp28828368"/><apply id="idp28828496"><csymbol id="idp28828624" cd="ambiguous">superscript</csymbol><ci id="idp28829184">\mathbb{R}</ci><ci id="idp28829472">n</ci></apply></apply><apply id="idp28829728"><times id="idp28829856"/><apply id="idp28829984"><divide id="idp28830112"/><apply id="idp28830240"><csymbol id="idp28830368" cd="ambiguous">superscript</csymbol><apply id="idp28830928"><abs id="idp28831056"/><apply id="idp28831184"><ci id="idp28831312">∇</ci><ci id="idp28831600">f</ci></apply></apply><cn id="idp28831856" type="integer">2</cn></apply><apply id="idp28832384"><csymbol id="idp28832512" cd="ambiguous">superscript</csymbol><ci id="idp28833072">f</ci><cn id="idp28833328" type="integer">2</cn></apply></apply><apply id="idp28833856"><csymbol id="idp28833984" cd="ambiguous">superscript</csymbol><apply id="idp28834544"><abs id="idp28834672"/><apply id="idp28834800"><csymbol id="idp28834928" cd="ambiguous">subscript</csymbol><ci id="idp28835488">u</ci><ci id="idp28835744">δ</ci></apply></apply><cn id="idp28836032" type="integer">2</cn></apply><ci id="idp28836560">d</ci><ci id="idp28836816">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp28837072" encoding="application/x-tex">\int _{{\R^{n}}}|\nabla u_{\delta}|^{2}\, dx\leq\left(\frac{1}{4}+\epsilon\right)\int _{{\R^{n}}}\frac{|\nabla f|^{2}}{f^{2}}|u_{\delta}|^{2}\, dx.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp328512"><h4>Hit idp328512</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 41</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/130/f051833.xhtml#idp328512</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1665377(000089%) VariableMap:[lower, M, by, x 3, TM, mbox, T, W x 15, nabla x 2, ] x 2, \ x 22, _ x 3, ^ x 5, X x 12, end, [ x 2, f x 6, g x 2, overline x 2, & x 4, otimes, a, * x 2, + x 3, rangle, ( x 16, langle, ) x 16, , x 6, and, frac x 3, - x 4, begin, 2 x 6, 1 x 3, quad, 6, eqref x 2, split x 2, | x 6, = x 4, eq] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp32798752" alttext="\begin{split}\langle X,\overline{\nabla}_{{W}}W^{{*}}\rangle _{{TM\otimes T^{{*}}M}}&=W(X(f))+g([X,W],W)-g(\overline{\nabla}_{{X}}W,W)\\ &=W(X(f))+[X,W](f)-\frac{1}{2}X(|W|^{{2}})\quad\mbox{by \eqref{lower} and \eqref{eq6a}}\\ &=W(X(f))+X(W(f))-W(X(f))-\frac{1}{2}X(|W|^{{2}})\\ &=\frac{1}{2}X(|W|^{{2}}),\end{split}" display="block"><semantics id="idp32798304"><mrow id="idp32798432"><mrow id="idp32798560"><mrow id="idp32799808"><msub id="idp32799936"><mrow id="idp32800064"><mo id="idp32800192">⟨</mo><mrow id="idp32800448"><mi id="idp32800576">X</mi><mo id="idp32800832">,</mo><mrow id="idp32801088"><msub id="idp32801216"><mover id="idp32801344" accent="true"><mo id="idp32801712">∇</mo><mo id="idp32801968">¯</mo></mover><mi id="idp32802224">W</mi></msub><mo id="idp32802480">⁢</mo><msup id="idp32802768"><mi id="idp32802896">W</mi><mo id="idp32803152">*</mo></msup></mrow></mrow><mo id="idp32803408">⟩</mo></mrow><mrow id="idp32803696"><mrow id="idp32803824"><mrow id="idp32803952"><mi id="idp32804080">T</mi><mo id="idp32804336">⁢</mo><mi id="idp32804624">M</mi></mrow><mo id="idp32804880">⊗</mo><msup id="idp32805168"><mi id="idp32805296">T</mi><mo id="idp32805552">*</mo></msup></mrow><mo id="idp32805808">⁢</mo><mi id="idp32806096">M</mi></mrow></msub><mo id="idp32806352">=</mo><mrow id="idp32806608"><mrow id="idp32806736"><mi id="idp32806864">W</mi><mo id="idp32807120">⁢</mo><mrow id="idp32807408"><mo id="idp32807536">(</mo><mrow id="idp32807792"><mi id="idp32807920">X</mi><mo id="idp32808176">⁢</mo><mrow id="idp32808464"><mo id="idp32808592">(</mo><mi id="idp32808848">f</mi><mo id="idp32809104">)</mo></mrow></mrow><mo id="idp32809360">)</mo></mrow></mrow><mo id="idp32809616">+</mo><mrow id="idp32809872"><mi id="idp32810000">g</mi><mo id="idp32810256">⁢</mo><mrow id="idp32810544"><mo id="idp32810672">(</mo><mrow id="idp32810928"><mrow id="idp32811056"><mo id="idp32811184">[</mo><mrow id="idp32811440"><mi id="idp32811568">X</mi><mo id="idp32811824">,</mo><mi id="idp32812080">W</mi></mrow><mo id="idp32812336">]</mo></mrow><mo id="idp32812592">,</mo><mi id="idp32812848">W</mi></mrow><mo id="idp32813104">)</mo></mrow></mrow><mo id="idp32813360">-</mo><mrow id="idp32813616"><mi id="idp32813744">g</mi><mo id="idp32814000">⁢</mo><mrow id="idp32814288"><mo id="idp32814416">(</mo><mrow id="idp32814672"><mrow id="idp32814800"><msub id="idp32814928"><mover id="idp32815056" accent="true"><mo id="idp32815456">∇</mo><mo id="idp32815744">¯</mo></mover><mi id="idp32816032">X</mi></msub><mo id="idp32816288">⁢</mo><mi id="idp32816576">W</mi></mrow><mo id="idp32816832">,</mo><mi id="idp32817088">W</mi></mrow><mo id="idp32817344">)</mo></mrow></mrow></mrow><mo 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id="idp32825536">⁢</mo><mrow id="idp32825824"><mo id="idp32825952">(</mo><msup id="idp32826208"><mrow id="idp32826336"><mo id="idp32826464" fence="true">|</mo><mi id="idp32826992">W</mi><mo id="idp32827248" fence="true">|</mo></mrow><mn id="idp32827776">2</mn></msup><mo id="idp32828032">)</mo></mrow></mrow></mrow></mrow><mo id="idp32828288" separator="true"> </mo><mrow id="idp32828848"><mrow id="idp32828976"><mtext id="idp32829104">by (</mtext><mtext id="idp32829392">2.1</mtext><mtext id="idp32829648">) and (</mtext><mtext id="idp32829936">6.3</mtext><mtext id="idp32830192">)</mtext></mrow><mo id="idp32830448">=</mo><mrow id="idp32830704"><mrow id="idp32830832"><mi id="idp32830960">W</mi><mo id="idp32831216">⁢</mo><mrow id="idp32831504"><mo id="idp32831632">(</mo><mrow id="idp32831888"><mi id="idp32832016">X</mi><mo id="idp32832272">⁢</mo><mrow id="idp32832560"><mo id="idp32832688">(</mo><mi id="idp32832944">f</mi><mo id="idp32833200">)</mo></mrow></mrow><mo id="idp32833456">)</mo></mrow></mrow><mo id="idp32833712">+</mo><mrow id="idp32833968"><mi id="idp32834096">X</mi><mo id="idp32834352">⁢</mo><mrow id="idp32834640"><mo id="idp32834768">(</mo><mrow id="idp32835024"><mi id="idp32835152">W</mi><mo id="idp32835408">⁢</mo><mrow id="idp32835696"><mo id="idp32835824">(</mo><mi id="idp32836080">f</mi><mo id="idp32836336">)</mo></mrow></mrow><mo id="idp32836592">)</mo></mrow></mrow><mo id="idp32836848">-</mo><mrow id="idp32837104"><mi id="idp32837232">W</mi><mo id="idp32837488">⁢</mo><mrow id="idp32837776"><mo id="idp32837904">(</mo><mrow id="idp32838160"><mi id="idp32838288">X</mi><mo id="idp32838544">⁢</mo><mrow id="idp32838832"><mo id="idp32838960">(</mo><mi id="idp32839216">f</mi><mo id="idp32839472">)</mo></mrow></mrow><mo id="idp32839728">)</mo></mrow></mrow><mo id="idp32839984">-</mo><mrow id="idp32840240"><mfrac id="idp32840368"><mn id="idp32840496">1</mn><mn id="idp32840752">2</mn></mfrac><mo id="idp32841008">⁢</mo><mi 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cd="ambiguous" name="formulae-sequence"/><apply id="idp32850080"><and id="idp32850208"/><apply id="idp32850336"><eq id="idp32850464"/><apply id="idp32850592"><csymbol id="idp32850720" cd="ambiguous">subscript</csymbol><apply id="idp32851280"><list id="idp32851408"/><ci id="idp32851536">X</ci><apply id="idp32851792"><times id="idp32851920"/><apply id="idp32852048"><csymbol id="idp32852176" cd="ambiguous">subscript</csymbol><apply id="idp32852736"><ci id="idp32852864">¯</ci><ci id="idp32853152">∇</ci></apply><ci id="idp32853440">W</ci></apply><apply id="idp32853696"><csymbol id="idp32853824" cd="ambiguous">superscript</csymbol><ci id="idp32854384">W</ci><times id="idp32854640"/></apply></apply></apply><apply id="idp32854768"><times id="idp32854896"/><apply id="idp32855024"><csymbol id="idp32855152" cd="latexml">tensor-product</csymbol><apply id="idp32855712"><times id="idp32855840"/><ci id="idp32855968">T</ci><ci id="idp32856224">M</ci></apply><apply id="idp32856480"><csymbol 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id="S6.Ex7.m1.sh2e.cmml">X</ci><ci id="S6.Ex7.m1.sh2f.cmml">f</ci></apply></apply><apply id="S6.Ex7.m1.sh2o.cmml"><times id="S6.Ex7.m1.sh2i.cmml"/><apply id="S6.Ex7.m1.sh2m.cmml"><interval closure="closed" id="S6.Ex7.m1.sh2j.cmml"/><ci id="S6.Ex7.m1.sh2k.cmml">X</ci><ci id="S6.Ex7.m1.sh2l.cmml">W</ci></apply><ci id="S6.Ex7.m1.sh2n.cmml">f</ci></apply></apply><apply id="S6.Ex7.m1.sh2ac.cmml"><times id="S6.Ex7.m1.sh2q.cmml"/><apply id="S6.Ex7.m1.sh2u.cmml"><divide id="S6.Ex7.m1.sh2r.cmml"/><cn type="integer" id="S6.Ex7.m1.sh2s.cmml">1</cn><cn type="integer" id="S6.Ex7.m1.sh2t.cmml">2</cn></apply><ci id="S6.Ex7.m1.sh2v.cmml">X</ci><apply id="S6.Ex7.m1.sh2ab.cmml"><csymbol cd="ambiguous" id="S6.Ex7.m1.sh2w.cmml">superscript</csymbol><apply id="S6.Ex7.m1.sh2z.cmml"><abs id="S6.Ex7.m1.sh2x.cmml"/><ci id="S6.Ex7.m1.sh2y.cmml">W</ci></apply><cn type="integer" id="S6.Ex7.m1.sh2aa.cmml">2</cn></apply></apply></apply></apply></apply><apply id="idp32891168"><and id="idp32891296"/><apply 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id="S6.Ex7.m1.sh3aj.cmml"><times id="S6.Ex7.m1.sh3x.cmml"/><apply id="S6.Ex7.m1.sh3ab.cmml"><divide id="S6.Ex7.m1.sh3y.cmml"/><cn type="integer" id="S6.Ex7.m1.sh3z.cmml">1</cn><cn type="integer" id="S6.Ex7.m1.sh3aa.cmml">2</cn></apply><ci id="S6.Ex7.m1.sh3ac.cmml">X</ci><apply id="S6.Ex7.m1.sh3ai.cmml"><csymbol cd="ambiguous" id="S6.Ex7.m1.sh3ad.cmml">superscript</csymbol><apply id="S6.Ex7.m1.sh3ag.cmml"><abs id="S6.Ex7.m1.sh3ae.cmml"/><ci id="S6.Ex7.m1.sh3af.cmml">W</ci></apply><cn type="integer" id="S6.Ex7.m1.sh3ah.cmml">2</cn></apply></apply></apply></apply><apply id="idp32910208"><eq id="idp32910336"/><share id="idp32910464" href="#S6.Ex7.m1.sh3.cmml"/><apply id="S6.Ex7.m1.sh4l.cmml"><times id="S6.Ex7.m1.sh4.cmml"/><apply id="S6.Ex7.m1.sh4d.cmml"><divide id="S6.Ex7.m1.sh4a.cmml"/><cn type="integer" id="S6.Ex7.m1.sh4b.cmml">1</cn><cn type="integer" id="S6.Ex7.m1.sh4c.cmml">2</cn></apply><ci id="S6.Ex7.m1.sh4e.cmml">X</ci><apply id="S6.Ex7.m1.sh4k.cmml"><csymbol cd="ambiguous" id="S6.Ex7.m1.sh4f.cmml">superscript</csymbol><apply id="S6.Ex7.m1.sh4i.cmml"><abs id="S6.Ex7.m1.sh4g.cmml"/><ci id="S6.Ex7.m1.sh4h.cmml">W</ci></apply><cn type="integer" id="S6.Ex7.m1.sh4j.cmml">2</cn></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp32917952" encoding="application/x-tex">\begin{split}\langle X,\overline{\nabla}_{{W}}W^{{*}}\rangle _{{TM\otimes T^{{*}}M}}&=W(X(f))+g([X,W],W)-g(\overline{\nabla}_{{X}}W,W)\\ &=W(X(f))+[X,W](f)-\frac{1}{2}X(|W|^{{2}})\quad\mbox{by \eqref{lower} and \eqref{eq6a}}\\ &=W(X(f))+X(W(f))-W(X(f))-\frac{1}{2}X(|W|^{{2}})\\ &=\frac{1}{2}X(|W|^{{2}}),\end{split}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp33982064"><h4>Hit idp33982064</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 42</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/130/f051833.xhtml#idp33982064</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1820755(000098%) VariableMap:[F x 2, b, leq, int x 3, +, M x 2, ( x 4, ) x 4, qquad x 2, 2 x 5, 0, t x 2, s, displaystyle, psi x 2, nabla x 2, \ x 15, left x 2, _ x 3, | x 4, ^ x 5, right x 2, ds, x x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp33982064" alttext="\displaystyle\qquad\qquad\leq\int _{{M}}\psi^{{2}}(t)\left|\nabla F(x)\right|^{{2}}+2{b^{{2}}}\int^{{t}}_{{0}}\int _{{M}}\left|\psi(s)\nabla F(x)\right|^{{2}}ds" display="inline"><semantics id="idp33982960"><mrow id="idp33983088"><none id="idp33983216"/><mo id="idp33983344">≤</mo><mrow id="idp33983600"><mrow id="idp33983728"><mstyle id="idp33983856" displaystyle="true"><msub id="idp33984224"><mo id="idp33984352">∫</mo><mi id="idp33984640">M</mi></msub></mstyle><mrow id="idp33984896"><msup id="idp33985024"><mi id="idp33985152">ψ</mi><mn id="idp33985440">2</mn></msup><mo id="idp33985696">⁢</mo><mrow id="idp33985984"><mo id="idp33986112">(</mo><mi id="idp33986368">t</mi><mo id="idp33986624">)</mo></mrow><mo id="idp33986880">⁢</mo><msup id="idp33987168"><mrow id="idp33987296"><mo id="idp33987424" fence="true">|</mo><mrow id="idp33987952"><mrow id="idp33988080"><mo id="idp33988208">∇</mo><mo id="idp33988496">⁡</mo><mi id="idp33988784">F</mi></mrow><mo id="idp33989040">⁢</mo><mrow id="idp33989328"><mo id="idp33989456">(</mo><mi id="idp33989712">x</mi><mo id="idp33989968">)</mo></mrow></mrow><mo id="idp33990224" fence="true">|</mo></mrow><mn id="idp33990752">2</mn></msup></mrow></mrow><mo id="idp33991008">+</mo><mrow id="idp33991264"><mn id="idp33991392">2</mn><mo id="idp33991648">⁢</mo><msup id="idp33991936"><mi id="idp33992064">b</mi><mn id="idp33992320">2</mn></msup><mo id="idp33992576">⁢</mo><mrow id="idp33992864"><mstyle id="idp33992992" displaystyle="true"><msubsup id="idp33993392"><mo id="idp33993520">∫</mo><mn id="idp33993808">0</mn><mi id="idp33994064">t</mi></msubsup></mstyle><mrow id="idp33994320"><mstyle id="idp33994448" displaystyle="true"><msub id="idp33994848"><mo id="idp33994976">∫</mo><mi id="idp33995264">M</mi></msub></mstyle><mrow id="idp33995520"><msup id="idp33995648"><mrow id="idp33995776"><mo id="idp33995904" fence="true">|</mo><mrow id="idp33996432"><mi id="idp33996560">ψ</mi><mo id="idp33996848">⁢</mo><mrow id="idp33997136"><mo id="idp33997264">(</mo><mi id="idp33997520">s</mi><mo id="idp33997776">)</mo></mrow><mo id="idp33998032">⁢</mo><mrow id="idp33998320"><mo id="idp33998448">∇</mo><mo id="idp33998736">⁡</mo><mi id="idp33999024">F</mi></mrow><mo id="idp33999280">⁢</mo><mrow id="idp33999568"><mo id="idp33999696">(</mo><mi id="idp33999952">x</mi><mo id="idp34000208">)</mo></mrow></mrow><mo id="idp34000464" fence="true">|</mo></mrow><mn id="idp34000992">2</mn></msup><mo id="idp34001248">⁢</mo><mi id="idp34001536">d</mi><mo id="idp34001792">⁢</mo><mi id="idp34002080">s</mi></mrow></mrow></mrow></mrow></mrow></mrow><annotation-xml id="idp34002336" encoding="MathML-Content"><apply id="idp34002736"><leq id="idp34002864"/><csymbol id="idp34002992" cd="latexml">absent</csymbol><apply id="idp34003552"><plus id="idp34003680"/><apply id="idp34003808"><apply id="idp34003936"><csymbol id="idp34004064" cd="ambiguous">subscript</csymbol><int id="idp34004624"/><ci id="idp34004752">M</ci></apply><apply id="idp34005008"><times id="idp34005136"/><apply id="idp34005264"><csymbol id="idp34005392" cd="ambiguous">superscript</csymbol><ci id="idp34005952">ψ</ci><cn id="idp34006240" type="integer">2</cn></apply><ci id="idp34006768">t</ci><apply id="idp34007024"><csymbol id="idp34007152" cd="ambiguous">superscript</csymbol><apply id="idp34007712"><abs id="idp34007840"/><apply id="idp34007968"><times id="idp34008096"/><apply id="idp34008224"><ci id="idp34008352">∇</ci><ci id="idp34008640">F</ci></apply><ci id="idp34008896">x</ci></apply></apply><cn id="idp34009152" type="integer">2</cn></apply></apply></apply><apply id="idp34009680"><times id="idp34009808"/><cn id="idp34009936" type="integer">2</cn><apply id="idp34010464"><csymbol id="idp34010592" cd="ambiguous">superscript</csymbol><ci id="idp34011152">b</ci><cn id="idp34011408" type="integer">2</cn></apply><apply id="idp34011936"><apply id="idp34012064"><csymbol id="idp34012192" cd="ambiguous">subscript</csymbol><apply id="idp34012752"><csymbol id="idp34012880" cd="ambiguous">superscript</csymbol><int id="idp34013440"/><ci id="idp34013568">t</ci></apply><cn id="idp34013824" type="integer">0</cn></apply><apply id="idp34014352"><apply id="idp34014480"><csymbol id="idp34014608" cd="ambiguous">subscript</csymbol><int id="idp34015168"/><ci id="idp34015296">M</ci></apply><apply id="idp34015552"><times id="idp34015680"/><apply id="idp34015808"><csymbol id="idp34015936" cd="ambiguous">superscript</csymbol><apply id="idp34016496"><abs id="idp34016624"/><apply id="idp34016752"><times id="idp34016880"/><ci id="idp34017008">ψ</ci><ci id="idp34017296">s</ci><apply id="idp34017552"><ci id="idp34017680">∇</ci><ci id="idp34017968">F</ci></apply><ci id="idp34018224">x</ci></apply></apply><cn id="idp34018480" type="integer">2</cn></apply><ci id="idp34019008">d</ci><ci id="idp34019264">s</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp34019520" encoding="application/x-tex">\displaystyle\qquad\qquad\leq\int _{{M}}\psi^{{2}}(t)\left|\nabla F(x)\right|^{{2}}+2{b^{{2}}}\int^{{t}}_{{0}}\int _{{M}}\left|\psi(s)\nabla F(x)\right|^{{2}}ds</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp6182384"><h4>Hit idp6182384</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 43</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/113/f044928.xhtml#idp6182384</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:756112(000088%) VariableMap:[limits x 2, dx, leq, int x 3, C, +, Omega x 2, ,, dot x 2, T, 2 x 2, dxdt, u x 2, 0, displaystyle, nabla, \ x 13, _ x 3, | x 4, ^ x 3, rho] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp6182384" alttext="\displaystyle\int\limits _{\Omega}\rho|\dot{u}|^{2}dx+\int^{T}_{0}\int\limits _{\Omega}|\nabla\dot{u}|^{2}dxdt\leq C," display="inline"><semantics id="idp6183232"><mrow id="idp6183360"><mrow id="idp6183488"><mrow id="idp6183616"><mrow id="idp6183744"><mstyle id="idp6183872" displaystyle="true"><munder id="idp6184240"><mo id="idp6184368" movablelimits="false">∫</mo><mi id="idp6184896" mathvariant="normal">Ω</mi></munder></mstyle><mrow id="idp6185456"><mi id="idp6185584">ρ</mi><mo id="idp6185872">⁢</mo><msup id="idp6186160"><mrow id="idp6186288"><mo id="idp6186416" fence="true">|</mo><mover id="idp6186944" accent="true"><mi id="idp6187344">u</mi><mo id="idp6187600">˙</mo></mover><mo id="idp6187888" fence="true">|</mo></mrow><mn id="idp6188416">2</mn></msup><mo id="idp6188672">⁢</mo><mi id="idp6188960">d</mi><mo id="idp6189216">⁢</mo><mi id="idp6189504">x</mi></mrow></mrow><mo id="idp6189760">+</mo><mrow id="idp6190016"><mstyle id="idp6190144" displaystyle="true"><msubsup id="idp6190544"><mo id="idp6190672">∫</mo><mn id="idp6190960">0</mn><mi id="idp6191216">T</mi></msubsup></mstyle><mrow id="idp6191472"><mstyle id="idp6191600" displaystyle="true"><munder id="idp6192000"><mo id="idp6192128" movablelimits="false">∫</mo><mi id="idp6192688" mathvariant="normal">Ω</mi></munder></mstyle><mrow id="idp6193248"><msup id="idp6193376"><mrow id="idp6193504"><mo id="idp6193632" fence="true">|</mo><mrow id="idp6194160"><mo id="idp6194288">∇</mo><mo id="idp6194576">⁡</mo><mover id="idp6194864" accent="true"><mi id="idp6195264">u</mi><mo id="idp6195520">˙</mo></mover></mrow><mo id="idp6195808" fence="true">|</mo></mrow><mn id="idp6196336">2</mn></msup><mo id="idp6196592">⁢</mo><mi id="idp6196880">d</mi><mo id="idp6197136">⁢</mo><mi id="idp6197424">x</mi><mo id="idp6197680">⁢</mo><mi id="idp6197968">d</mi><mo id="idp6198224">⁢</mo><mi id="idp6198512">t</mi></mrow></mrow></mrow></mrow><mo id="idp6198768">≤</mo><mi id="idp6199056">C</mi></mrow><mo id="idp6199312">,</mo></mrow><annotation-xml id="idp6199568" encoding="MathML-Content"><apply id="idp6199968"><leq id="idp6200096"/><apply id="idp6200224"><plus id="idp6200352"/><apply id="idp6200480"><apply id="idp6200608"><csymbol id="idp6200736" cd="ambiguous">subscript</csymbol><int id="idp6201296"/><ci id="idp6201424">Ω</ci></apply><apply id="idp6201712"><times id="idp6201840"/><ci id="idp6201968">ρ</ci><apply id="idp6202256"><csymbol id="idp6202384" cd="ambiguous">superscript</csymbol><apply id="idp6202944"><abs id="idp6203072"/><apply id="idp6203200"><ci id="idp6203328">˙</ci><ci id="idp6203616">u</ci></apply></apply><cn id="idp6203872" type="integer">2</cn></apply><ci id="idp6204400">d</ci><ci id="idp6204656">x</ci></apply></apply><apply id="idp6204912"><apply id="idp6205040"><csymbol id="idp6205168" cd="ambiguous">subscript</csymbol><apply id="idp6205728"><csymbol id="idp6205856" cd="ambiguous">superscript</csymbol><int id="idp6206416"/><ci id="idp6206544">T</ci></apply><cn id="idp6206800" type="integer">0</cn></apply><apply id="idp6207328"><apply id="idp6207456"><csymbol id="idp6207584" cd="ambiguous">subscript</csymbol><int id="idp6208144"/><ci id="idp6208272">Ω</ci></apply><apply id="idp6208560"><times id="idp6208688"/><apply id="idp6208816"><csymbol id="idp6208944" cd="ambiguous">superscript</csymbol><apply id="idp6209504"><abs id="idp6209632"/><apply id="idp6209760"><ci id="idp6209888">∇</ci><apply id="idp6210176"><ci id="idp6210304">˙</ci><ci id="idp6210592">u</ci></apply></apply></apply><cn id="idp6210848" type="integer">2</cn></apply><ci id="idp6211376">d</ci><ci id="idp6211632">x</ci><ci id="idp6211888">d</ci><ci id="idp6212144">t</ci></apply></apply></apply></apply><ci id="idp6212400">C</ci></apply></annotation-xml><annotation id="idp6212656" encoding="application/x-tex">\displaystyle\int\limits _{\Omega}\rho|\dot{u}|^{2}dx+\int^{T}_{0}\int\limits _{\Omega}|\nabla\dot{u}|^{2}dxdt\leq C,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp6231536"><h4>Hit idp6231536</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 44</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/19/f007372.xhtml#idp6231536</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:781907(000077%) VariableMap:[eta x 4, ln, dx x 2, leq, int x 2, C, n x 4, + x 2, ( x 2, ) x 2, Omega x 2, ,, 1, r, displaystyle x 2, nabla x 4, \ x 18, left, _ x 6, ^, | x 8, right] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 2 occurences for '^' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp6231536" alttext="{\displaystyle\int _{{\Omega}}}|\nabla\eta _{n}|\ln(1+|\nabla\eta _{n}|)dx\leq C{\displaystyle\int _{{\Omega}}}\left(|\nabla\eta _{n}|^{r}+|\nabla\eta _{n}|\right)dx," display="block"><semantics id="idp6232432"><mrow id="idp6232560"><mrow id="idp6232688"><mrow id="idp6232816"><msub id="idp6232944"><mo id="idp6233072">∫</mo><mi id="idp6233328" mathvariant="normal">Ω</mi></msub><mrow id="idp6233856"><mrow id="idp6233984"><mo id="idp6234112" fence="true">|</mo><mrow id="idp6234640"><mo id="idp6234768">∇</mo><mo id="idp6235056">⁡</mo><msub id="idp6235344"><mi id="idp6235472">η</mi><mi id="idp6235760">n</mi></msub></mrow><mo id="idp6236016" fence="true">|</mo></mrow><mo id="idp6236544">⁢</mo><mrow id="idp6236832"><mi id="idp6236960">ln</mi><mo id="idp6237216">⁡</mo><mrow id="idp6237504"><mo id="idp6237632">(</mo><mrow id="idp6237888"><mn id="idp6238016">1</mn><mo id="idp6238272">+</mo><mrow id="idp6238528"><mo id="idp6238656" fence="true">|</mo><mrow id="idp6239184"><mo id="idp6239312">∇</mo><mo id="idp6239600">⁡</mo><msub id="idp6239888"><mi id="idp6240016">η</mi><mi id="idp6240304">n</mi></msub></mrow><mo id="idp6240560" fence="true">|</mo></mrow></mrow><mo id="idp6241088">)</mo></mrow></mrow><mo id="idp6241344">⁢</mo><mi id="idp6241632">d</mi><mo id="idp6241888">⁢</mo><mi id="idp6242176">x</mi></mrow></mrow><mo id="idp6242432">≤</mo><mrow id="idp6242720"><mi id="idp6242848">C</mi><mo id="idp6243104">⁢</mo><mrow id="idp6243392"><msub id="idp6243520"><mo id="idp6243648">∫</mo><mi id="idp6243936" mathvariant="normal">Ω</mi></msub><mrow id="idp6244496"><mrow id="idp6244624"><mo id="idp6244752">(</mo><mrow id="idp6245008"><msup id="idp6245136"><mrow id="idp6245264"><mo id="idp6245392" fence="true">|</mo><mrow id="idp6245920"><mo id="idp6246048">∇</mo><mo id="idp6246336">⁡</mo><msub id="idp6246624"><mi id="idp6246752">η</mi><mi id="idp6247040">n</mi></msub></mrow><mo id="idp6247296" fence="true">|</mo></mrow><mi id="idp6247824">r</mi></msup><mo id="idp6248080">+</mo><mrow id="idp6248336"><mo id="idp6248464" fence="true">|</mo><mrow id="idp6248992"><mo id="idp6249120">∇</mo><mo id="idp6249408">⁡</mo><msub id="idp6249696"><mi id="idp6249824">η</mi><mi id="idp6250112">n</mi></msub></mrow><mo id="idp6250368" fence="true">|</mo></mrow></mrow><mo id="idp6250896">)</mo></mrow><mo id="idp6251152">⁢</mo><mi id="idp6251440">d</mi><mo id="idp6251696">⁢</mo><mi id="idp6251984">x</mi></mrow></mrow></mrow></mrow><mo id="idp6252240">,</mo></mrow><annotation-xml id="idp6252496" encoding="MathML-Content"><apply id="idp6252896"><leq id="idp6253024"/><apply id="idp6253152"><apply id="idp6253280"><csymbol id="idp6253408" cd="ambiguous">subscript</csymbol><int id="idp6253968"/><ci id="idp6254096">Ω</ci></apply><apply id="idp6254384"><times id="idp6254512"/><apply id="idp6254640"><abs id="idp6254768"/><apply id="idp6254896"><ci id="idp6255024">∇</ci><apply id="idp6255312"><csymbol id="idp6255440" cd="ambiguous">subscript</csymbol><ci id="idp6256000">η</ci><ci id="idp6256288">n</ci></apply></apply></apply><apply id="idp6256544"><ln id="idp6256672"/><apply id="idp6256800"><plus id="idp6256928"/><cn id="idp6257056" type="integer">1</cn><apply id="idp6257584"><abs id="idp6257712"/><apply id="idp6257840"><ci id="idp6257968">∇</ci><apply id="idp6258256"><csymbol id="idp6258384" cd="ambiguous">subscript</csymbol><ci id="idp6258944">η</ci><ci id="idp6259232">n</ci></apply></apply></apply></apply></apply><ci id="idp6259488">d</ci><ci id="idp6259744">x</ci></apply></apply><apply id="idp6260000"><times id="idp6260128"/><ci id="idp6260256">C</ci><apply id="idp6260512"><apply id="idp6260640"><csymbol id="idp6260768" cd="ambiguous">subscript</csymbol><int id="idp6261328"/><ci id="idp6261456">Ω</ci></apply><apply id="idp6261744"><times id="idp6261872"/><apply id="idp6262000"><plus id="idp6262128"/><apply id="idp6262256"><csymbol id="idp6262384" cd="ambiguous">superscript</csymbol><apply id="idp6262944"><abs id="idp6263072"/><apply id="idp6263200"><ci id="idp6263328">∇</ci><apply id="idp6263616"><csymbol id="idp6263744" cd="ambiguous">subscript</csymbol><ci id="idp6264304">η</ci><ci id="idp6264592">n</ci></apply></apply></apply><ci id="idp6264848">r</ci></apply><apply id="idp6265104"><abs id="idp6265232"/><apply id="idp6265360"><ci id="idp6265488">∇</ci><apply id="idp6265776"><csymbol id="idp6265904" cd="ambiguous">subscript</csymbol><ci id="idp6266464">η</ci><ci id="idp6266752">n</ci></apply></apply></apply></apply><ci id="idp6267008">d</ci><ci id="idp6267264">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp6267520" encoding="application/x-tex">{\displaystyle\int _{{\Omega}}}|\nabla\eta _{n}|\ln(1+|\nabla\eta _{n}|)dx\leq C{\displaystyle\int _{{\Omega}}}\left(|\nabla\eta _{n}|^{r}+|\nabla\eta _{n}|\right)dx,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp833216"><h4>Hit idp833216</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 45</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/16/f006068.xhtml#idp833216</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:98323(000008%) VariableMap:[dx x 3, H, nabla, \ x 16, _ x 4, ^ x 4, geq, int x 3, delta, +, ( x 2, Omega x 4, ) x 2, forall, in, /, , x 2, frac, 2 x 3, u x 4, 1 x 2, 0, displaystyle x 2, 4, | x 2, Lambda] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp833216" alttext="\displaystyle\int _{{\Omega}}|\nabla u|^{2}dx\geq\frac{1}{4}\displaystyle\int _{{\Omega}}(u/\delta)^{2}dx+\Lambda\int _{{\Omega}}u^{2}dx,\forall u\in H^{1}_{0}(\Omega)," display="block"><semantics id="idp834128"><mrow id="idp834256"><mrow id="idp834384"><mrow id="idp834512"><mrow id="idp834640"><msub id="idp834768"><mo id="idp834896">∫</mo><mi id="idp835152" mathvariant="normal">Ω</mi></msub><mrow id="idp835680"><msup id="idp835808"><mrow id="idp835936"><mo id="idp836064" fence="true">|</mo><mrow id="idp836592"><mo id="idp836720">∇</mo><mo id="idp837008">⁡</mo><mi id="idp837296">u</mi></mrow><mo id="idp837552" fence="true">|</mo></mrow><mn id="idp838080">2</mn></msup><mo id="idp838336">⁢</mo><mi id="idp838624">d</mi><mo id="idp838880">⁢</mo><mi id="idp839168">x</mi></mrow></mrow><mo id="idp839424">≥</mo><mrow id="idp839712"><mrow id="idp839840"><mfrac id="idp839968"><mn id="idp840096">1</mn><mn id="idp840352">4</mn></mfrac><mo id="idp840608">⁢</mo><mrow id="idp840896"><msub id="idp841024"><mo id="idp841152">∫</mo><mi id="idp841440" mathvariant="normal">Ω</mi></msub><mrow id="idp842000"><msup id="idp842128"><mrow id="idp842256"><mo id="idp842384">(</mo><mrow id="idp842640"><mi id="idp842768">u</mi><mo id="idp843024">/</mo><mi id="idp843280">δ</mi></mrow><mo id="idp843568">)</mo></mrow><mn id="idp843824">2</mn></msup><mo id="idp844080">⁢</mo><mi id="idp844368">d</mi><mo id="idp844624">⁢</mo><mi id="idp844912">x</mi></mrow></mrow></mrow><mo id="idp845168">+</mo><mrow id="idp845424"><mi id="idp845552" mathvariant="normal">Λ</mi><mo id="idp846112">⁢</mo><mrow id="idp846400"><msub id="idp846528"><mo id="idp846656">∫</mo><mi id="idp846944" mathvariant="normal">Ω</mi></msub><mrow id="idp847504"><msup id="idp847632"><mi id="idp847760">u</mi><mn id="idp848016">2</mn></msup><mo id="idp848272">⁢</mo><mi id="idp848560">d</mi><mo id="idp848816">⁢</mo><mi id="idp849104">x</mi></mrow></mrow></mrow></mrow></mrow><mo id="idp849360">,</mo><mrow id="idp849616"><mrow id="idp849744"><mo id="idp849872">∀</mo><mi id="idp850160">u</mi></mrow><mo id="idp850416">∈</mo><mrow id="idp850704"><msubsup id="idp850832"><mi id="idp850960">H</mi><mn id="idp851216">0</mn><mn id="idp851472">1</mn></msubsup><mo id="idp851728">⁢</mo><mrow id="idp852016"><mo id="idp852144">(</mo><mi id="idp852400" mathvariant="normal">Ω</mi><mo id="idp852960">)</mo></mrow></mrow></mrow></mrow><mo id="idp853216">,</mo></mrow><annotation-xml id="idp853472" encoding="MathML-Content"><apply id="idp853872"><csymbol id="idp854000" cd="ambiguous" name="formulae-sequence"/><apply id="idp854672"><geq id="idp854800"/><apply id="idp854928"><apply id="idp855056"><csymbol id="idp855184" cd="ambiguous">subscript</csymbol><int id="idp855744"/><ci id="idp855872">Ω</ci></apply><apply id="idp856160"><times id="idp856288"/><apply id="idp856416"><csymbol id="idp856544" cd="ambiguous">superscript</csymbol><apply id="idp857104"><abs id="idp857232"/><apply id="idp857360"><ci id="idp857488">∇</ci><ci id="idp857776">u</ci></apply></apply><cn id="idp858032" type="integer">2</cn></apply><ci id="idp858560">d</ci><ci id="idp858816">x</ci></apply></apply><apply id="idp859072"><plus id="idp859200"/><apply id="idp859328"><times id="idp859456"/><apply id="idp859584"><divide id="idp859712"/><cn id="idp859840" type="integer">1</cn><cn id="idp860368" type="integer">4</cn></apply><apply id="idp860896"><apply id="idp861024"><csymbol id="idp861152" cd="ambiguous">subscript</csymbol><int id="idp861712"/><ci id="idp861840">Ω</ci></apply><apply id="idp862128"><times id="idp862256"/><apply id="idp862384"><csymbol id="idp862512" cd="ambiguous">superscript</csymbol><apply id="idp863072"><divide id="idp863200"/><ci id="idp863328">u</ci><ci id="idp863584">δ</ci></apply><cn id="idp863872" type="integer">2</cn></apply><ci id="idp864400">d</ci><ci id="idp864656">x</ci></apply></apply></apply><apply id="idp864912"><times id="idp865040"/><ci id="idp865168">Λ</ci><apply id="idp865456"><apply id="idp865584"><csymbol id="idp865712" cd="ambiguous">subscript</csymbol><int id="idp866272"/><ci id="idp866400">Ω</ci></apply><apply id="idp866688"><times id="idp866816"/><apply id="idp866944"><csymbol id="idp867072" cd="ambiguous">superscript</csymbol><ci id="idp867632">u</ci><cn id="idp867888" type="integer">2</cn></apply><ci id="idp868416">d</ci><ci id="idp868672">x</ci></apply></apply></apply></apply></apply><apply id="idp868928"><in id="idp869056"/><apply id="idp869184"><csymbol id="idp869312" cd="latexml">for-all</csymbol><ci id="idp869872">u</ci></apply><apply id="idp870128"><times id="idp870256"/><apply id="idp870384"><csymbol id="idp870512" cd="ambiguous">subscript</csymbol><apply id="idp871072"><csymbol id="idp871200" cd="ambiguous">superscript</csymbol><ci id="idp871760">H</ci><cn id="idp872016" type="integer">1</cn></apply><cn id="idp872544" type="integer">0</cn></apply><ci id="idp873072">Ω</ci></apply></apply></apply></annotation-xml><annotation id="idp873360" encoding="application/x-tex">\displaystyle\int _{{\Omega}}|\nabla u|^{2}dx\geq\frac{1}{4}\displaystyle\int _{{\Omega}}(u/\delta)^{2}dx+\Lambda\int _{{\Omega}}u^{2}dx,\forall u\in H^{1}_{0}(\Omega),</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp90880"><h4>Hit idp90880</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 2</li> <li>Formulasearchengine rank: 46</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/203/f080893.xhtml#idp90880</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:107650(000008%) VariableMap:[0, \ x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 2 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 2</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp907312" alttext="\{ 0\}" display="inline"><semantics id="idp908032"><mrow id="idp908160"><mo id="idp908288">{</mo><mn id="idp908544">0</mn><mo id="idp908800">}</mo></mrow><annotation-xml id="idp909056" encoding="MathML-Content"><apply id="idp909424"><set id="idp909552"/><cn id="idp909680" type="integer">0</cn></apply></annotation-xml><annotation id="idp910208" encoding="application/x-tex">\{ 0\}</annotation></semantics></math> <br /> End of MathML <br /> .</div> <h3>Detailed results for reviewer score 0</h3> <div id="idp8511248"><h4>Hit idp8511248</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 3</li> <li>Formulasearchengine score: 12146</li> <li>Reference to collection: _PREFIX_/206/f082385.xhtml#idp8511248</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\begin{array}[]{lcl}\displaystyle\frac{J^{{\prime}}(r)}{J(r)}&=&\displaystyle\frac{\int _{{\partial B_{r}(0)}}|\nabla u_{1}|^{2}d\sigma}{\int _{{B_{r}(0)}}|\nabla u_{1}|^{2}dx}+\displaystyle\frac{\int _{{\partial B_{r}(0)}}|\nabla u_{2}|^{2}d\sigma}{\int _{{B_{r}(0)}}|\nabla u_{2}|^{2}dx}-\frac{4}{r}\\ &\geq&\displaystyle\frac{\left(\int _{{\partial B_{r}(0)}}(u_{1})_{\theta}^{2}d\sigma\right)^{{1/2}}}{\left(\int _{{\partial B_{r}(0)}}u_{1}^{2}d\sigma\right)^{{1/2}}}+\displaystyle\frac{\left(\int _{{\partial B_{r}(0)}}(u_{2})^{2}_{\theta}d\sigma\right)^{{1/2}}}{\left(\int _{{\partial B_{r}(0)}}u_{2}^{2}d\sigma\right)^{{1/2}}}-\frac{2}{r}.\end{array}$ at pos:1094731(79%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.984375 * TOKEN_SCORE[d] + 1.99609375 * TOKEN_SCORE[int] + 1.0 * TOKEN_SCORE[leq] + 1.75 * TOKEN_SCORE[+] + 1.9999847412109375 * TOKEN_SCORE[(] + 1.9999847412109375 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.99609375 * TOKEN_SCORE[0] + 1.9375 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999999999999998 * TOKEN_SCORE[\] + 1.9999999850988388 * TOKEN_SCORE[_] + 1.99609375 * TOKEN_SCORE[|] + 1.9998779296875 * TOKEN_SCORE[^] =+100.0+0.0+1.984375*0.158568544552516+1.99609375*0.279351653691737+1.0*2.71610004241772+1.75*0.0160883895861106+1.9999847412109375*0.00418257496311516+1.9999847412109375*0.00417601612706465+1.0*4.28403503219485+1.99609375*0.0483458611105983+1.9375*6.39416349760091+1.0*0.855340292115138+1.9999999999999998*5.92879328325965E-4+1.9999999850988388*0.00257082788077282+1.99609375*0.0975909302497933+1.9998779296875*0.00338742677192689 = 12146.57157968752' final score ~ 12146 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp8511248" alttext="\begin{array}[]{lcl}\displaystyle\frac{J^{{\prime}}(r)}{J(r)}&=&\displaystyle\frac{\int _{{\partial B_{r}(0)}}|\nabla u_{1}|^{2}d\sigma}{\int _{{B_{r}(0)}}|\nabla u_{1}|^{2}dx}+\displaystyle\frac{\int _{{\partial B_{r}(0)}}|\nabla u_{2}|^{2}d\sigma}{\int _{{B_{r}(0)}}|\nabla u_{2}|^{2}dx}-\frac{4}{r}\\ &\geq&\displaystyle\frac{\left(\int _{{\partial B_{r}(0)}}(u_{1})_{\theta}^{2}d\sigma\right)^{{1/2}}}{\left(\int _{{\partial B_{r}(0)}}u_{1}^{2}d\sigma\right)^{{1/2}}}+\displaystyle\frac{\left(\int _{{\partial B_{r}(0)}}(u_{2})^{2}_{\theta}d\sigma\right)^{{1/2}}}{\left(\int _{{\partial B_{r}(0)}}u_{2}^{2}d\sigma\right)^{{1/2}}}-\frac{2}{r}.\end{array}" display="block"><semantics id="idp8510368"><mtable id="idp8510496" rowspacing="0.2ex" columnspacing="0.4em"><mtr id="idp8511104"><mtd id="idp8512640" columnalign="left"><mfrac id="idp8513040"><mrow id="idp8513168"><msup id="idp8513296"><mi id="idp8513424">J</mi><mo id="idp8513680">′</mo></msup><mo id="idp8513968">⁢</mo><mrow id="idp8514256"><mo id="idp8514384">(</mo><mi id="idp8514640">r</mi><mo id="idp8514896">)</mo></mrow></mrow><mrow id="idp8515152"><mi id="idp8515280">J</mi><mo id="idp8515536">⁢</mo><mrow id="idp8515824"><mo 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id="idp8540560">B</mi><mi id="idp8540816">r</mi></msub><mo id="idp8541072">⁢</mo><mrow id="idp8541360"><mo id="idp8541488">(</mo><mn id="idp8541744">0</mn><mo id="idp8542000">)</mo></mrow></mrow></msub><mrow id="idp8542256"><msup id="idp8542384"><mrow id="idp8542512"><mo id="idp8542640" fence="true">|</mo><mrow id="idp8543168"><mo id="idp8543296">∇</mo><mo id="idp8543584">⁡</mo><msub id="idp8543872"><mi id="idp8544000">u</mi><mn id="idp8544256">2</mn></msub></mrow><mo id="idp8544512" fence="true">|</mo></mrow><mn id="idp8545040">2</mn></msup><mo id="idp8545296">⁢</mo><mi id="idp8545584">d</mi><mo id="idp8545840">⁢</mo><mi id="idp8546128">x</mi></mrow></mrow></mfrac><mo id="idp8546384">-</mo><mfrac id="idp8546640"><mn id="idp8546768">4</mn><mi id="idp8547024">r</mi></mfrac></mrow></mtd></mtr><mtr id="idp8547280"><mtd id="idp8547408"/><mtd id="idp8547536" columnalign="center"><mo id="idp8547936">≥</mo></mtd><mtd id="idp8548224" columnalign="left"><mrow id="idp8548624"><mrow 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id="idp8556560">/</mo><mn id="idp8556816">2</mn></mrow></msup><msup id="idp8557072"><mrow id="idp8557200"><mo id="idp8557328">(</mo><mrow id="idp8557584"><msub id="idp8557712"><mo id="idp8557840">∫</mo><mrow id="idp8558128"><mrow id="idp8558256"><mo id="idp8558384">∂</mo><mo id="idp8558672">⁡</mo><msub id="idp8558960"><mi id="idp8559088">B</mi><mi id="idp8559344">r</mi></msub></mrow><mo id="idp8559600">⁢</mo><mrow id="idp8559888"><mo id="idp8560016">(</mo><mn id="idp8560272">0</mn><mo id="idp8560528">)</mo></mrow></mrow></msub><mrow id="idp8560784"><msubsup id="idp8560912"><mi id="idp8561040">u</mi><mn id="idp8561296">1</mn><mn id="idp8561552">2</mn></msubsup><mo id="idp8561808">⁢</mo><mi id="idp8562096">d</mi><mo id="idp8562352">⁢</mo><mi id="idp8562640">σ</mi></mrow></mrow><mo id="idp8562928">)</mo></mrow><mrow id="idp8563184"><mn id="idp8563312">1</mn><mo id="idp8563568">/</mo><mn id="idp8563824">2</mn></mrow></msup></mfrac><mo id="idp8564080">+</mo><mfrac id="idp8564336"><msup 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id="idp8572272">2</mn></mrow></msup><msup id="idp8572528"><mrow id="idp8572656"><mo id="idp8572784">(</mo><mrow id="idp8573040"><msub id="idp8573168"><mo id="idp8573296">∫</mo><mrow id="idp8573584"><mrow id="idp8573712"><mo id="idp8573840">∂</mo><mo id="idp8574128">⁡</mo><msub id="idp8574416"><mi id="idp8574544">B</mi><mi id="idp8574800">r</mi></msub></mrow><mo id="idp8575056">⁢</mo><mrow id="idp8575344"><mo id="idp8575472">(</mo><mn id="idp8575728">0</mn><mo id="idp8575984">)</mo></mrow></mrow></msub><mrow id="idp8576240"><msubsup id="idp8576368"><mi id="idp8576496">u</mi><mn id="idp8576752">2</mn><mn id="idp8577008">2</mn></msubsup><mo id="idp8577264">⁢</mo><mi id="idp8577552">d</mi><mo id="idp8577808">⁢</mo><mi id="idp8578096">σ</mi></mrow></mrow><mo id="idp8578384">)</mo></mrow><mrow id="idp8578640"><mn id="idp8578768">1</mn><mo id="idp8579024">/</mo><mn id="idp8579280">2</mn></mrow></msup></mfrac><mo id="idp8579536">-</mo><mfrac id="idp8579792"><mn id="idp8579920">2</mn><mi id="idp8580176">r</mi></mfrac></mrow><mo id="idp8580432">.</mo></mrow></mtd></mtr></mtable><annotation-xml id="idp8580688" encoding="MathML-Content"><mtext id="idp8581088">⁢J′r⁢Jr=-+∫⁢∂Br0⁢∇u12dσ∫⁢Br0⁢∇u12dx∫⁢∂Br0⁢∇u22dσ∫⁢Br0⁢∇u22dx4r≥-+∫⁢∂Br0⁢u1θ2dσ/12∫⁢∂Br0⁢u12dσ/12∫⁢∂Br0⁢u22θdσ/12∫⁢∂Br0⁢u22dσ/122r</mtext></annotation-xml><annotation id="idp8581568" encoding="application/x-tex">\begin{array}[]{lcl}\displaystyle\frac{J^{{\prime}}(r)}{J(r)}&=&\displaystyle\frac{\int _{{\partial B_{r}(0)}}|\nabla u_{1}|^{2}d\sigma}{\int _{{B_{r}(0)}}|\nabla u_{1}|^{2}dx}+\displaystyle\frac{\int _{{\partial B_{r}(0)}}|\nabla u_{2}|^{2}d\sigma}{\int _{{B_{r}(0)}}|\nabla u_{2}|^{2}dx}-\frac{4}{r}\\ &\geq&\displaystyle\frac{\left(\int _{{\partial B_{r}(0)}}(u_{1})_{\theta}^{2}d\sigma\right)^{{1/2}}}{\left(\int _{{\partial B_{r}(0)}}u_{1}^{2}d\sigma\right)^{{1/2}}}+\displaystyle\frac{\left(\int _{{\partial B_{r}(0)}}(u_{2})^{2}_{\theta}d\sigma\right)^{{1/2}}}{\left(\int _{{\partial B_{r}(0)}}u_{2}^{2}d\sigma\right)^{{1/2}}}-\frac{2}{r}.\end{array}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp10149248"><h4>Hit idp10149248</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 5</li> <li>Formulasearchengine score: 12140</li> <li>Reference to collection: _PREFIX_/206/f082385.xhtml#idp10149248</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\begin{array}[]{lcl}\displaystyle\frac{J^{{\prime}}(1)}{J(1)}&=&\displaystyle\frac{\int _{{\partial B_{1}(0)}}|\nabla u_{1}|^{2}d\sigma}{\int _{{B_{1}(0)}}|\nabla u_{1}|^{2}dx}+\displaystyle\frac{\int _{{\partial B_{1}(0)}}|\nabla u_{2}|^{2}d\sigma}{\int _{{B_{1}(0)}}|\nabla u_{2}|^{2}dx}-4.\end{array}$ at pos:1306701(95%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.75 * TOKEN_SCORE[d] + 1.9375 * TOKEN_SCORE[int] + 1.0 * TOKEN_SCORE[leq] + 1.5 * TOKEN_SCORE[+] + 1.984375 * TOKEN_SCORE[(] + 1.984375 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.9375 * TOKEN_SCORE[0] + 1.9375 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999995231628418 * TOKEN_SCORE[\] + 1.999755859375 * TOKEN_SCORE[_] + 1.99609375 * TOKEN_SCORE[|] + 1.96875 * TOKEN_SCORE[^] =+100.0+0.0+1.75*0.158568544552516+1.9375*0.279351653691737+1.0*2.71610004241772+1.5*0.0160883895861106+1.984375*0.00418257496311516+1.984375*0.00417601612706465+1.0*4.28403503219485+1.9375*0.0483458611105983+1.9375*6.39416349760091+1.0*0.855340292115138+1.9999995231628418*5.92879328325965E-4+1.999755859375*0.00257082788077282+1.99609375*0.0975909302497933+1.96875*0.00338742677192689 = 12140.509162367714' final score ~ 12140 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp10149248" alttext="\begin{array}[]{lcl}\displaystyle\frac{J^{{\prime}}(1)}{J(1)}&=&\displaystyle\frac{\int _{{\partial B_{1}(0)}}|\nabla u_{1}|^{2}d\sigma}{\int _{{B_{1}(0)}}|\nabla u_{1}|^{2}dx}+\displaystyle\frac{\int _{{\partial B_{1}(0)}}|\nabla u_{2}|^{2}d\sigma}{\int _{{B_{1}(0)}}|\nabla u_{2}|^{2}dx}-4.\end{array}" display="block"><semantics id="idp10148800"><mtable id="idp10148928" rowspacing="0.2ex" columnspacing="0.4em"><mtr id="idp10150656"><mtd id="idp10150784" columnalign="left"><mfrac id="idp10151152"><mrow id="idp10151280"><msup id="idp10151408"><mi id="idp10151536">J</mi><mo id="idp10151792">′</mo></msup><mo id="idp10152048">⁢</mo><mrow id="idp10152336"><mo id="idp10152464">(</mo><mn id="idp10152720">1</mn><mo id="idp10152976">)</mo></mrow></mrow><mrow id="idp10153232"><mi id="idp10153360">J</mi><mo id="idp10153616">⁢</mo><mrow id="idp10153904"><mo id="idp10154032">(</mo><mn id="idp10154288">1</mn><mo id="idp10154544">)</mo></mrow></mrow></mfrac></mtd><mtd id="idp10154800" columnalign="center"><mo id="idp10155200">=</mo></mtd><mtd id="idp10155456" columnalign="left"><mrow id="idp10155856"><mfrac id="idp10155984"><mrow id="idp10156112"><msub 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id="idp10172240">1</mn></msub></mrow><mo id="idp10172496">⁢</mo><mrow id="idp10172784"><mo id="idp10172912">(</mo><mn id="idp10173168">0</mn><mo id="idp10173424">)</mo></mrow></mrow></msub><mrow id="idp10173680"><msup id="idp10173808"><mrow id="idp10173936"><mo id="idp10174064" fence="true">|</mo><mrow id="idp10174592"><mo id="idp10174720">∇</mo><mo id="idp10175008">⁡</mo><msub id="idp10175296"><mi id="idp10175424">u</mi><mn id="idp10175680">2</mn></msub></mrow><mo id="idp10175936" fence="true">|</mo></mrow><mn id="idp10176464">2</mn></msup><mo id="idp10176720">⁢</mo><mi id="idp10177008">d</mi><mo id="idp10177264">⁢</mo><mi id="idp10177552">σ</mi></mrow></mrow><mrow id="idp10177840"><msub id="idp10177968"><mo id="idp10178096">∫</mo><mrow id="idp10178384"><msub id="idp10178512"><mi id="idp10178640">B</mi><mn id="idp10178896">1</mn></msub><mo id="idp10179152">⁢</mo><mrow id="idp10179440"><mo id="idp10179568">(</mo><mn id="idp10179824">0</mn><mo id="idp10180080">)</mo></mrow></mrow></msub><mrow id="idp10180336"><msup id="idp10180464"><mrow id="idp10180592"><mo id="idp10180720" fence="true">|</mo><mrow id="idp10181248"><mo id="idp10181376">∇</mo><mo id="idp10181664">⁡</mo><msub id="idp10181952"><mi id="idp10182080">u</mi><mn id="idp10182336">2</mn></msub></mrow><mo id="idp10182592" fence="true">|</mo></mrow><mn id="idp10183120">2</mn></msup><mo id="idp10183376">⁢</mo><mi id="idp10183664">d</mi><mo id="idp10183920">⁢</mo><mi id="idp10184208">x</mi></mrow></mrow></mfrac><mo id="idp10184464">-</mo><mn id="idp10184720">4.</mn></mrow></mtd></mtr></mtable><annotation-xml id="idp10184976" encoding="MathML-Content"><mtext id="idp10185376">⁢J′1⁢J1=-+∫⁢∂B10⁢∇u12dσ∫⁢B10⁢∇u12dx∫⁢∂B10⁢∇u22dσ∫⁢B10⁢∇u22dx4.</mtext></annotation-xml><annotation id="idp10185760" encoding="application/x-tex">\begin{array}[]{lcl}\displaystyle\frac{J^{{\prime}}(1)}{J(1)}&=&\displaystyle\frac{\int _{{\partial B_{1}(0)}}|\nabla u_{1}|^{2}d\sigma}{\int _{{B_{1}(0)}}|\nabla u_{1}|^{2}dx}+\displaystyle\frac{\int _{{\partial B_{1}(0)}}|\nabla u_{2}|^{2}d\sigma}{\int _{{B_{1}(0)}}|\nabla u_{2}|^{2}dx}-4.\end{array}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp20569264"><h4>Hit idp20569264</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 6</li> <li>Formulasearchengine score: 12099</li> <li>Reference to collection: _PREFIX_/206/f082086.xhtml#idp20569264</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $\mathcal{D}:=\frac{1}{L_{x}L_{y}L_{z}}\int _{{0}}^{{L_{x}}}\int _{{-1}}^{{1}}\int _{{0}}^{{L_{z}}}\left(|\nabla u|^{2}+|\nabla v|^{2}+|\nabla w|^{2}\right)\;{\rm d}x\,{\rm d}y\,{\rm d}z\,,$ at pos:129227(35%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.875 * TOKEN_SCORE[d] + 1.875 * TOKEN_SCORE[int] + 1.0 * TOKEN_SCORE[leq] + 1.75 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.75 * TOKEN_SCORE[0] + 1.875 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9999923706054688 * TOKEN_SCORE[\] + 1.99609375 * TOKEN_SCORE[_] + 1.984375 * TOKEN_SCORE[|] + 1.984375 * TOKEN_SCORE[^] =+100.0+0.0+1.875*0.158568544552516+1.875*0.279351653691737+1.0*2.71610004241772+1.75*0.0160883895861106+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*4.28403503219485+1.75*0.0483458611105983+1.875*6.39416349760091+1.0*0.855340292115138+1.9999923706054688*5.92879328325965E-4+1.99609375*0.00257082788077282+1.984375*0.0975909302497933+1.984375*0.00338742677192689 = 12099.762641660536' final score ~ 12099 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp20569264" alttext="\mathcal{D}:=\frac{1}{L_{x}L_{y}L_{z}}\int _{{0}}^{{L_{x}}}\int _{{-1}}^{{1}}\int _{{0}}^{{L_{z}}}\left(|\nabla u|^{2}+|\nabla v|^{2}+|\nabla w|^{2}\right)\;{\rm d}x\,{\rm d}y\,{\rm d}z\,," display="block"><semantics id="idp20570192"><mrow id="idp20570320"><mrow id="idp20570448"><mi id="idp20570576" mathvariant="script">D</mi><mo id="idp20571072">:=</mo><mrow id="idp20571328"><mfrac id="idp20571456"><mn id="idp20571584">1</mn><mrow id="idp20571840"><msub id="idp20571968"><mi id="idp20572272">L</mi><mi id="idp20572528">x</mi></msub><mo id="idp20572784">⁢</mo><msub id="idp20573040"><mi id="idp20573168">L</mi><mi id="idp20573424">y</mi></msub><mo id="idp20573680">⁢</mo><msub id="idp20573968"><mi id="idp20574096">L</mi><mi id="idp20574352">z</mi></msub></mrow></mfrac><mo id="idp20574608">⁢</mo><mrow id="idp20574896"><msubsup id="idp20575024"><mo id="idp20575152">∫</mo><mn id="idp20575440">0</mn><msub id="idp20575696"><mi id="idp20575824">L</mi><mi id="idp20576080">x</mi></msub></msubsup><mrow id="idp20576336"><msubsup id="idp20576464"><mo id="idp20576592">∫</mo><mrow id="idp20576880"><mo id="idp20577008">-</mo><mn id="idp37664">1</mn></mrow><mn id="idp20577936">1</mn></msubsup><mrow id="idp20578192"><msubsup id="idp20578320"><mo id="idp20578448">∫</mo><mn id="idp20578704">0</mn><msub id="idp20578960"><mi id="idp20579088">L</mi><mi id="idp20579344">z</mi></msub></msubsup><mrow id="idp20579600"><mrow id="idp20579728"><mo id="idp20579856">(</mo><mrow id="idp20580112"><msup id="idp20580240"><mrow id="idp20580368"><mo id="idp20580496" fence="true">|</mo><mrow id="idp20581024"><mo id="idp20581152">∇</mo><mo id="idp20581440">⁡</mo><mi id="idp20581728">u</mi></mrow><mo id="idp20581984" fence="true">|</mo></mrow><mn id="idp20582512">2</mn></msup><mo id="idp20582768">+</mo><msup id="idp20583024"><mrow id="idp20583152"><mo id="idp20583280" fence="true">|</mo><mrow id="idp20583808"><mo id="idp20583936">∇</mo><mo id="idp20584224">⁡</mo><mi id="idp20584512">v</mi></mrow><mo id="idp20584768" fence="true">|</mo></mrow><mn id="idp20585296">2</mn></msup><mo id="idp20585552">+</mo><msup id="idp20585808"><mrow id="idp20585936"><mo id="idp20586064" fence="true">|</mo><mrow id="idp20586592"><mo id="idp20586720">∇</mo><mo id="idp20587008">⁡</mo><mi id="idp20587296">w</mi></mrow><mo id="idp20587552" fence="true">|</mo></mrow><mn id="idp20588080">2</mn></msup></mrow><mo id="idp20588336">)</mo></mrow><mo id="idp20588592">⁢</mo><mi id="idp20588880" mathvariant="normal">d</mi><mo id="idp20589408">⁢</mo><mpadded id="idp20589696" width="+1.666667pt"><mi id="idp20590096">x</mi></mpadded><mo id="idp20590352">⁢</mo><mi id="idp20590640" mathvariant="normal">d</mi><mo id="idp20591168">⁢</mo><mpadded id="idp20591456" width="+1.666667pt"><mi id="idp20591856">y</mi></mpadded><mo id="idp20592112">⁢</mo><mi id="idp20592400" mathvariant="normal">d</mi><mo id="idp20592928">⁢</mo><mpadded id="idp20593216" width="+1.666667pt"><mi id="idp20593616">z</mi></mpadded></mrow></mrow></mrow></mrow></mrow></mrow><mo id="idp20593872">,</mo></mrow><annotation-xml id="idp20594128" encoding="MathML-Content"><apply id="idp20594528"><csymbol id="idp20594656" cd="latexml">assign</csymbol><ci id="idp20595216">D</ci><apply id="idp20595472"><times id="idp20595600"/><apply id="idp20595728"><divide id="idp20595856"/><cn id="idp20595984" type="integer">1</cn><apply id="idp20596512"><times id="idp20596640"/><apply id="idp20596768"><csymbol id="idp20596896" cd="ambiguous">subscript</csymbol><ci id="idp20597456">L</ci><ci id="idp20597712">x</ci></apply><apply id="idp20597968"><csymbol id="idp20598096" cd="ambiguous">subscript</csymbol><ci id="idp20598656">L</ci><ci id="idp20598912">y</ci></apply><apply id="idp20599168"><csymbol id="idp20599296" cd="ambiguous">subscript</csymbol><ci id="idp20599856">L</ci><ci id="idp20600112">z</ci></apply></apply></apply><apply id="idp20600368"><apply id="idp20600496"><csymbol id="idp20600624" cd="ambiguous">superscript</csymbol><apply id="idp20601184"><csymbol id="idp20601312" cd="ambiguous">subscript</csymbol><int id="idp20601872"/><cn id="idp20602000" type="integer">0</cn></apply><apply id="idp20602528"><csymbol id="idp20602656" cd="ambiguous">subscript</csymbol><ci id="idp20603216">L</ci><ci id="idp20603472">x</ci></apply></apply><apply id="idp20603728"><apply id="idp20603856"><csymbol id="idp20603984" cd="ambiguous">superscript</csymbol><apply id="idp20604544"><csymbol id="idp20604672" cd="ambiguous">subscript</csymbol><int id="idp20605232"/><apply id="idp20605360"><minus id="idp20605488"/><cn id="idp20605616" type="integer">1</cn></apply></apply><cn id="idp20606144" type="integer">1</cn></apply><apply id="idp20606672"><apply id="idp20606800"><csymbol id="idp20606928" cd="ambiguous">superscript</csymbol><apply id="idp20607488"><csymbol id="idp20607616" cd="ambiguous">subscript</csymbol><int id="idp20608176"/><cn id="idp20608304" type="integer">0</cn></apply><apply id="idp20608832"><csymbol id="idp20608960" cd="ambiguous">subscript</csymbol><ci id="idp20609520">L</ci><ci id="idp20609776">z</ci></apply></apply><apply id="idp20610032"><times id="idp20610160"/><apply id="idp20610288"><plus id="idp20610416"/><apply id="idp20610544"><csymbol id="idp20610672" cd="ambiguous">superscript</csymbol><apply id="idp20611232"><abs id="idp20611360"/><apply id="idp20611488"><ci id="idp20611616">∇</ci><ci id="idp20611904">u</ci></apply></apply><cn id="idp20612160" type="integer">2</cn></apply><apply id="idp20612688"><csymbol id="idp20612816" cd="ambiguous">superscript</csymbol><apply id="idp20613376"><abs id="idp20613504"/><apply id="idp20613632"><ci id="idp20613760">∇</ci><ci id="idp20614048">v</ci></apply></apply><cn id="idp20614304" type="integer">2</cn></apply><apply id="idp20614832"><csymbol id="idp20614960" cd="ambiguous">superscript</csymbol><apply id="idp20615520"><abs id="idp20615648"/><apply id="idp20615776"><ci id="idp20615904">∇</ci><ci id="idp20616192">w</ci></apply></apply><cn id="idp20616448" type="integer">2</cn></apply></apply><ci id="idp20616976">d</ci><ci id="idp20617232">x</ci><ci id="idp20617488">d</ci><ci id="idp20617744">y</ci><ci id="idp20618000">d</ci><ci id="idp20618256">z</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp20618512" encoding="application/x-tex">\mathcal{D}:=\frac{1}{L_{x}L_{y}L_{z}}\int _{{0}}^{{L_{x}}}\int _{{-1}}^{{1}}\int _{{0}}^{{L_{z}}}\left(|\nabla u|^{2}+|\nabla v|^{2}+|\nabla w|^{2}\right)\;{\rm d}x\,{\rm d}y\,{\rm d}z\,,</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp21821328"><h4>Hit idp21821328</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 13</li> <li>Formulasearchengine score: 11972</li> <li>Reference to collection: _PREFIX_/203/f080815.xhtml#idp21821328</li> </ul><blockcode linenumbers="off" title="justification"> found all required tokens in TeX $d_{t}\leq e^{{\int _{{t_{0}}}^{t}\frac{\sup _{{M_{s}}}R}{\arrowvert\nabla f\arrowvert^{2}(s)}ds}}d_{{t_{0}}},$ at pos:279371(27%) Scoringfunction: ' + TeX_HIT_SCORE + NO_TEXT_SCORE + 1.75 * TOKEN_SCORE[d] + 1.5 * TOKEN_SCORE[int] + 1.5 * TOKEN_SCORE[leq] + 1.0 * TOKEN_SCORE[+] + 1.5 * TOKEN_SCORE[(] + 1.5 * TOKEN_SCORE[)] + 1.0 * TOKEN_SCORE[neq] + 1.75 * TOKEN_SCORE[0] + 1.5 * TOKEN_SCORE[nabla] + 1.0 * TOKEN_SCORE[q] + 1.9921875 * TOKEN_SCORE[\] + 1.9921875 * TOKEN_SCORE[_] + 1.0 * TOKEN_SCORE[|] + 1.875 * TOKEN_SCORE[^] =+100.0+0.0+1.75*0.158568544552516+1.5*0.279351653691737+1.5*2.71610004241772+1.0*0.0160883895861106+1.5*0.00418257496311516+1.5*0.00417601612706465+1.0*4.28403503219485+1.75*0.0483458611105983+1.5*6.39416349760091+1.0*0.855340292115138+1.9921875*5.92879328325965E-4+1.9921875*0.00257082788077282+1.0*0.0975909302497933+1.875*0.00338742677192689 = 11972.476965441017' final score ~ 11972 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp21821328" alttext="d_{t}\leq e^{{\int _{{t_{0}}}^{t}\frac{\sup _{{M_{s}}}R}{\arrowvert\nabla f\arrowvert^{2}(s)}ds}}d_{{t_{0}}}," display="block"><semantics id="idp21822176"><mrow id="idp21822304"><mrow id="idp21822432"><msub id="idp21822560"><mi id="idp21822688">d</mi><mi id="idp21822944">t</mi></msub><mo id="idp21823200">≤</mo><mrow id="idp21823456"><msup id="idp21823584"><mi id="idp21823712">e</mi><mrow id="idp21823968"><msubsup id="idp21824096"><mo id="idp21824224">∫</mo><msub id="idp21824480"><mi id="idp21824608">t</mi><mn id="idp21824864">0</mn></msub><mi id="idp21825120">t</mi></msubsup><mrow id="idp21825376"><mfrac id="idp21825504"><mrow id="idp21825632"><msub id="idp21825760"><mo id="idp21825888">sup</mo><msub id="idp21826144"><mi id="idp21826272">M</mi><mi id="idp21826528">s</mi></msub></msub><mo id="idp21826784">⁡</mo><mi id="idp21827072">R</mi></mrow><mrow id="idp21827328"><msup id="idp21827456"><mrow id="idp21827584"><mo id="idp21827712" fence="true">|</mo><mrow id="idp21828240"><mo id="idp21828368">∇</mo><mo id="idp21828656">⁡</mo><mi id="idp21828944">f</mi></mrow><mo id="idp21829200" fence="true">|</mo></mrow><mn id="idp21829728">2</mn></msup><mo id="idp21829984">⁢</mo><mrow id="idp21830272"><mo id="idp21830400">(</mo><mi id="idp21830656">s</mi><mo id="idp21830912">)</mo></mrow></mrow></mfrac><mo id="idp21831168">⁢</mo><mi id="idp21831456">d</mi><mo id="idp21831712">⁢</mo><mi id="idp21832000">s</mi></mrow></mrow></msup><mo id="idp21832256">⁢</mo><msub id="idp21832544"><mi id="idp21832672">d</mi><msub id="idp21832928"><mi id="idp21833056">t</mi><mn id="idp21833312">0</mn></msub></msub></mrow></mrow><mo id="idp21833568">,</mo></mrow><annotation-xml id="idp21833824" encoding="MathML-Content"><apply id="idp21834224"><leq id="idp21834352"/><apply id="idp21834480"><csymbol id="idp21834608" cd="ambiguous">subscript</csymbol><ci id="idp21835168">d</ci><ci id="idp21835424">t</ci></apply><apply id="idp21835680"><times id="idp21835808"/><apply id="idp21835936"><csymbol id="idp21836064" cd="ambiguous">superscript</csymbol><ci id="idp21836624">e</ci><apply id="idp21836880"><apply id="idp21837008"><csymbol id="idp21837136" cd="ambiguous">superscript</csymbol><apply id="idp21837696"><csymbol id="idp21837824" cd="ambiguous">subscript</csymbol><int id="idp21838384"/><apply id="idp21838512"><csymbol id="idp21838640" cd="ambiguous">subscript</csymbol><ci id="idp21839200">t</ci><cn id="idp21839456" type="integer">0</cn></apply></apply><ci id="idp21839984">t</ci></apply><apply id="idp21840240"><times id="idp21840368"/><apply id="idp21840496"><divide id="idp21840624"/><apply id="idp21840752"><apply id="idp21840880"><csymbol id="idp21841008" cd="ambiguous">subscript</csymbol><csymbol id="idp21841568" cd="latexml">supremum</csymbol><apply id="idp21842128"><csymbol id="idp21842256" cd="ambiguous">subscript</csymbol><ci id="idp21842816">M</ci><ci id="idp21843072">s</ci></apply></apply><ci id="idp21843328">R</ci></apply><apply id="idp21843584"><times id="idp21843712"/><apply id="idp21843840"><csymbol id="idp21843968" cd="ambiguous">superscript</csymbol><apply id="idp21844528"><abs id="idp21844656"/><apply id="idp21844784"><ci id="idp21844912">∇</ci><ci id="idp21845200">f</ci></apply></apply><cn id="idp21845456" type="integer">2</cn></apply><ci id="idp21845984">s</ci></apply></apply><ci id="idp21846240">d</ci><ci id="idp21846496">s</ci></apply></apply></apply><apply id="idp21846752"><csymbol id="idp21846880" cd="ambiguous">subscript</csymbol><ci id="idp21847440">d</ci><apply id="idp21847696"><csymbol id="idp21847824" cd="ambiguous">subscript</csymbol><ci id="idp21848384">t</ci><cn id="idp21848640" type="integer">0</cn></apply></apply></apply></apply></annotation-xml><annotation id="idp21849168" encoding="application/x-tex">d_{t}\leq e^{{\int _{{t_{0}}}^{t}\frac{\sup _{{M_{s}}}R}{\arrowvert\nabla f\arrowvert^{2}(s)}ds}}d_{{t_{0}}},</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="id121336"><h4>Hit id121336</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 47</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/81/f032345.xhtml#id121336</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1030999(000050%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id121336" display="block"><m:semantics id="id121339"><m:mrow id="id121340"><m:mrow id="id121341"><m:mrow id="id121342"><m:mi id="id121343">cos</m:mi><m:mo id="id121345">⁡</m:mo><m:msub id="id121348"><m:mi id="id121349">χ</m:mi><m:mrow id="id121351"><m:mover id="id121352" accent="true"><m:mi id="id121356">i</m:mi><m:mo id="id121358">~</m:mo></m:mover><m:mo id="id121360">⁢</m:mo><m:mover id="id121362" accent="true"><m:mi id="id121366">k</m:mi><m:mo id="id121368">~</m:mo></m:mover></m:mrow></m:msub></m:mrow><m:mo id="id121370">=</m:mo><m:mrow id="id121372"><m:mn id="id121373">1</m:mn><m:mo id="id121375">-</m:mo><m:mrow id="id121377"><m:mn id="id121378">2</m:mn><m:mo id="id121380">⁢</m:mo><m:msub id="id121383"><m:mi id="id121384">Y</m:mi><m:mrow id="id121386"><m:mrow id="id121387"><m:mover id="id121388" accent="true"><m:mi id="id121392">i</m:mi><m:mo id="id121394">~</m:mo></m:mover><m:mo id="id121396">⁢</m:mo><m:mover id="id121398" accent="true"><m:mi id="id121402">k</m:mi><m:mo id="id121404">~</m:mo></m:mover></m:mrow><m:mo id="id121406">,</m:mo><m:mi id="id121408">Q</m:mi></m:mrow></m:msub></m:mrow></m:mrow></m:mrow><m:mo id="id121410">.</m:mo></m:mrow><m:annotation-xml id="id121412" encoding="MathML-Content"><m:apply id="id121416"><m:eq id="id121417"/><m:apply id="id121418"><m:cos id="id121419"/><m:apply id="id121420"><m:csymbol id="id121421" cd="ambiguous">subscript</m:csymbol><m:ci id="id121426">χ</m:ci><m:apply id="id121428"><m:times id="id121429"/><m:apply id="id121430"><m:ci id="id121431">~</m:ci><m:ci id="id121433">i</m:ci></m:apply><m:apply id="id121435"><m:ci id="id121436">~</m:ci><m:ci id="id121439">k</m:ci></m:apply></m:apply></m:apply></m:apply><m:apply id="id121441"><m:minus id="id121442"/><m:cn id="id121443">1</m:cn><m:apply id="id121445"><m:times id="id121446"/><m:cn id="id121447">2</m:cn><m:apply id="id121449"><m:csymbol id="id121450" cd="ambiguous">subscript</m:csymbol><m:ci id="id121455">Y</m:ci><m:apply id="id121457"><m:list id="id121458"/><m:apply id="id121459"><m:times id="id121460"/><m:apply id="id121461"><m:ci id="id121462">~</m:ci><m:ci id="id121465">i</m:ci></m:apply><m:apply id="id121467"><m:ci id="id121468">~</m:ci><m:ci id="id121470">k</m:ci></m:apply></m:apply><m:ci id="id121472">Q</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id129515"><h4>Hit id129515</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 48</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/225/f089692.xhtml#id129515</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1195892(000077%) VariableMap:[f x 2, g, overline, C x 2, n x 3, * x 3, (, ), \ x 3, _ x 5, cal x 2, ^ x 3, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 3 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id129515" alttext="{\cal C}_{{\overline{f}_{n}^{*}}}=g_{n}^{*}({\cal C}_{{f_{n}^{*}}})" display="inline"><m:semantics id="id129521"><m:mrow id="id129522"><m:msub id="id129523"><m:mi id="id129524" mathvariant="script">C</m:mi><m:msubsup id="id129528"><m:mover id="id129529" accent="true"><m:mi id="id129533">f</m:mi><m:mo id="id129535">¯</m:mo></m:mover><m:mi id="id129537">n</m:mi><m:mo id="id129539">*</m:mo></m:msubsup></m:msub><m:mo id="id129541">=</m:mo><m:mrow id="id129544"><m:msubsup id="id129545"><m:mi id="id129546">g</m:mi><m:mi id="id129548">n</m:mi><m:mo id="id129550">*</m:mo></m:msubsup><m:mo id="id129552">⁢</m:mo><m:mfenced id="id129554" open="(" close=")"><m:msub id="id129560"><m:mi id="id129561" mathvariant="script">C</m:mi><m:msubsup id="id129565"><m:mi id="id129566">f</m:mi><m:mi id="id129568">n</m:mi><m:mo id="id129570">*</m:mo></m:msubsup></m:msub></m:mfenced></m:mrow></m:mrow><m:annotation-xml id="id129572" encoding="MathML-Content"><m:apply id="id129576"><m:eq id="id129577"/><m:apply id="id129578"><m:csymbol id="id129579" cd="ambiguous">subscript</m:csymbol><m:ci id="id129584">C</m:ci><m:apply id="id129586"><m:csymbol id="id129587" cd="ambiguous">superscript</m:csymbol><m:apply id="id129592"><m:csymbol id="id129593" cd="ambiguous">subscript</m:csymbol><m:apply id="id129597"><m:ci id="id129598">¯</m:ci><m:ci id="id129601">f</m:ci></m:apply><m:ci id="id129603">n</m:ci></m:apply><m:times id="id129605"/></m:apply></m:apply><m:apply id="id129606"><m:times id="id129607"/><m:apply id="id129608"><m:csymbol id="id129609" cd="ambiguous">superscript</m:csymbol><m:apply id="id129614"><m:csymbol id="id129615" cd="ambiguous">subscript</m:csymbol><m:ci id="id129620">g</m:ci><m:ci id="id129622">n</m:ci></m:apply><m:times id="id129624"/></m:apply><m:apply id="id129625"><m:csymbol id="id129626" cd="ambiguous">subscript</m:csymbol><m:ci id="id129631">C</m:ci><m:apply id="id129633"><m:csymbol id="id129634" cd="ambiguous">superscript</m:csymbol><m:apply id="id129639"><m:csymbol id="id129640" cd="ambiguous">subscript</m:csymbol><m:ci id="id129644">f</m:ci><m:ci id="id129646">n</m:ci></m:apply><m:times id="id129649"/></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id129650" encoding="application/x-tex">{\cal C}_{{\overline{f}_{n}^{*}}}=g_{n}^{*}({\cal C}_{{f_{n}^{*}}})</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id53746"><h4>Hit id53746</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 49</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/84/f033435.xhtml#id53746</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:6820(000002%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id53746" display="block"><m:semantics id="id53749"><m:mrow id="id53751"><m:mi id="id53752">S</m:mi><m:mo id="id53754">=</m:mo><m:mrow id="id53757"><m:mo id="id53758">∫</m:mo><m:msup id="id53760"><m:mi id="id53761">d</m:mi><m:mn id="id53763">4</m:mn></m:msup><m:mo id="id53765">⁢</m:mo><m:mi id="id53768">x</m:mi><m:mo id="id52801">⁢</m:mo><m:mfenced id="id52804" open="[" close="]"><m:mrow id="id52809"><m:mrow id="id52810"><m:mfrac id="id52811"><m:mn id="id52814">1</m:mn><m:mn id="id52816">2</m:mn></m:mfrac><m:mo id="id52818">⁢</m:mo><m:msup id="id52820"><m:mfenced id="id52821" open="(" close=")"><m:mrow id="id52826"><m:mo id="id53734">∂</m:mo><m:mo id="id52833">⁡</m:mo><m:mi id="id53976">ϕ</m:mi></m:mrow></m:mfenced><m:mn id="id53979">2</m:mn></m:msup></m:mrow><m:mo id="id53981">-</m:mo><m:mrow id="id53983"><m:mfrac id="id53984"><m:mi id="id53985">λ</m:mi><m:mn id="id53987">4</m:mn></m:mfrac><m:mo id="id53989">⁢</m:mo><m:msup id="id53992"><m:mi id="id53993">ϕ</m:mi><m:mn id="id53995">4</m:mn></m:msup></m:mrow></m:mrow></m:mfenced></m:mrow></m:mrow><m:annotation-xml id="id53997" encoding="MathML-Content"><m:apply id="id54001"><m:eq id="id54002"/><m:ci id="id54003">S</m:ci><m:apply id="id54005"><m:int id="id54006"/><m:apply id="id54007"><m:times id="id54008"/><m:apply id="id54009"><m:csymbol id="id54010" cd="ambiguous">superscript</m:csymbol><m:ci id="id54015">d</m:ci><m:cn id="id54017">4</m:cn></m:apply><m:ci id="id54019">x</m:ci><m:apply id="id54021"><m:minus id="id54022"/><m:apply id="id54023"><m:times id="id54024"/><m:apply id="id54026"><m:divide id="id54027"/><m:cn id="id54028">1</m:cn><m:cn id="id54030">2</m:cn></m:apply><m:apply id="id54032"><m:csymbol id="id54033" cd="ambiguous">superscript</m:csymbol><m:apply id="id54038"><m:partialdiff id="id54039"/><m:ci id="id54040">ϕ</m:ci></m:apply><m:cn id="id54042">2</m:cn></m:apply></m:apply><m:apply id="id54044"><m:times id="id54045"/><m:apply id="id54046"><m:divide id="id54048"/><m:ci id="id54049">λ</m:ci><m:cn id="id54051">4</m:cn></m:apply><m:apply id="id54053"><m:csymbol id="id54054" cd="ambiguous">superscript</m:csymbol><m:ci id="id54059">ϕ</m:ci><m:cn id="id54061">4</m:cn></m:apply></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id54191"><h4>Hit id54191</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 50</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/123/f049074.xhtml#id54191</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:11223(000004%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id54191" display="inline"><m:semantics id="id54194"><m:mrow id="id54195"><m:mrow id="id54196"><m:mi id="id54197">S</m:mi><m:mo id="id54199">=</m:mo><m:mrow id="id54202"><m:mo id="id54203">-</m:mo><m:mrow id="id54205"><m:mstyle id="id54206" displaystyle="true"><m:mfrac id="id54209"><m:mn id="id54210">1</m:mn><m:mn id="id54212">4</m:mn></m:mfrac></m:mstyle><m:mo id="id54214">⁢</m:mo><m:mrow id="id54217"><m:mo id="id54218">∫</m:mo><m:msup id="id54220"><m:mi id="id54221">d</m:mi><m:mn id="id54224">3</m:mn></m:msup><m:mo id="id54226">⁢</m:mo><m:mi id="id54228">x</m:mi><m:mo id="id54230">⁢</m:mo><m:mi id="id54233">tr</m:mi><m:mo id="id54235">⁢</m:mo><m:msub id="id54237"><m:mi id="id54238">F</m:mi><m:mrow id="id54240"><m:mi id="id54241">m</m:mi><m:mo id="id54244">⁢</m:mo><m:mi id="id54246">n</m:mi></m:mrow></m:msub><m:mo id="id54248">⁢</m:mo><m:msup id="id54250"><m:mi id="id54252">F</m:mi><m:mrow id="id54254"><m:mi id="id54255">m</m:mi><m:mo id="id54257">⁢</m:mo><m:mi id="id54259">n</m:mi></m:mrow></m:msup></m:mrow></m:mrow></m:mrow></m:mrow><m:mo id="id54261">,</m:mo></m:mrow><m:annotation-xml id="id54264" encoding="MathML-Content"><m:apply id="id54267"><m:eq id="id54268"/><m:ci id="id54269">S</m:ci><m:apply id="id54271"><m:minus id="id54272"/><m:apply id="id54273"><m:times id="id54274"/><m:apply id="id54275"><m:divide id="id54276"/><m:cn id="id54278">1</m:cn><m:cn id="id54280">4</m:cn></m:apply><m:apply id="id54282"><m:int id="id54283"/><m:apply id="id54284"><m:times id="id54285"/><m:apply id="id54286"><m:csymbol id="id54287" cd="ambiguous">superscript</m:csymbol><m:ci id="id54292">d</m:ci><m:cn id="id54294">3</m:cn></m:apply><m:ci id="id54296">x</m:ci><m:ci id="id54298">tr</m:ci><m:apply id="id54300"><m:csymbol id="id54301" cd="ambiguous">subscript</m:csymbol><m:ci id="id54306">F</m:ci><m:apply id="id54308"><m:times id="id54311"/><m:ci id="id54312">m</m:ci><m:ci id="id54314">n</m:ci></m:apply></m:apply><m:apply id="id54316"><m:csymbol id="id54317" cd="ambiguous">superscript</m:csymbol><m:ci id="id54322">F</m:ci><m:apply id="id54324"><m:times id="id54325"/><m:ci id="id54326">m</m:ci><m:ci id="id54328">n</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id54417"><h4>Hit id54417</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 51</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/12/f004730.xhtml#id54417</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:13718(000005%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id54417" display="block"><m:semantics id="id54420"><m:mrow id="id54421"><m:mrow id="id54422"><m:mrow id="id54423"><m:mrow id="id54424"><m:mfenced id="id54425" open="(" close=")"><m:mrow id="id54430"><m:msubsup id="id54432"><m:mo id="id54433">∂</m:mo><m:mn id="id54435">0</m:mn><m:mn id="id54437">2</m:mn></m:msubsup><m:mo id="id54439">-</m:mo><m:msubsup id="id54441"><m:mo id="id54442">∂</m:mo><m:mn id="id54445">1</m:mn><m:mn id="id54447">2</m:mn></m:msubsup></m:mrow></m:mfenced><m:mo id="id54449">⁢</m:mo><m:mi id="id54452">q</m:mi><m:mo id="id54454">⁢</m:mo><m:mfenced id="id54456" open="(" close=")"><m:mi id="id54461">X</m:mi></m:mfenced></m:mrow><m:mo id="id54463">+</m:mo><m:mrow id="id54465"><m:mi id="id54466" mathvariant="normal">Λ</m:mi><m:mo id="id54471">⁢</m:mo><m:msup id="id54474"><m:mi id="id54475">e</m:mi><m:mrow id="id54477"><m:mi id="id54478">q</m:mi><m:mo id="id54480">⁢</m:mo><m:mfenced id="id54482" open="(" close=")"><m:mi id="id54487">X</m:mi></m:mfenced></m:mrow></m:msup></m:mrow></m:mrow><m:mo id="id54490">=</m:mo><m:mn id="id54492">0</m:mn></m:mrow><m:mo id="id54494">,</m:mo></m:mrow><m:annotation-xml id="id54496" encoding="MathML-Content"><m:apply id="id54499"><m:eq id="id54500"/><m:apply id="id54501"><m:plus id="id54502"/><m:apply id="id54504"><m:times id="id54505"/><m:apply id="id54506"><m:minus id="id54507"/><m:apply id="id54508"><m:csymbol id="id54509" cd="ambiguous">subscript</m:csymbol><m:apply id="id54514"><m:csymbol id="id54515" cd="ambiguous">superscript</m:csymbol><m:partialdiff id="id54519"/><m:cn id="id54520">2</m:cn></m:apply><m:cn id="id54522">0</m:cn></m:apply><m:apply id="id54525"><m:csymbol id="id54526" cd="ambiguous">subscript</m:csymbol><m:apply id="id54530"><m:csymbol id="id54531" cd="ambiguous">superscript</m:csymbol><m:partialdiff id="id54536"/><m:cn id="id54537">2</m:cn></m:apply><m:cn id="id54539">1</m:cn></m:apply></m:apply><m:ci id="id54541">q</m:ci><m:ci id="id54544">X</m:ci></m:apply><m:apply id="id54546"><m:times id="id54547"/><m:ci id="id54548">Λ</m:ci><m:apply id="id54550"><m:csymbol id="id54551" cd="ambiguous">superscript</m:csymbol><m:ci id="id54556">e</m:ci><m:apply id="id54558"><m:times id="id54559"/><m:ci id="id54560">q</m:ci><m:ci id="id54562">X</m:ci></m:apply></m:apply></m:apply></m:apply><m:cn id="id54564">0</m:cn></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id54778"><h4>Hit id54778</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 52</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/193/f076870.xhtml#id54778</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:21698(000003%) VariableMap:[3, 0, A x 2, B x 2, alpha x 5, sum, \ x 6, _ x 3, ^ x 3, = x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 6 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id54778" alttext="A_{{\alpha}}B^{{\alpha}}=\sum _{{\alpha=0}}^{{3}}A_{{\alpha}}B^{{\alpha}}" display="block"><m:semantics id="id54784"><m:mrow id="id54786"><m:mrow id="id54787"><m:msub id="id54788"><m:mi id="id54789">A</m:mi><m:mi id="id54791">α</m:mi></m:msub><m:mo id="id54793">⁢</m:mo><m:msup id="id54796"><m:mi id="id54797">B</m:mi><m:mi id="id54799">α</m:mi></m:msup></m:mrow><m:mo id="id54801">=</m:mo><m:mrow id="id54803"><m:mover id="id54804"><m:munder id="id54806"><m:mo id="id54807" movablelimits="false">∑</m:mo><m:mrow id="id54811"><m:mi id="id54812">α</m:mi><m:mo id="id54815" movablelimits="false">=</m:mo><m:mn id="id54819">0</m:mn></m:mrow></m:munder><m:mn id="id54821">3</m:mn></m:mover><m:msub id="id54823"><m:mi id="id54824">A</m:mi><m:mi id="id54827">α</m:mi></m:msub><m:mo id="id54829">⁢</m:mo><m:msup id="id54831"><m:mi id="id54832">B</m:mi><m:mi id="id54835">α</m:mi></m:msup></m:mrow></m:mrow><m:annotation-xml id="id54837" encoding="MathML-Content"><m:apply id="id54840"><m:eq id="id54841"/><m:apply id="id54842"><m:times id="id54844"/><m:apply id="id54845"><m:csymbol id="id54846" cd="ambiguous">subscript</m:csymbol><m:ci id="id54850">A</m:ci><m:ci id="id54852">α</m:ci></m:apply><m:apply id="id54855"><m:csymbol id="id54856" cd="ambiguous">superscript</m:csymbol><m:ci id="id54861">B</m:ci><m:ci id="id54863">α</m:ci></m:apply></m:apply><m:apply id="id54865"><m:apply id="id54866"><m:csymbol id="id54867" cd="ambiguous">superscript</m:csymbol><m:apply id="id54872"><m:csymbol id="id54873" cd="ambiguous">subscript</m:csymbol><m:sum id="id54878"/><m:apply id="id54879"><m:eq id="id54881"/><m:ci id="id54882">α</m:ci><m:cn id="id54885" type="integer">0</m:cn></m:apply></m:apply><m:cn id="id54889" type="integer">3</m:cn></m:apply><m:apply id="id54894"><m:times id="id54895"/><m:apply id="id54896"><m:csymbol id="id54897" cd="ambiguous">subscript</m:csymbol><m:ci id="id54901">A</m:ci><m:ci id="id54904">α</m:ci></m:apply><m:apply id="id54906"><m:csymbol id="id54907" cd="ambiguous">superscript</m:csymbol><m:ci id="id54912">B</m:ci><m:ci id="id54914">α</m:ci></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id54916" encoding="application/x-tex">A_{{\alpha}}B^{{\alpha}}=\sum _{{\alpha=0}}^{{3}}A_{{\alpha}}B^{{\alpha}}</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id56024"><h4>Hit id56024</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 53</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/39/f015551.xhtml#id56024</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:40037(000010%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id56024" display="block"><m:semantics id="id56027"><m:mrow id="id56028"><m:mrow id="id56030"><m:mrow id="id56031"><m:msubsup id="id56032"><m:mi id="id56033">E</m:mi><m:mi id="id56035">a</m:mi><m:mi id="id56037">A</m:mi></m:msubsup><m:mo id="id56039">⁢</m:mo><m:msubsup id="id56042"><m:mi id="id56043">E</m:mi><m:mi id="id56045">b</m:mi><m:mi id="id56047">B</m:mi></m:msubsup><m:mo id="id56049">⁢</m:mo><m:msup id="id56052"><m:mi id="id56053">δ</m:mi><m:mrow id="id56055"><m:mi id="id56056">a</m:mi><m:mo id="id56058">⁢</m:mo><m:mi id="id56061">b</m:mi></m:mrow></m:msup></m:mrow><m:mo id="id56063">=</m:mo><m:msup id="id56065"><m:mi id="id56066">G</m:mi><m:mrow id="id56068"><m:mi id="id56069">A</m:mi><m:mo id="id56072">⁢</m:mo><m:mi id="id56074">B</m:mi></m:mrow></m:msup></m:mrow><m:mo id="id56076">,</m:mo></m:mrow><m:annotation-xml id="id56078" encoding="MathML-Content"><m:apply id="id56082"><m:eq id="id56083"/><m:apply id="id56084"><m:times id="id56085"/><m:apply id="id56086"><m:csymbol id="id56087" cd="ambiguous">subscript</m:csymbol><m:apply id="id56092"><m:csymbol id="id56093" cd="ambiguous">superscript</m:csymbol><m:ci id="id56097">E</m:ci><m:ci id="id56099">A</m:ci></m:apply><m:ci id="id56102">a</m:ci></m:apply><m:apply id="id56104"><m:csymbol id="id56105" cd="ambiguous">subscript</m:csymbol><m:apply id="id56109"><m:csymbol id="id56110" cd="ambiguous">superscript</m:csymbol><m:ci id="id56115">E</m:ci><m:ci id="id56117">B</m:ci></m:apply><m:ci id="id56119">b</m:ci></m:apply><m:apply id="id56122"><m:csymbol id="id56123" cd="ambiguous">superscript</m:csymbol><m:ci id="id56127">δ</m:ci><m:apply id="id56130"><m:times id="id56131"/><m:ci id="id56132">a</m:ci><m:ci id="id56134">b</m:ci></m:apply></m:apply></m:apply><m:apply id="id56136"><m:csymbol id="id56137" cd="ambiguous">superscript</m:csymbol><m:ci id="id56142">G</m:ci><m:apply id="id56144"><m:times id="id56145"/><m:ci id="id56146">A</m:ci><m:ci id="id56148">B</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id56383"><h4>Hit id56383</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 54</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/36/f014201.xhtml#id56383</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:44910(000013%) VariableMap:[eta, Phi, A x 2, ( x 3, ) x 3, partial x 4, i x 2, frac, - x 2, 2, 1, 0 x 2, displaystyle, \ x 10, _ x 4, left, right] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id56383" alttext="\displaystyle\frac{\partial}{\partial\eta}\left((1-2\Phi)(\partial _{i}A_{0}-\partial _{0}A_{i})\right)" display="inline"><m:semantics id="id56389"><m:mrow id="id56390"><m:mstyle id="id56391" displaystyle="true"><m:mfrac id="id56394"><m:mo id="id56396">∂</m:mo><m:mrow id="id56398"><m:mo id="id56399">∂</m:mo><m:mo id="id56401">⁡</m:mo><m:mi id="id56404">η</m:mi></m:mrow></m:mfrac></m:mstyle><m:mo id="id56406">⁢</m:mo><m:mfenced id="id56409" open="(" close=")"><m:mrow id="id56414"><m:mfenced id="id56415" open="(" close=")"><m:mrow id="id56420"><m:mn id="id56421">1</m:mn><m:mo id="id56423">-</m:mo><m:mrow id="id56425"><m:mn id="id56426">2</m:mn><m:mo id="id56428">⁢</m:mo><m:mi id="id56431" mathvariant="normal">Φ</m:mi></m:mrow></m:mrow></m:mfenced><m:mo id="id56435">⁢</m:mo><m:mfenced id="id56438" open="(" close=")"><m:mrow id="id56443"><m:mrow id="id56444"><m:msub id="id56445"><m:mo id="id56446">∂</m:mo><m:mi id="id56448">i</m:mi></m:msub><m:mo id="id56451">⁡</m:mo><m:msub id="id56453"><m:mi id="id56454">A</m:mi><m:mn id="id56456">0</m:mn></m:msub></m:mrow><m:mo id="id56458">-</m:mo><m:mrow id="id56460"><m:msub id="id56462"><m:mo id="id56463">∂</m:mo><m:mn id="id56465">0</m:mn></m:msub><m:mo id="id56467">⁡</m:mo><m:msub id="id56470"><m:mi id="id56471">A</m:mi><m:mi id="id56473">i</m:mi></m:msub></m:mrow></m:mrow></m:mfenced></m:mrow></m:mfenced></m:mrow><m:annotation-xml id="id56475" encoding="MathML-Content"><m:apply id="id56478"><m:times id="id56479"/><m:apply id="id56480"><m:divide id="id56481"/><m:partialdiff id="id56482"/><m:apply id="id56484"><m:partialdiff id="id56485"/><m:ci id="id56486">η</m:ci></m:apply></m:apply><m:apply id="id56488"><m:times id="id56489"/><m:apply id="id56490"><m:minus id="id56491"/><m:cn id="id56492" type="integer">1</m:cn><m:apply id="id56497"><m:times id="id56498"/><m:cn id="id56499" type="integer">2</m:cn><m:ci id="id56503">Φ</m:ci></m:apply></m:apply><m:apply id="id56506"><m:minus id="id56507"/><m:apply id="id56508"><m:apply id="id56509"><m:csymbol id="id56510" cd="ambiguous">subscript</m:csymbol><m:partialdiff id="id56515"/><m:ci id="id56516">i</m:ci></m:apply><m:apply id="id56518"><m:csymbol id="id56519" cd="ambiguous">subscript</m:csymbol><m:ci id="id56524">A</m:ci><m:cn id="id56526" type="integer">0</m:cn></m:apply></m:apply><m:apply id="id56530"><m:apply id="id56531"><m:csymbol id="id56532" cd="ambiguous">subscript</m:csymbol><m:partialdiff id="id56537"/><m:cn id="id56538" type="integer">0</m:cn></m:apply><m:apply id="id56542"><m:csymbol id="id56543" cd="ambiguous">subscript</m:csymbol><m:ci id="id56548">A</m:ci><m:ci id="id56550">i</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id56552" encoding="application/x-tex">\displaystyle\frac{\partial}{\partial\eta}\left((1-2\Phi)(\partial _{i}A_{0}-\partial _{0}A_{i})\right)</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id56602"><h4>Hit id56602</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 55</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/5/f001666.xhtml#id56602</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:46514(000017%) VariableMap:[G, L x 2, ( x 3, ) x 3, , x 5, frac, qxy, qy, q, qx, \, y x 2, =, x x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 7 occurences for '\' but has only 1 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id56602" alttext="G(x,y,q)=qxy\frac{L(qx,qy)}{L(x,y)}," display="block"><m:semantics id="id56608"><m:mrow id="id56609"><m:mrow id="id56610"><m:mrow id="id56611"><m:mi id="id56612">G</m:mi><m:mo id="id56614">⁢</m:mo><m:mfenced id="id56616" open="(" close=")"><m:mrow id="id56622"><m:mi id="id56623">x</m:mi><m:mo id="id56625">,</m:mo><m:mi id="id56627">y</m:mi><m:mo id="id56629">,</m:mo><m:mi id="id56631">q</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id56633">=</m:mo><m:mrow id="id56635"><m:mi id="id56636">q</m:mi><m:mo id="id56639">⁢</m:mo><m:mi id="id56641">x</m:mi><m:mo id="id56643">⁢</m:mo><m:mi id="id56646">y</m:mi><m:mo id="id56648">⁢</m:mo><m:mfrac id="id56650"><m:mrow id="id56651"><m:mi id="id56652">L</m:mi><m:mo id="id56654">⁢</m:mo><m:mfenced id="id56657" open="(" close=")"><m:mrow id="id56662"><m:mrow id="id56663"><m:mi id="id56664">q</m:mi><m:mo id="id56666">⁢</m:mo><m:mi id="id56668">x</m:mi></m:mrow><m:mo id="id56671">,</m:mo><m:mrow id="id56673"><m:mi id="id56674">q</m:mi><m:mo id="id56676">⁢</m:mo><m:mi id="id56678">y</m:mi></m:mrow></m:mrow></m:mfenced></m:mrow><m:mrow id="id56680"><m:mi id="id56682">L</m:mi><m:mo id="id56684">⁢</m:mo><m:mfenced id="id56686" open="(" close=")"><m:mrow id="id56691"><m:mi id="id56692">x</m:mi><m:mo id="id56694">,</m:mo><m:mi id="id56696">y</m:mi></m:mrow></m:mfenced></m:mrow></m:mfrac></m:mrow></m:mrow><m:mo id="id56699">,</m:mo></m:mrow><m:annotation-xml id="id56701" encoding="MathML-Content"><m:apply id="id56704"><m:eq id="id56705"/><m:apply id="id56706"><m:times id="id56707"/><m:ci id="id56708">G</m:ci><m:apply id="id56710"><m:vector id="id56712"/><m:ci id="id56713">x</m:ci><m:ci id="id56715">y</m:ci><m:ci id="id56717">q</m:ci></m:apply></m:apply><m:apply id="id56719"><m:times id="id56720"/><m:ci id="id56721">q</m:ci><m:ci id="id56723">x</m:ci><m:ci id="id56725">y</m:ci><m:apply id="id56728"><m:divide id="id56729"/><m:apply id="id56730"><m:times id="id56731"/><m:ci id="id56732">L</m:ci><m:apply id="id56734"><m:interval id="id56735" closure="open"/><m:apply id="id56738"><m:times id="id56739"/><m:ci id="id56740">q</m:ci><m:ci id="id56743">x</m:ci></m:apply><m:apply id="id56745"><m:times id="id56746"/><m:ci id="id56747">q</m:ci><m:ci id="id56749">y</m:ci></m:apply></m:apply></m:apply><m:apply id="id56751"><m:times id="id56752"/><m:ci id="id56753">L</m:ci><m:apply id="id56755"><m:interval id="id56756" closure="open"/><m:ci id="id56760">x</m:ci><m:ci id="id56762">y</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id56764" encoding="application/x-tex">G(x,y,q)=qxy\frac{L(qx,qy)}{L(x,y)},</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id57618"><h4>Hit id57618</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 56</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/123/f049168.xhtml#id57618</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:61375(000009%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id57618" display="inline"><m:semantics id="id57622"><m:mrow id="id57623"><m:msub id="id57624"><m:mi id="id57625">g</m:mi><m:mrow id="id57627"><m:mi id="id57628">α</m:mi><m:mo id="id57631">⁢</m:mo><m:mover id="id57633" accent="true"><m:mi id="id57636">β</m:mi><m:mo id="id57639">¯</m:mo></m:mover></m:mrow></m:msub><m:mo id="id57641">=</m:mo><m:mfenced id="id57643" open="(" close=")"><m:mfrac id="id57648"><m:mrow id="id57649"><m:msup id="id57650"><m:mo id="id57652">∂</m:mo><m:mn id="id57654">2</m:mn></m:msup><m:mo id="id57656">⁡</m:mo><m:mi id="id57658" mathvariant="normal">Φ</m:mi></m:mrow><m:mrow id="id57663"><m:mrow id="id57664"><m:mo id="id57665">∂</m:mo><m:mo id="id57668">⁡</m:mo><m:msub id="id57670"><m:mi id="id57671">z</m:mi><m:mi id="id57673">α</m:mi></m:msub></m:mrow><m:mo id="id57676">⁢</m:mo><m:mrow id="id57678"><m:mo id="id57679">∂</m:mo><m:mo id="id57682">⁡</m:mo><m:msub id="id57684"><m:mover id="id57685" accent="true"><m:mi id="id57688">z</m:mi><m:mo id="id57690">¯</m:mo></m:mover><m:mi id="id57693">β</m:mi></m:msub></m:mrow></m:mrow></m:mfrac></m:mfenced></m:mrow><m:annotation-xml id="id57695" encoding="MathML-Content"><m:apply id="id57699"><m:eq id="id57700"/><m:apply id="id57701"><m:csymbol id="id57702" cd="ambiguous">subscript</m:csymbol><m:ci id="id57706">g</m:ci><m:apply id="id57709"><m:times id="id57710"/><m:ci id="id57711">α</m:ci><m:apply id="id57713"><m:ci id="id57714">¯</m:ci><m:ci id="id57717">β</m:ci></m:apply></m:apply></m:apply><m:apply id="id57719"><m:divide id="id57720"/><m:apply id="id57721"><m:apply id="id57722"><m:csymbol id="id57723" cd="ambiguous">superscript</m:csymbol><m:partialdiff id="id57728"/><m:cn id="id57729">2</m:cn></m:apply><m:ci id="id57731">Φ</m:ci></m:apply><m:apply id="id57734"><m:times id="id57735"/><m:apply id="id57736"><m:partialdiff id="id57737"/><m:apply id="id57738"><m:csymbol id="id57739" cd="ambiguous">subscript</m:csymbol><m:ci id="id57744">z</m:ci><m:ci id="id57746">α</m:ci></m:apply></m:apply><m:apply id="id57748"><m:partialdiff id="id57749"/><m:apply id="id57750"><m:csymbol id="id57751" cd="ambiguous">subscript</m:csymbol><m:apply id="id57756"><m:ci id="id57757">¯</m:ci><m:ci id="id57759">z</m:ci></m:apply><m:ci id="id57762">β</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id58711"><h4>Hit id58711</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 57</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/116/f046273.xhtml#id58711</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:77215(000048%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id58711" display="inline"><m:semantics id="id58715"><m:mrow id="id58716"><m:mrow id="id58717"><m:mi id="id58718">R</m:mi><m:mo id="id58720">⁢</m:mo><m:mi id="id58722">e</m:mi><m:mo id="id58725">⁢</m:mo><m:mfenced id="id58727" open="(" close=")"><m:mrow id="id58732"><m:mi id="id58733">a</m:mi><m:mo id="id58735">⁢</m:mo><m:mi id="id58738">b</m:mi><m:mo id="id58740">⁢</m:mo><m:mi id="id58742">c</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id58744">=</m:mo><m:mrow id="id58746"><m:mrow id="id58748"><m:msub id="id58749"><m:mfenced id="id58750" open="(" close=")"><m:mrow id="id58755"><m:mi id="id58756">a</m:mi><m:mo id="id58758">⁢</m:mo><m:mi id="id58760">b</m:mi></m:mrow></m:mfenced><m:mn id="id58762">0</m:mn></m:msub><m:mo id="id58765">⁢</m:mo><m:msub id="id58767"><m:mi id="id58768">c</m:mi><m:mn id="id58770">0</m:mn></m:msub></m:mrow><m:mo id="id58772">-</m:mo><m:mrow id="id58774"><m:mfenced id="id58776" open="(" close=")"><m:mrow id="id58781"><m:mi id="id58782">a</m:mi><m:mo id="id58784">⁢</m:mo><m:mi id="id58786">b</m:mi></m:mrow></m:mfenced><m:mo id="id58788">⋅</m:mo><m:mi id="id58791" mathvariant="bold">c</m:mi></m:mrow></m:mrow><m:mo id="id58795">=</m:mo><m:none id="id58797"/></m:mrow><m:annotation-xml id="id58798" encoding="MathML-Content"><m:apply id="id58802"><m:ci id="id58803"/><m:apply id="id58804"><m:times id="id58805"/><m:ci id="id58806">R</m:ci><m:ci id="id58808">e</m:ci><m:apply id="id58810"><m:times id="id58811"/><m:ci id="id58812">a</m:ci><m:ci id="id58814">b</m:ci><m:ci id="id58817">c</m:ci></m:apply></m:apply><m:eq id="id58819"/><m:apply id="id58820"><m:minus id="id58821"/><m:apply id="id58822"><m:times id="id58823"/><m:apply id="id58824"><m:csymbol id="id58825" cd="ambiguous">subscript</m:csymbol><m:apply id="id58830"><m:times id="id58831"/><m:ci id="id58832">a</m:ci><m:ci id="id58834">b</m:ci></m:apply><m:mtext id="id58836">0</m:mtext></m:apply><m:apply id="id58838"><m:csymbol id="id58839" cd="ambiguous">subscript</m:csymbol><m:ci id="id58844">c</m:ci><m:mtext id="id58846">0</m:mtext></m:apply></m:apply><m:apply id="id58848"><m:ci id="id58849">⋅</m:ci><m:apply id="id58852"><m:times id="id58853"/><m:ci id="id58854">a</m:ci><m:ci id="id58856">b</m:ci></m:apply><m:ci id="id58858">c</m:ci></m:apply></m:apply><m:eq id="id58860"/><m:ci id="id58861"/></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id59617"><h4>Hit id59617</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 58</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/70/f027998.xhtml#id59617</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:93571(000035%) VariableMap:[f x 2, rm, +, ( x 4, gf, ) x 4, , x 4, 1, 0, Q x 2, p x 3, bf x 2, \ x 3, _, ^ x 2, =, eq, x x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 3 Expects 2 occurences for '_' but has only 1 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id59617" alttext="f(x,{\bf p},Q)=f^{{\rm eq}}(p_{0})+gf^{{(1)}}(x,{\bf p},Q)" display="inline"><m:semantics id="id59623"><m:mrow id="id59624"><m:mrow id="id59625"><m:mi id="id59626">f</m:mi><m:mo id="id59628">⁢</m:mo><m:mfenced id="id59631" open="(" close=")"><m:mrow id="id59636"><m:mi id="id59637">x</m:mi><m:mo id="id59639">,</m:mo><m:mi id="id59641" mathvariant="bold">p</m:mi><m:mo id="id59646">,</m:mo><m:mi id="id59648">Q</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id59650">=</m:mo><m:mrow id="id59652"><m:mrow id="id59653"><m:msup id="id59654"><m:mi id="id59655">f</m:mi><m:mi id="id59657">eq</m:mi></m:msup><m:mo id="id59660">⁢</m:mo><m:mfenced id="id59662" open="(" close=")"><m:msub id="id59667"><m:mi id="id59668">p</m:mi><m:mn id="id59670">0</m:mn></m:msub></m:mfenced></m:mrow><m:mo id="id59672">+</m:mo><m:mrow id="id59674"><m:mi id="id59676">g</m:mi><m:mo id="id59678">⁢</m:mo><m:msup id="id59680"><m:mi id="id59681">f</m:mi><m:mfenced id="id59683" open="(" close=")"><m:mn id="id59688">1</m:mn></m:mfenced></m:msup><m:mo id="id59690">⁢</m:mo><m:mfenced id="id59693" open="(" close=")"><m:mrow id="id59698"><m:mi id="id59699">x</m:mi><m:mo id="id59701">,</m:mo><m:mi id="id59703" mathvariant="bold">p</m:mi><m:mo id="id59708">,</m:mo><m:mi id="id59710">Q</m:mi></m:mrow></m:mfenced></m:mrow></m:mrow></m:mrow><m:annotation-xml id="id59712" encoding="MathML-Content"><m:apply id="id59715"><m:eq id="id59716"/><m:apply id="id59717"><m:times id="id59718"/><m:ci id="id59720">f</m:ci><m:apply id="id59722"><m:vector id="id59723"/><m:ci id="id59724">x</m:ci><m:ci id="id59726">p</m:ci><m:ci id="id59728">Q</m:ci></m:apply></m:apply><m:apply id="id59730"><m:plus id="id59731"/><m:apply id="id59732"><m:times id="id59733"/><m:apply id="id59734"><m:csymbol id="id59736" cd="ambiguous">superscript</m:csymbol><m:ci id="id59740">f</m:ci><m:ci id="id59742">eq</m:ci></m:apply><m:apply id="id59744"><m:csymbol id="id59746" cd="ambiguous">subscript</m:csymbol><m:ci id="id59750">p</m:ci><m:cn id="id59752" type="integer">0</m:cn></m:apply></m:apply><m:apply id="id59757"><m:times id="id59758"/><m:ci id="id59759">g</m:ci><m:apply id="id59761"><m:csymbol id="id59762" cd="ambiguous">superscript</m:csymbol><m:ci id="id59767">f</m:ci><m:cn id="id59769" type="integer">1</m:cn></m:apply><m:apply id="id59773"><m:vector id="id59774"/><m:ci id="id59775">x</m:ci><m:ci id="id59778">p</m:ci><m:ci id="id59780">Q</m:ci></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id59782" encoding="application/x-tex">f(x,{\bf p},Q)=f^{{\rm eq}}(p_{0})+gf^{{(1)}}(x,{\bf p},Q)</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id59625"><h4>Hit id59625</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 59</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/101/f040398.xhtml#id59625</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:87928(000044%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id59625" display="block"><m:semantics id="id59628"><m:mrow id="id59629"><m:mrow id="id59630"><m:mrow id="id59631"><m:mrow id="id59632"><m:mi id="id59633">f</m:mi><m:mo id="id59635">⁢</m:mo><m:mfenced id="id59638" open="(" close=")"><m:mi id="id59643">x</m:mi></m:mfenced></m:mrow><m:mo id="id59645">=</m:mo><m:mrow id="id59647"><m:mrow id="id59648"><m:mi id="id59649">f</m:mi><m:mo id="id59651">⁢</m:mo><m:mfenced id="id59654" open="(" close=")"><m:mi id="id59659">c</m:mi></m:mfenced></m:mrow><m:mo id="id59661">+</m:mo><m:mrow id="id59663"><m:mfrac id="id59664"><m:mrow id="id59665"><m:mrow id="id59666"><m:mi id="id59667">f</m:mi><m:mo id="id59670">⁢</m:mo><m:mfenced id="id59672" open="(" close=")"><m:mi id="id59677">x</m:mi></m:mfenced></m:mrow><m:mo id="id59679">-</m:mo><m:mrow id="id59681"><m:mi id="id59682">f</m:mi><m:mo id="id59684">⁢</m:mo><m:mfenced id="id59687" open="(" close=")"><m:mi id="id59692">c</m:mi></m:mfenced></m:mrow></m:mrow><m:mrow id="id59694"><m:mi id="id59695">ρ</m:mi><m:mo id="id59698">⁢</m:mo><m:mfenced id="id59700" open="(" close=")"><m:mi id="id59705">x</m:mi></m:mfenced></m:mrow></m:mfrac><m:mo id="id59707">⁢</m:mo><m:mi id="id59710">ρ</m:mi><m:mo id="id59712">⁢</m:mo><m:mfenced id="id59714" open="(" close=")"><m:mi id="id59719">x</m:mi></m:mfenced></m:mrow></m:mrow></m:mrow><m:mo id="id59722">,</m:mo><m:mrow id="id59724"><m:mi id="id59725">x</m:mi><m:mo id="id59727">≠</m:mo><m:mi id="id59729">c</m:mi></m:mrow></m:mrow><m:mo id="id59731">,</m:mo></m:mrow><m:annotation-xml id="id59734" encoding="MathML-Content"><m:apply id="id59737"><m:ci id="id59738"/><m:apply id="id59739"><m:eq id="id59740"/><m:apply id="id59741"><m:times id="id59742"/><m:ci id="id59743">f</m:ci><m:ci id="id59745">x</m:ci></m:apply><m:apply id="id59748"><m:plus id="id59749"/><m:apply id="id59750"><m:times id="id59751"/><m:ci id="id59752">f</m:ci><m:ci id="id59754">c</m:ci></m:apply><m:apply id="id59756"><m:times id="id59757"/><m:apply id="id59758"><m:divide id="id59759"/><m:apply id="id59760"><m:minus id="id59761"/><m:apply id="id59762"><m:times id="id59764"/><m:ci id="id59765">f</m:ci><m:ci id="id59767">x</m:ci></m:apply><m:apply id="id59769"><m:times id="id59770"/><m:ci id="id59771">f</m:ci><m:ci id="id59773">c</m:ci></m:apply></m:apply><m:apply id="id59775"><m:times id="id59776"/><m:ci id="id59777">ρ</m:ci><m:ci id="id59780">x</m:ci></m:apply></m:apply><m:ci id="id59782">ρ</m:ci><m:ci id="id59784">x</m:ci></m:apply></m:apply></m:apply><m:apply id="id59786"><m:neq id="id59788"/><m:ci id="id59789">x</m:ci><m:ci id="id59791">c</m:ci></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id61588"><h4>Hit id61588</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 60</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/242/f096424.xhtml#id61588</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:120045(000048%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id61588" display="inline"><m:semantics id="id61592"><m:mrow id="id61593"><m:mrow id="id61594"><m:msubsup id="id61595"><m:mi id="id61596" mathvariant="normal">Π</m:mi><m:mi id="id61600">L</m:mi><m:mi id="id61603">D</m:mi></m:msubsup><m:mo id="id61605">⁢</m:mo><m:mfenced id="id61607" open="(" close=")"><m:mi id="id61612">q</m:mi></m:mfenced></m:mrow><m:mo id="id61614">=</m:mo><m:mrow id="id61616"><m:mo id="id61618">-</m:mo><m:msubsup id="id61620"><m:mi id="id61621" mathvariant="normal">Π</m:mi><m:mn id="id61625">00</m:mn><m:mi id="id61628">D</m:mi></m:msubsup><m:mo id="id61630">+</m:mo><m:mrow id="id61632"><m:msubsup id="id61633"><m:mi id="id61634" mathvariant="normal">Π</m:mi><m:mn id="id61639">11</m:mn><m:mi id="id61641">D</m:mi></m:msubsup><m:mo id="id61643">⁢</m:mo><m:mfenced id="id61645" open="(" close=")"><m:mi id="id61650">q</m:mi></m:mfenced></m:mrow></m:mrow></m:mrow><m:annotation-xml id="id61652" encoding="MathML-Content"><m:apply id="id61656"><m:eq id="id61657"/><m:apply id="id61658"><m:times id="id61659"/><m:apply id="id61660"><m:csymbol id="id61661" cd="ambiguous">subscript</m:csymbol><m:apply id="id61666"><m:csymbol id="id61667" cd="ambiguous">superscript</m:csymbol><m:ci id="id61672">Π</m:ci><m:ci id="id61674">D</m:ci></m:apply><m:ci id="id61676">L</m:ci></m:apply><m:ci id="id61678">q</m:ci></m:apply><m:apply id="id61680"><m:plus id="id61681"/><m:apply id="id61682"><m:minus id="id61684"/><m:apply id="id61685"><m:csymbol id="id61686" cd="ambiguous">superscript</m:csymbol><m:apply id="id61690"><m:csymbol id="id61691" cd="ambiguous">subscript</m:csymbol><m:ci id="id61696">Π</m:ci><m:cn id="id61698">00</m:cn></m:apply><m:ci id="id61701">D</m:ci></m:apply></m:apply><m:apply id="id61703"><m:times id="id61704"/><m:apply id="id61705"><m:csymbol id="id61706" cd="ambiguous">superscript</m:csymbol><m:apply id="id61711"><m:csymbol id="id61712" cd="ambiguous">subscript</m:csymbol><m:ci id="id61716">Π</m:ci><m:cn id="id61719">11</m:cn></m:apply><m:ci id="id61721">D</m:ci></m:apply><m:ci id="id61723">q</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id62117"><h4>Hit id62117</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 61</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/217/f086747.xhtml#id62117</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:134499(000040%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id62117" display="inline"><m:semantics id="id62120"><m:mrow id="id62121"><m:mrow id="id62122"><m:mrow id="id62124"><m:msubsup id="id62125"><m:mi id="id62126">G</m:mi><m:mi id="id62128">E</m:mi><m:mi id="id62130">p</m:mi></m:msubsup><m:mo id="id62132">⁢</m:mo><m:mfenced id="id62134" open="(" close=")"><m:mn id="id62140">0</m:mn></m:mfenced></m:mrow><m:mo id="id62142">=</m:mo><m:mn id="id62144">1</m:mn></m:mrow><m:mo id="id62146">,</m:mo><m:mrow id="id62148"><m:mrow id="id62149"><m:msubsup id="id62150"><m:mi id="id62151">G</m:mi><m:mi id="id62153">M</m:mi><m:mi id="id62156">p</m:mi></m:msubsup><m:mo id="id62158">⁢</m:mo><m:mfenced id="id62160" open="(" close=")"><m:mn id="id62165">0</m:mn></m:mfenced></m:mrow><m:mo id="id62167">=</m:mo><m:msub id="id62169"><m:mi id="id62170">μ</m:mi><m:mi id="id62173">p</m:mi></m:msub><m:mo id="id62175">=</m:mo><m:mn id="id62177">2.793</m:mn></m:mrow></m:mrow><m:annotation-xml id="id62180" encoding="MathML-Content"><m:apply id="id62183"><m:ci id="id62184"/><m:apply id="id62185"><m:eq id="id62186"/><m:apply id="id62187"><m:times id="id62188"/><m:apply id="id62189"><m:csymbol id="id62190" cd="ambiguous">superscript</m:csymbol><m:apply id="id62195"><m:csymbol id="id62196" cd="ambiguous">subscript</m:csymbol><m:ci id="id62201">G</m:ci><m:ci id="id62203">E</m:ci></m:apply><m:ci id="id62205">p</m:ci></m:apply><m:cn id="id62207">0</m:cn></m:apply><m:cn id="id62209">1</m:cn></m:apply><m:apply id="id62211"><m:ci id="id62212"/><m:apply id="id62214"><m:times id="id62215"/><m:apply id="id62216"><m:csymbol id="id62217" cd="ambiguous">superscript</m:csymbol><m:apply id="id62221"><m:csymbol id="id62222" cd="ambiguous">subscript</m:csymbol><m:ci id="id62227">G</m:ci><m:ci id="id62229">M</m:ci></m:apply><m:ci id="id62231">p</m:ci></m:apply><m:cn id="id62234">0</m:cn></m:apply><m:eq id="id62236"/><m:apply id="id62237"><m:csymbol id="id62238" cd="ambiguous">subscript</m:csymbol><m:ci id="id62242">μ</m:ci><m:ci id="id62245">p</m:ci></m:apply><m:eq id="id62247"/><m:cn id="id62248">2.793</m:cn></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id62997"><h4>Hit id62997</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 62</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/25/f009941.xhtml#id62997</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:141407(000010%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id62997" display="inline"><m:semantics id="id63001"><m:mrow id="id63002"><m:msub id="id63003"><m:mo id="id63004">lim</m:mo><m:mrow id="id63006"><m:mi id="id63007">n</m:mi><m:mo id="id63009">→</m:mo><m:mi id="id63012" mathvariant="normal">∞</m:mi></m:mrow></m:msub><m:mo id="id63016">⁡</m:mo><m:mrow id="id63019"><m:msubsup id="id63020"><m:mo id="id63021">∑</m:mo><m:mrow id="id63023"><m:mi id="id63024">k</m:mi><m:mo id="id63026">=</m:mo><m:mn id="id63029">1</m:mn></m:mrow><m:mi id="id63031">n</m:mi></m:msubsup><m:msub id="id63033"><m:mi id="id63034">χ</m:mi><m:mi id="id63036" mathvariant="normal">Λ</m:mi></m:msub><m:mo id="id63041">⁢</m:mo><m:msup id="id63043"><m:mi id="id63044">G</m:mi><m:mi id="id63047">k</m:mi></m:msup><m:mo id="id63049">⁢</m:mo><m:msub id="id63051"><m:mi id="id63052">χ</m:mi><m:mi id="id63055" mathvariant="normal">Λ</m:mi></m:msub></m:mrow></m:mrow><m:annotation-xml id="id63059" encoding="MathML-Content"><m:apply id="id63063"><m:apply id="id63064"><m:csymbol id="id63065" cd="ambiguous">subscript</m:csymbol><m:limit id="id63069"/><m:apply id="id63070"><m:ci id="id63072">→</m:ci><m:ci id="id63074">n</m:ci><m:infinity id="id63076"/></m:apply></m:apply><m:apply id="id63077"><m:apply id="id63078"><m:csymbol id="id63079" cd="ambiguous">superscript</m:csymbol><m:apply id="id63084"><m:csymbol id="id63085" cd="ambiguous">subscript</m:csymbol><m:sum id="id63090"/><m:apply id="id63091"><m:eq id="id63092"/><m:ci id="id63093">k</m:ci><m:cn id="id63095">1</m:cn></m:apply></m:apply><m:ci id="id63097">n</m:ci></m:apply><m:apply id="id63099"><m:times id="id63100"/><m:apply id="id63101"><m:csymbol id="id63102" cd="ambiguous">subscript</m:csymbol><m:ci id="id63107">χ</m:ci><m:ci id="id63110">Λ</m:ci></m:apply><m:apply id="id63112"><m:csymbol id="id63113" cd="ambiguous">superscript</m:csymbol><m:ci id="id63118">G</m:ci><m:ci id="id63120">k</m:ci></m:apply><m:apply id="id63122"><m:csymbol id="id63123" cd="ambiguous">subscript</m:csymbol><m:ci id="id63128">χ</m:ci><m:ci id="id63130">Λ</m:ci></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id64046"><h4>Hit id64046</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 63</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/123/f049136.xhtml#id64046</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:164805(000042%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id64046" display="inline"><m:semantics id="id64049"><m:mrow id="id64050"><m:mi id="id64051">H</m:mi><m:mo id="id64053">=</m:mo><m:mrow id="id64055"><m:mrow id="id64056"><m:mfrac id="id64058"><m:mn id="id64059">1</m:mn><m:mrow id="id64061"><m:mn id="id64062">2</m:mn><m:mo id="id64064">⁢</m:mo><m:mi id="id64066">m</m:mi></m:mrow></m:mfrac><m:mo id="id64068">⁢</m:mo><m:msup id="id64071"><m:mi id="id64072">g</m:mi><m:mrow id="id64074"><m:mi id="id64075">a</m:mi><m:mo id="id64077">⁢</m:mo><m:mi id="id64080">b</m:mi></m:mrow></m:msup><m:mo id="id64082">⁢</m:mo><m:msub id="id64084"><m:mi id="id64085">p</m:mi><m:mi id="id64087">a</m:mi></m:msub><m:mo id="id64090">⁢</m:mo><m:msub id="id64092"><m:mi id="id64093">p</m:mi><m:mi id="id64095">b</m:mi></m:msub></m:mrow><m:mo id="id64097">+</m:mo><m:mrow id="id64099"><m:mi id="id64100">λ</m:mi><m:mo id="id64103">⁢</m:mo><m:mi id="id64105">F</m:mi><m:mo id="id64107">⁢</m:mo><m:mfenced id="id64110" open="(" close=")"><m:mi id="id64115">q</m:mi></m:mfenced></m:mrow></m:mrow></m:mrow><m:annotation-xml id="id64117" encoding="MathML-Content"><m:apply id="id64120"><m:eq id="id64121"/><m:ci id="id64122">H</m:ci><m:apply id="id64125"><m:plus id="id64126"/><m:apply id="id64127"><m:times id="id64128"/><m:apply id="id64129"><m:divide id="id64130"/><m:cn id="id64131">1</m:cn><m:apply id="id64133"><m:times id="id64134"/><m:cn id="id64135">2</m:cn><m:ci id="id64137">m</m:ci></m:apply></m:apply><m:apply id="id64140"><m:csymbol id="id64141" cd="ambiguous">superscript</m:csymbol><m:ci id="id64145">g</m:ci><m:apply id="id64147"><m:times id="id64148"/><m:ci id="id64150">a</m:ci><m:ci id="id64152">b</m:ci></m:apply></m:apply><m:apply id="id64154"><m:csymbol id="id64155" cd="ambiguous">subscript</m:csymbol><m:ci id="id64160">p</m:ci><m:ci id="id64162">a</m:ci></m:apply><m:apply id="id64164"><m:csymbol id="id64165" cd="ambiguous">subscript</m:csymbol><m:ci id="id64170">p</m:ci><m:ci id="id64172">b</m:ci></m:apply></m:apply><m:apply id="id64174"><m:times id="id64175"/><m:ci id="id64176">λ</m:ci><m:ci id="id64178">F</m:ci><m:ci id="id64180">q</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id64438"><h4>Hit id64438</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 64</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/138/f054803.xhtml#id64438</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:163424(000045%) VariableMap:[F x 2, G, A, rangle, (, ), langle, k x 3, ,, - x 2, 2, 1, bf x 3, sim, \ x 7, _ x 3, | x 2, cal, ^ x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id64438" alttext="\langle{\cal A}^{{-1}}({\bf k}_{{G}},{\bf k}_{{F}})\rangle\sim|{\bf k}_{{F}}|^{{-2}}" display="inline"><m:semantics id="id64444"><m:mrow id="id64445"><m:mfenced id="id64448" open="⟨" close="⟩"><m:mrow id="id64453"><m:msup id="id64454"><m:mi id="id64455" mathvariant="script">A</m:mi><m:mrow id="id64459"><m:mo id="id64460">-</m:mo><m:mn id="id64462">1</m:mn></m:mrow></m:msup><m:mo id="id64464">⁢</m:mo><m:mfenced id="id64467" open="(" close=")"><m:mrow id="id64471"><m:msub id="id64472"><m:mi id="id64473" mathvariant="bold">k</m:mi><m:mi id="id64477">G</m:mi></m:msub><m:mo id="id64479">,</m:mo><m:msub id="id64482"><m:mi id="id64483" mathvariant="bold">k</m:mi><m:mi id="id64487">F</m:mi></m:msub></m:mrow></m:mfenced></m:mrow></m:mfenced><m:mo id="id64489">∼</m:mo><m:mrow id="id64492"><m:mi id="id64493" mathvariant="normal">|</m:mi><m:mo id="id64497">⁢</m:mo><m:msub id="id64499"><m:mi id="id64500" mathvariant="bold">k</m:mi><m:mi id="id64505">F</m:mi></m:msub><m:mo id="id64507">⁢</m:mo><m:msup id="id64509"><m:mi id="id64510" mathvariant="normal">|</m:mi><m:mrow id="id64515"><m:mo id="id64516">-</m:mo><m:mn id="id64518">2</m:mn></m:mrow></m:msup></m:mrow></m:mrow><m:annotation-xml id="id64520" encoding="MathML-Content"><m:apply id="id64524"><m:ci id="id64525">∼</m:ci><m:apply id="id64527"><m:times id="id64528"/><m:apply id="id64529"><m:csymbol id="id64530" cd="ambiguous">superscript</m:csymbol><m:ci id="id64535">A</m:ci><m:apply id="id64537"><m:minus id="id64538"/><m:cn id="id64539" type="integer">1</m:cn></m:apply></m:apply><m:apply id="id64544"><m:interval id="id64545" closure="open"/><m:apply id="id64548"><m:csymbol id="id64549" cd="ambiguous">subscript</m:csymbol><m:ci id="id64554">k</m:ci><m:ci id="id64556">G</m:ci></m:apply><m:apply id="id64558"><m:csymbol id="id64559" cd="ambiguous">subscript</m:csymbol><m:ci id="id64564">k</m:ci><m:ci id="id64566">F</m:ci></m:apply></m:apply></m:apply><m:apply id="id64568"><m:times id="id64569"/><m:ci id="id64570">|</m:ci><m:apply id="id64572"><m:csymbol id="id64573" cd="ambiguous">subscript</m:csymbol><m:ci id="id64578">k</m:ci><m:ci id="id64580">F</m:ci></m:apply><m:apply id="id64582"><m:csymbol id="id64583" cd="ambiguous">superscript</m:csymbol><m:ci id="id64588">|</m:ci><m:apply id="id64590"><m:minus id="id64591"/><m:cn id="id64592" type="integer">2</m:cn></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id64597" encoding="application/x-tex">\langle{\cal A}^{{-1}}({\bf k}_{{G}},{\bf k}_{{F}})\rangle\sim|{\bf k}_{{F}}|^{{-2}}</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id65276"><h4>Hit id65276</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 65</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/164/f065344.xhtml#id65276</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:175470(000049%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id65276" display="inline"><m:semantics id="id65280"><m:mrow id="id65281"><m:mrow id="id65282"><m:msub id="id65283"><m:mi id="id65284" mathvariant="script">P</m:mi><m:mrow id="id65288"><m:mi id="id65289">K</m:mi><m:mo id="id65291">⁢</m:mo><m:mi id="id65294">J</m:mi></m:mrow></m:msub><m:mo id="id65296">⁢</m:mo><m:mfenced id="id65298" open="(" close=")"><m:mrow id="id65303"><m:mi id="id65304">t</m:mi><m:mo id="id65307">,</m:mo><m:mi id="id65309">z</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id65311">=</m:mo><m:mrow id="id65313"><m:mn id="id65314"> 2</m:mn><m:mo id="id65316">⁢</m:mo><m:msub id="id65319"><m:mi id="id65320">P</m:mi><m:mrow id="id65322"><m:mi id="id65323">K</m:mi><m:mo id="id65325">⁢</m:mo><m:mi id="id65328">J</m:mi></m:mrow></m:msub><m:mo id="id65330">⁢</m:mo><m:mfenced id="id65332" open="(" close=")"><m:mrow id="id65337"><m:mrow id="id65338"><m:msub id="id65339"><m:mi id="id65340">α</m:mi><m:mi id="id65343">s</m:mi></m:msub><m:mo id="id65345">⁢</m:mo><m:mfenced id="id65347" open="(" close=")"><m:mi id="id65352">t</m:mi></m:mfenced></m:mrow><m:mo id="id65355">,</m:mo><m:mi id="id65357">z</m:mi></m:mrow></m:mfenced></m:mrow></m:mrow><m:annotation-xml id="id65359" encoding="MathML-Content"><m:apply id="id65362"><m:eq id="id65363"/><m:apply id="id65364"><m:times id="id65365"/><m:apply id="id65366"><m:csymbol id="id65368" cd="ambiguous">subscript</m:csymbol><m:ci id="id65372">P</m:ci><m:apply id="id65374"><m:times id="id65375"/><m:ci id="id65376">K</m:ci><m:ci id="id65379">J</m:ci></m:apply></m:apply><m:apply id="id65381"><m:interval id="id65382" closure="open"/><m:ci id="id65385">t</m:ci><m:ci id="id65387">z</m:ci></m:apply></m:apply><m:apply id="id65389"><m:times id="id65390"/><m:cn id="id65392"> 2</m:cn><m:apply id="id65394"><m:csymbol id="id65395" cd="ambiguous">subscript</m:csymbol><m:ci id="id65400">P</m:ci><m:apply id="id65402"><m:times id="id65403"/><m:ci id="id65404">K</m:ci><m:ci id="id65406">J</m:ci></m:apply></m:apply><m:apply id="id65408"><m:interval id="id65409" closure="open"/><m:apply id="id65413"><m:times id="id65414"/><m:apply id="id65415"><m:csymbol id="id65416" cd="ambiguous">subscript</m:csymbol><m:ci id="id65420">α</m:ci><m:ci id="id65423">s</m:ci></m:apply><m:ci id="id65425">t</m:ci></m:apply><m:ci id="id65427">z</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id66859"><h4>Hit id66859</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 66</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/226/f090105.xhtml#id66859</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:203050(000031%) VariableMap:[f x 2, d, mathbb, a, n x 3, sum, ( x 3, ) x 3, m x 2, in, , x 3, -, t x 2, alpha, \ x 4, _ x 2, ^, =, Z] Expects 2 occurences for 'd' but has only 1 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 4 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id66859" alttext="(\alpha f)(t,m)=\sum _{{n\in\mathbb{Z}^{d}}}a_{n}f(t,m-n)," display="block"><m:semantics id="id66865"><m:mrow id="id66866"><m:mrow id="id66867"><m:mrow id="id66868"><m:mi id="id66869">α</m:mi><m:mo id="id66872">⁢</m:mo><m:mi id="id66874">f</m:mi><m:mo id="id66876">⁢</m:mo><m:mfenced id="id66879" open="(" close=")"><m:mrow id="id66884"><m:mi id="id66885">t</m:mi><m:mo id="id66887">,</m:mo><m:mi id="id66889">m</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id66891">=</m:mo><m:mrow id="id66893"><m:munder id="id66894"><m:mo id="id66896" movablelimits="false">∑</m:mo><m:mrow id="id66900"><m:mi id="id66901">n</m:mi><m:mo id="id66903">∈</m:mo><m:msup id="id66906"><m:mi id="id66907" mathvariant="double-struck">Z</m:mi><m:mi id="id66911">d</m:mi></m:msup></m:mrow></m:munder><m:msub id="id66913"><m:mi id="id66914">a</m:mi><m:mi id="id66917">n</m:mi></m:msub><m:mo id="id66919">⁢</m:mo><m:mi id="id66921">f</m:mi><m:mo id="id66923">⁢</m:mo><m:mfenced id="id66926" open="(" close=")"><m:mrow id="id66931"><m:mi id="id66932">t</m:mi><m:mo id="id66934">,</m:mo><m:mrow id="id66936"><m:mi id="id66937">m</m:mi><m:mo id="id66939">-</m:mo><m:mi id="id66941">n</m:mi></m:mrow></m:mrow></m:mfenced></m:mrow></m:mrow><m:mo id="id66944">,</m:mo></m:mrow><m:annotation-xml id="id66946" encoding="MathML-Content"><m:apply id="id66949"><m:eq id="id66950"/><m:apply id="id66951"><m:times id="id66952"/><m:ci id="id66953">α</m:ci><m:ci id="id66956">f</m:ci><m:apply id="id66958"><m:interval id="id66959" closure="open"/><m:ci id="id66962">t</m:ci><m:ci id="id66964">m</m:ci></m:apply></m:apply><m:apply id="id66966"><m:apply id="id66968"><m:csymbol id="id66969" cd="ambiguous">subscript</m:csymbol><m:sum id="id66973"/><m:apply id="id66974"><m:in id="id66975"/><m:ci id="id66976">n</m:ci><m:apply id="id66979"><m:csymbol id="id66980" cd="ambiguous">superscript</m:csymbol><m:ci id="id66984">Z</m:ci><m:ci id="id66986">d</m:ci></m:apply></m:apply></m:apply><m:apply id="id66989"><m:times id="id66990"/><m:apply id="id66991"><m:csymbol id="id66992" cd="ambiguous">subscript</m:csymbol><m:ci id="id66996">a</m:ci><m:ci id="id66999">n</m:ci></m:apply><m:ci id="id67001">f</m:ci><m:apply id="id67003"><m:interval id="id67004" closure="open"/><m:ci id="id67007">t</m:ci><m:apply id="id67009"><m:minus id="id67010"/><m:ci id="id67012">m</m:ci><m:ci id="id67014">n</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id67016" encoding="application/x-tex">(\alpha f)(t,m)=\sum _{{n\in\mathbb{Z}^{d}}}a_{n}f(t,m-n),</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id67369"><h4>Hit id67369</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 67</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/83/f032963.xhtml#id67369</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:199960(000071%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id67369" display="inline"><m:semantics id="id67372"><m:mrow id="id67373"><m:mrow id="id67374"><m:mrow id="id67375"><m:mi id="id67376">d</m:mi><m:mo id="id67378">⁢</m:mo><m:mi id="id67381">μ</m:mi><m:mo id="id67383">⁢</m:mo><m:mfenced id="id67386" open="(" close=")"><m:mi id="id67391">p</m:mi></m:mfenced></m:mrow><m:mo id="id67393">=</m:mo><m:mstyle id="id67395" displaystyle="true"><m:mfrac id="id67398"><m:mrow id="id67399"><m:msup id="id67400"><m:mi id="id67402">d</m:mi><m:mn id="id67404">4</m:mn></m:msup><m:mo id="id67406">⁢</m:mo><m:mi id="id67408">p</m:mi></m:mrow><m:mrow id="id67410"><m:msup id="id67411"><m:mfenced id="id67412" open="(" close=")"><m:mrow id="id67418"><m:mn id="id67419">2</m:mn><m:mo id="id67421">⁢</m:mo><m:mi id="id67423">π</m:mi></m:mrow></m:mfenced><m:mn id="id67426">4</m:mn></m:msup><m:mo id="id67428">⁢</m:mo><m:mfenced id="id67430" open="(" close=")"><m:mrow id="id67435"><m:mn id="id67436">1</m:mn><m:mo id="id67438">+</m:mo><m:mfrac id="id67440"><m:msub id="id67442"><m:mi id="id67443">p</m:mi><m:mn id="id67445">0</m:mn></m:msub><m:mi id="id67447">κ</m:mi></m:mfrac></m:mrow></m:mfenced></m:mrow></m:mfrac></m:mstyle></m:mrow><m:mo id="id67449">.</m:mo></m:mrow><m:annotation-xml id="id67451" encoding="MathML-Content"><m:apply id="id67455"><m:eq id="id67456"/><m:apply id="id67457"><m:times id="id67458"/><m:ci id="id67459">d</m:ci><m:ci id="id67461">μ</m:ci><m:ci id="id67464">p</m:ci></m:apply><m:apply id="id67466"><m:divide id="id67467"/><m:apply id="id67468"><m:times id="id67469"/><m:apply id="id67470"><m:csymbol id="id67471" cd="ambiguous">superscript</m:csymbol><m:ci id="id67476">d</m:ci><m:cn id="id67478">4</m:cn></m:apply><m:ci id="id67480">p</m:ci></m:apply><m:apply id="id67482"><m:times id="id67483"/><m:apply id="id67484"><m:csymbol id="id67485" cd="ambiguous">superscript</m:csymbol><m:apply id="id67490"><m:times id="id67491"/><m:cn id="id67492">2</m:cn><m:ci id="id67494">π</m:ci></m:apply><m:cn id="id67497">4</m:cn></m:apply><m:apply id="id67499"><m:plus id="id67500"/><m:cn id="id67501">1</m:cn><m:apply id="id67503"><m:divide id="id67504"/><m:apply id="id67505"><m:csymbol id="id67506" cd="ambiguous">subscript</m:csymbol><m:ci id="id67511">p</m:ci><m:cn id="id67513">0</m:cn></m:apply><m:ci id="id67515">κ</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id68373"><h4>Hit id68373</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 68</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/195/f077777.xhtml#id68373</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:218511(000056%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id68373" display="block"><m:semantics id="id68376"><m:mrow id="id68377"><m:mrow id="id68378"><m:mrow id="id68379"><m:mrow id="id68380"><m:mi id="id68382">g</m:mi><m:mo id="id68384">⁢</m:mo><m:msubsup id="id68386"><m:mi id="id68387" mathvariant="bold">D</m:mi><m:mi id="id68392">x</m:mi><m:mi id="id68394">α</m:mi></m:msubsup><m:mo id="id68396">⁢</m:mo><m:mi id="id68398" mathvariant="normal">Ψ</m:mi><m:mo id="id68403">⁢</m:mo><m:mfenced id="id68406" open="(" close=")"><m:mi id="id68411">x</m:mi></m:mfenced></m:mrow><m:mo id="id68413">+</m:mo><m:mrow id="id68415"><m:mi id="id68416">a</m:mi><m:mo id="id68418">⁢</m:mo><m:mfenced id="id68420" open="(" close=")"><m:mi id="id68426">x</m:mi></m:mfenced><m:mo id="id68428">⁢</m:mo><m:mi id="id68430" mathvariant="normal">Ψ</m:mi><m:mo id="id68435">⁢</m:mo><m:mfenced id="id68437" open="(" close=")"><m:mi id="id68442">x</m:mi></m:mfenced></m:mrow><m:mo id="id68444">+</m:mo><m:mrow id="id68446"><m:mi id="id68448">b</m:mi><m:mo id="id68450">⁢</m:mo><m:mfenced id="id68452" open="(" close=")"><m:mi id="id68457">x</m:mi></m:mfenced><m:mo id="id68459">⁢</m:mo><m:msup id="id68462"><m:mi id="id68463" mathvariant="normal">Ψ</m:mi><m:mn id="id68467">3</m:mn></m:msup><m:mo id="id68470">⁢</m:mo><m:mfenced id="id68472" open="(" close=")"><m:mi id="id68477">x</m:mi></m:mfenced></m:mrow></m:mrow><m:mo id="id68479">=</m:mo><m:mn id="id68481">0</m:mn></m:mrow><m:mo id="id68483">,</m:mo></m:mrow><m:annotation-xml id="id68486" encoding="MathML-Content"><m:apply id="id68489"><m:eq id="id68490"/><m:apply id="id68491"><m:plus id="id68492"/><m:apply id="id68493"><m:times id="id68494"/><m:ci id="id68495">g</m:ci><m:apply id="id68497"><m:csymbol id="id68498" cd="ambiguous">subscript</m:csymbol><m:apply id="id68503"><m:csymbol id="id68504" cd="ambiguous">superscript</m:csymbol><m:ci id="id68509">D</m:ci><m:ci id="id68511">α</m:ci></m:apply><m:ci id="id68513">x</m:ci></m:apply><m:ci id="id68516">Ψ</m:ci><m:ci id="id68518">x</m:ci></m:apply><m:apply id="id68520"><m:times id="id68521"/><m:ci id="id68522">a</m:ci><m:ci id="id68524">x</m:ci><m:ci id="id68526">Ψ</m:ci><m:ci id="id68529">x</m:ci></m:apply><m:apply id="id68531"><m:times id="id68532"/><m:ci id="id68533">b</m:ci><m:ci id="id68535">x</m:ci><m:apply id="id68537"><m:csymbol id="id68538" cd="ambiguous">superscript</m:csymbol><m:ci id="id68543">Ψ</m:ci><m:cn id="id68546">3</m:cn></m:apply><m:ci id="id68548">x</m:ci></m:apply></m:apply><m:cn id="id68550">0</m:cn></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id68839"><h4>Hit id68839</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 69</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/67/f026628.xhtml#id68839</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:224100(000069%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id68839" display="block"><m:semantics id="id68842"><m:mrow id="id68843"><m:mrow id="id68844"><m:mi id="id68845">H</m:mi><m:mo id="id68848">=</m:mo><m:mrow id="id68850"><m:mrow id="id68851"><m:msub id="id68852"><m:mo id="id68853">∫</m:mo><m:mi id="id68855">V</m:mi></m:msub><m:msup id="id68857"><m:mi id="id68858">d</m:mi><m:mn id="id68861">3</m:mn></m:msup><m:mo id="id68863">⁢</m:mo><m:mi id="id68865" mathvariant="bold">x</m:mi><m:mo id="id68870">⁢</m:mo><m:mfenced id="id68872" open="(" close=")"><m:mrow id="id68877"><m:msub id="id68878"><m:mi id="id68879">π</m:mi><m:mi id="id68882">k</m:mi></m:msub><m:mo id="id68884">,</m:mo><m:msup id="id68886"><m:mover id="id68887" accent="true"><m:mi id="id68890">A</m:mi><m:mo id="id68892">˙</m:mo></m:mover><m:mi id="id68895">k</m:mi></m:msup></m:mrow></m:mfenced></m:mrow><m:mo id="id68897">-</m:mo><m:msub id="id68899"><m:mi id="id68900">L</m:mi><m:mn id="id68902">00</m:mn></m:msub></m:mrow></m:mrow><m:mo id="id68904">,</m:mo></m:mrow><m:annotation-xml id="id68906" encoding="MathML-Content"><m:apply id="id68910"><m:eq id="id68911"/><m:ci id="id68912">H</m:ci><m:apply id="id68914"><m:minus id="id68915"/><m:apply id="id68916"><m:apply id="id68917"><m:csymbol id="id68918" cd="ambiguous">subscript</m:csymbol><m:int id="id68923"/><m:ci id="id68924">V</m:ci></m:apply><m:apply id="id68926"><m:times id="id68927"/><m:apply id="id68928"><m:csymbol id="id68929" cd="ambiguous">superscript</m:csymbol><m:ci id="id68934">d</m:ci><m:cn id="id68936">3</m:cn></m:apply><m:ci id="id68938">x</m:ci><m:apply id="id68940"><m:interval id="id68942" closure="open"/><m:apply id="id68945"><m:csymbol id="id68946" cd="ambiguous">subscript</m:csymbol><m:ci id="id68951">π</m:ci><m:ci id="id68953">k</m:ci></m:apply><m:apply id="id68955"><m:csymbol id="id68956" cd="ambiguous">superscript</m:csymbol><m:apply id="id68961"><m:ci id="id68962">˙</m:ci><m:ci id="id68964">A</m:ci></m:apply><m:ci id="id68966">k</m:ci></m:apply></m:apply></m:apply></m:apply><m:apply id="id68969"><m:csymbol id="id68970" cd="ambiguous">subscript</m:csymbol><m:ci id="id68974">L</m:ci><m:cn id="id68976">00</m:cn></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id69078"><h4>Hit id69078</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 70</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/3/f001042.xhtml#id69078</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:233653(000095%) VariableMap:[g, F x 2, d, rm, int, PYM, , x 4, frac, 1, S, 4, ~, \ x 7, _ x 2, ^, ab x 2, cal, =] Expects 2 occurences for 'd' but has only 1 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id69078" alttext="{\cal S}_{{PYM}}=\int\,{\rm d}g\,\frac{1}{4}\, F_{{ab}}F^{{ab}}~," display="block"><m:semantics id="id69084"><m:mrow id="id69085"><m:mrow id="id69086"><m:msub id="id69087"><m:mi id="id69088" mathvariant="script">S</m:mi><m:mrow id="id69092"><m:mi id="id69093">P</m:mi><m:mo id="id69095">⁢</m:mo><m:mi id="id69098">Y</m:mi><m:mo id="id69100">⁢</m:mo><m:mi id="id69102">M</m:mi></m:mrow></m:msub><m:mo id="id69104">=</m:mo><m:mrow id="id69107"><m:mo id="id69108">∫</m:mo><m:mi id="id69110" mathvariant="normal">d</m:mi><m:mo id="id69114">⁢</m:mo><m:mi id="id69117">g</m:mi><m:mo id="id69119">⁢</m:mo><m:mfrac id="id69121"><m:mn id="id69122">1</m:mn><m:mn id="id69125">4</m:mn></m:mfrac><m:mo id="id69127">⁢</m:mo><m:msub id="id69129"><m:mi id="id69130">F</m:mi><m:mrow id="id69132"><m:mi id="id69133">a</m:mi><m:mo id="id69136">⁢</m:mo><m:mi id="id69138">b</m:mi></m:mrow></m:msub><m:mo id="id69140">⁢</m:mo><m:msup id="id69142"><m:mi id="id69144">F</m:mi><m:mrow id="id69146"><m:mi id="id69147">a</m:mi><m:mo id="id69149">⁢</m:mo><m:mi id="id69151">b</m:mi></m:mrow></m:msup></m:mrow></m:mrow><m:mo id="id69153">,</m:mo></m:mrow><m:annotation-xml id="id69156" encoding="MathML-Content"><m:apply id="id69159"><m:eq id="id69160"/><m:apply id="id69161"><m:csymbol id="id69162" cd="ambiguous">subscript</m:csymbol><m:ci id="id69167">S</m:ci><m:apply id="id69169"><m:times id="id69170"/><m:ci id="id69171">P</m:ci><m:ci id="id69173">Y</m:ci><m:ci id="id69175">M</m:ci></m:apply></m:apply><m:apply id="id69177"><m:int id="id69178"/><m:apply id="id69180"><m:times id="id69181"/><m:ci id="id69182">d</m:ci><m:ci id="id69184">g</m:ci><m:apply id="id69186"><m:divide id="id69187"/><m:cn id="id69188" type="integer">1</m:cn><m:cn id="id69192" type="integer">4</m:cn></m:apply><m:apply id="id69197"><m:csymbol id="id69198" cd="ambiguous">subscript</m:csymbol><m:ci id="id69203">F</m:ci><m:apply id="id69205"><m:times id="id69206"/><m:ci id="id69207">a</m:ci><m:ci id="id69209">b</m:ci></m:apply></m:apply><m:apply id="id69211"><m:csymbol id="id69212" cd="ambiguous">superscript</m:csymbol><m:ci id="id69217">F</m:ci><m:apply id="id69219"><m:times id="id69220"/><m:ci id="id69221">a</m:ci><m:ci id="id69223">b</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id69225" encoding="application/x-tex">{\cal S}_{{PYM}}=\int\,{\rm d}g\,\frac{1}{4}\, F_{{ab}}F^{{ab}}~,</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id69338"><h4>Hit id69338</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 71</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/213/f084947.xhtml#id69338</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:231033(000059%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id69338" display="block"><m:semantics id="id69342"><m:mrow id="id69343"><m:mrow id="id69344"><m:mrow id="id69345"><m:mi id="id69346">F</m:mi><m:mo id="id69348">⁢</m:mo><m:mfenced id="id69350" open="(" close=")"><m:mrow id="id69355"><m:msub id="id69356"><m:mi id="id69358">x</m:mi><m:mi id="id69360">ε</m:mi></m:msub><m:mo id="id69362">,</m:mo><m:mi id="id69364">ε</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id69367">=</m:mo><m:mfrac id="id69369"><m:mrow id="id69370"><m:mrow id="id69371"><m:mn id="id69372">11</m:mn><m:mo id="id69374">⁢</m:mo><m:mi id="id69376">ε</m:mi></m:mrow><m:mo id="id69379">+</m:mo><m:mrow id="id69381"><m:mi id="id69382">o</m:mi><m:mo id="id69384">⁢</m:mo><m:mfenced id="id69387" open="(" close=")"><m:mi id="id69392">ε</m:mi></m:mfenced></m:mrow></m:mrow><m:msup id="id69394"><m:mfenced id="id69395" open="|" close="|"><m:mrow id="id69400"><m:mn id="id69401">1</m:mn><m:mo id="id69403">+</m:mo><m:msub id="id69406"><m:mi id="id69407">x</m:mi><m:mi id="id69409">ε</m:mi></m:msub></m:mrow></m:mfenced><m:mn id="id69411">3</m:mn></m:msup></m:mfrac></m:mrow><m:mo id="id69413">.</m:mo></m:mrow><m:annotation-xml id="id69415" encoding="MathML-Content"><m:apply id="id69419"><m:eq id="id69420"/><m:apply id="id69421"><m:times id="id69422"/><m:ci id="id69423">F</m:ci><m:apply id="id69425"><m:interval id="id69426" closure="open"/><m:apply id="id69430"><m:csymbol id="id69431" cd="ambiguous">subscript</m:csymbol><m:ci id="id69435">x</m:ci><m:ci id="id69437">ε</m:ci></m:apply><m:ci id="id69440">ε</m:ci></m:apply></m:apply><m:apply id="id69442"><m:divide id="id69443"/><m:apply id="id69444"><m:plus id="id69445"/><m:apply id="id69446"><m:times id="id69448"/><m:cn id="id69449">11</m:cn><m:ci id="id69451">ε</m:ci></m:apply><m:apply id="id69453"><m:times id="id69454"/><m:ci id="id69455">o</m:ci><m:ci id="id69457">ε</m:ci></m:apply></m:apply><m:apply id="id69460"><m:csymbol id="id69461" cd="ambiguous">superscript</m:csymbol><m:apply id="id69466"><m:abs id="id69467"/><m:apply id="id69468"><m:plus id="id69469"/><m:cn id="id69470">1</m:cn><m:apply id="id69472"><m:csymbol id="id69473" cd="ambiguous">subscript</m:csymbol><m:ci id="id69478">x</m:ci><m:ci id="id69480">ε</m:ci></m:apply></m:apply></m:apply><m:cn id="id69482">3</m:cn></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id69509"><h4>Hit id69509</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 72</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/189/f075227.xhtml#id69509</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:244066(000031%) VariableMap:[A x 3, mathbb, ast x 2, ( x 3, mathrm x 2, ) x 3, ., ChW x 2, sigma, alpha x 2, p, \ x 9, _ x 3, ^ x 2, bar, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id69509" alttext="\sigma _{{A}}^{{\ast}}(\mathrm{ChW}_{{\mathbb{A}}}(\bar{p}^{{\ast}}\alpha))=\mathrm{ChW}_{{A}}(\alpha)." display="block"><m:semantics id="id69515"><m:mrow id="id69516"><m:mrow id="id69517"><m:mrow id="id69518"><m:msubsup id="id69519"><m:mi id="id69520">σ</m:mi><m:mi id="id69523">A</m:mi><m:mo id="id69525">∗</m:mo></m:msubsup><m:mo id="id69527">⁢</m:mo><m:mfenced id="id69530" open="(" close=")"><m:mrow id="id69535"><m:msub id="id69536"><m:mi id="id69537">ChW</m:mi><m:mi id="id69539" mathvariant="double-struck">A</m:mi></m:msub><m:mo id="id69544">⁢</m:mo><m:mfenced id="id69546" open="(" close=")"><m:mrow id="id69551"><m:msup id="id69552"><m:mover id="id69553" accent="true"><m:mi id="id69556">p</m:mi><m:mo id="id69559">¯</m:mo></m:mover><m:mo id="id69561">∗</m:mo></m:msup><m:mo id="id69563">⁢</m:mo><m:mi id="id69566">α</m:mi></m:mrow></m:mfenced></m:mrow></m:mfenced></m:mrow><m:mo id="id69568">=</m:mo><m:mrow id="id69570"><m:msub id="id69571"><m:mi id="id69572">ChW</m:mi><m:mi id="id69575">A</m:mi></m:msub><m:mo id="id69577">⁢</m:mo><m:mfenced id="id69579" open="(" close=")"><m:mi id="id69584">α</m:mi></m:mfenced></m:mrow></m:mrow><m:mo id="id69587">.</m:mo></m:mrow><m:annotation-xml id="id69589" encoding="MathML-Content"><m:apply id="id69592"><m:eq id="id69593"/><m:apply id="id69594"><m:times id="id69595"/><m:apply id="id69596"><m:csymbol id="id69597" cd="ambiguous">superscript</m:csymbol><m:apply id="id69602"><m:csymbol id="id69603" cd="ambiguous">subscript</m:csymbol><m:ci id="id69608">σ</m:ci><m:ci id="id69610">A</m:ci></m:apply><m:ci id="id69612">∗</m:ci></m:apply><m:apply id="id69615"><m:times id="id69616"/><m:apply id="id69617"><m:csymbol id="id69618" cd="ambiguous">subscript</m:csymbol><m:ci id="id69623">ChW</m:ci><m:ci id="id69625">A</m:ci></m:apply><m:apply id="id69627"><m:times id="id69628"/><m:apply id="id69629"><m:csymbol id="id69630" cd="ambiguous">superscript</m:csymbol><m:apply id="id69635"><m:ci id="id69636">¯</m:ci><m:ci id="id69638">p</m:ci></m:apply><m:ci id="id69640">∗</m:ci></m:apply><m:ci id="id69643">α</m:ci></m:apply></m:apply></m:apply><m:apply id="id69645"><m:times id="id69646"/><m:apply id="id69647"><m:csymbol id="id69648" cd="ambiguous">subscript</m:csymbol><m:ci id="id69653">ChW</m:ci><m:ci id="id69655">A</m:ci></m:apply><m:ci id="id69657">α</m:ci></m:apply></m:apply></m:annotation-xml><m:annotation id="id69660" encoding="application/x-tex">\sigma _{{A}}^{{\ast}}(\mathrm{ChW}_{{\mathbb{A}}}(\bar{p}^{{\ast}}\alpha))=\mathrm{ChW}_{{A}}(\alpha).</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id69716"><h4>Hit id69716</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 73</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/51/f020019.xhtml#id69716</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:245960(000026%) VariableMap:[f x 3, g x 2, A, ( x 2, ) x 2, partial x 2, , x 2, -, p x 2, bf, \ x 5, _ x 5, 8, X, =, x x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 5 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id69716" alttext="{\bf(A8)}\,\, X_{f}g=(f_{p}\partial _{x}-f_{x}\partial _{p})g" display="inline"><m:semantics id="id69722"><m:mrow id="id69723"><m:mrow id="id69724"><m:mfenced id="id69725" open="(" close=")"><m:mi id="id69730" mathvariant="bold">A8</m:mi></m:mfenced><m:mo id="id69735">⁢</m:mo><m:msub id="id69738"><m:mi id="id69739">X</m:mi><m:mi id="id69741">f</m:mi></m:msub><m:mo id="id69743">⁢</m:mo><m:mi id="id69745">g</m:mi></m:mrow><m:mo id="id69748">=</m:mo><m:mrow id="id69750"><m:mfenced id="id69751" open="(" close=")"><m:mrow id="id69756"><m:mrow id="id69757"><m:msub id="id69758"><m:mi id="id69759">f</m:mi><m:mi id="id69761">p</m:mi></m:msub><m:mo id="id69763">⁢</m:mo><m:msub id="id69766"><m:mo id="id69767">∂</m:mo><m:mi id="id69769">x</m:mi></m:msub></m:mrow><m:mo id="id69771">-</m:mo><m:mrow id="id69773"><m:msub id="id69774"><m:mi id="id69776">f</m:mi><m:mi id="id69778">x</m:mi></m:msub><m:mo id="id69780">⁢</m:mo><m:msub id="id69782"><m:mo id="id69783">∂</m:mo><m:mi id="id69786">p</m:mi></m:msub></m:mrow></m:mrow></m:mfenced><m:mo id="id69788">⁢</m:mo><m:mi id="id69790">g</m:mi></m:mrow></m:mrow><m:annotation-xml id="id69792" encoding="MathML-Content"><m:apply id="id69796"><m:eq id="id69797"/><m:apply id="id69798"><m:times id="id69799"/><m:ci id="id69800">A8</m:ci><m:apply id="id69802"><m:csymbol id="id69803" cd="ambiguous">subscript</m:csymbol><m:ci id="id69808">X</m:ci><m:ci id="id69810">f</m:ci></m:apply><m:ci id="id69812">g</m:ci></m:apply><m:apply id="id69814"><m:times id="id69815"/><m:apply id="id69816"><m:minus id="id69817"/><m:apply id="id69818"><m:times id="id69820"/><m:apply id="id69821"><m:csymbol id="id69822" cd="ambiguous">subscript</m:csymbol><m:ci id="id69826">f</m:ci><m:ci id="id69828">p</m:ci></m:apply><m:apply id="id69831"><m:csymbol id="id69832" cd="ambiguous">subscript</m:csymbol><m:partialdiff id="id69836"/><m:ci id="id69837">x</m:ci></m:apply></m:apply><m:apply id="id69840"><m:times id="id69841"/><m:apply id="id69842"><m:csymbol id="id69843" cd="ambiguous">subscript</m:csymbol><m:ci id="id69847">f</m:ci><m:ci id="id69850">x</m:ci></m:apply><m:apply id="id69852"><m:csymbol id="id69853" cd="ambiguous">subscript</m:csymbol><m:partialdiff id="id69857"/><m:ci id="id69858">p</m:ci></m:apply></m:apply></m:apply><m:ci id="id69861">g</m:ci></m:apply></m:apply></m:annotation-xml><m:annotation id="id69863" encoding="application/x-tex">{\bf(A8)}\,\, X_{f}g=(f_{p}\partial _{x}-f_{x}\partial _{p})g</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id70138"><h4>Hit id70138</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 74</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/190/f075917.xhtml#id70138</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:255518(000035%) VariableMap:[f x 3, lim, delta, ( x 2, ) x 2, ., ,, -, frac, U x 2, exp, t, \ x 4, :, _ x 2, roman, X, tX, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 4 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id70138" alttext="\delta U_{X}(f):=\roman{lim}\,\frac{U_{{exp(tX)}}f-f}{t}." display="block"><m:semantics id="id70144"><m:mrow id="id70145"><m:mrow id="id70146"><m:mrow id="id70147"><m:mi id="id70148">δ</m:mi><m:mo id="id70150">⁢</m:mo><m:msub id="id70153"><m:mi id="id70154">U</m:mi><m:mi id="id70156">X</m:mi></m:msub><m:mo id="id70158">⁢</m:mo><m:mfenced id="id70161" open="(" close=")"><m:mi id="id70166">f</m:mi></m:mfenced></m:mrow><m:mo id="id70168">:=</m:mo><m:mrow id="id70170"><m:mi id="id70171">lim</m:mi><m:mo id="id70207">⁢</m:mo><m:mfrac id="id70209"><m:mrow id="id70210"><m:mrow id="id70211"><m:msub id="id70212"><m:mi id="id70214">U</m:mi><m:mrow id="id70216"><m:mi id="id70217">e</m:mi><m:mo id="id70219">⁢</m:mo><m:mi id="id70221">x</m:mi><m:mo id="id70223">⁢</m:mo><m:mi id="id70226">p</m:mi><m:mo id="id70228">⁢</m:mo><m:mfenced id="id70230" open="(" close=")"><m:mrow id="id70235"><m:mi id="id70236">t</m:mi><m:mo id="id70239">⁢</m:mo><m:mi id="id70241">X</m:mi></m:mrow></m:mfenced></m:mrow></m:msub><m:mo id="id70243">⁢</m:mo><m:mi id="id70246">f</m:mi></m:mrow><m:mo id="id70248">-</m:mo><m:mi id="id70250">f</m:mi></m:mrow><m:mi id="id70252">t</m:mi></m:mfrac></m:mrow></m:mrow><m:mo id="id70254">.</m:mo></m:mrow><m:annotation-xml id="id70256" encoding="MathML-Content"><m:apply id="id70260"><m:ci id="id70261">:=</m:ci><m:apply id="id70263"><m:times id="id70264"/><m:ci id="id70265">δ</m:ci><m:apply id="id70267"><m:csymbol id="id70268" cd="ambiguous">subscript</m:csymbol><m:ci id="id70273">U</m:ci><m:ci id="id70275">X</m:ci></m:apply><m:ci id="id70277">f</m:ci></m:apply><m:apply id="id70279"><m:times id="id70280"/><m:ci id="id70282">lim</m:ci><m:apply id="id70284"><m:divide id="id70285"/><m:apply id="id70286"><m:minus id="id70287"/><m:apply id="id70288"><m:times id="id70289"/><m:apply id="id70290"><m:csymbol id="id70291" cd="ambiguous">subscript</m:csymbol><m:ci id="id70296">U</m:ci><m:apply id="id70298"><m:times id="id70299"/><m:ci id="id70300">e</m:ci><m:ci id="id70302">x</m:ci><m:ci id="id70304">p</m:ci><m:apply id="id70306"><m:times id="id70308"/><m:ci id="id70309">t</m:ci><m:ci id="id70311">X</m:ci></m:apply></m:apply></m:apply><m:ci id="id70313">f</m:ci></m:apply><m:ci id="id70315">f</m:ci></m:apply><m:ci id="id70317">t</m:ci></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id70319" encoding="application/x-tex">\delta U_{X}(f):=\roman{lim}\,\frac{U_{{exp(tX)}}f-f}{t}.</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id71017"><h4>Hit id71017</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 75</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/94/f037482.xhtml#id71017</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:263524(000038%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id71017" display="block"><m:semantics id="id71020"><m:mrow id="id71022"><m:mrow id="id71023"><m:msubsup id="id71024"><m:mi id="id71025">ω</m:mi><m:mi id="id71027">F</m:mi><m:mn id="id71029">2</m:mn></m:msubsup><m:mo id="id71031">=</m:mo><m:mfrac id="id71034"><m:mrow id="id71035"><m:mi id="id71036">e</m:mi><m:mo id="id71038">⁢</m:mo><m:msub id="id71040"><m:mi id="id71041">a</m:mi><m:mi id="id71043">F</m:mi></m:msub></m:mrow><m:mrow id="id71046"><m:msub id="id71047"><m:mi id="id71048">p</m:mi><m:mn id="id71050">0</m:mn></m:msub><m:mo id="id71052">⁢</m:mo><m:msub id="id71054"><m:mi id="id71055">β</m:mi><m:mi id="id71058">e</m:mi></m:msub><m:mo id="id71060">⁢</m:mo><m:msub id="id71062"><m:mi id="id71063">γ</m:mi><m:mi id="id71066">e</m:mi></m:msub></m:mrow></m:mfrac></m:mrow><m:mo id="id71068">.</m:mo></m:mrow><m:annotation-xml id="id71070" encoding="MathML-Content"><m:apply id="id71073"><m:eq id="id71074"/><m:apply id="id71076"><m:csymbol id="id71077" cd="ambiguous">superscript</m:csymbol><m:apply id="id71081"><m:csymbol id="id71082" cd="ambiguous">subscript</m:csymbol><m:ci id="id71087">ω</m:ci><m:ci id="id71089">F</m:ci></m:apply><m:cn id="id71092">2</m:cn></m:apply><m:apply id="id71094"><m:divide id="id71095"/><m:apply id="id71096"><m:times id="id71097"/><m:ci id="id71098">e</m:ci><m:apply id="id71100"><m:csymbol id="id71101" cd="ambiguous">subscript</m:csymbol><m:ci id="id71106">a</m:ci><m:ci id="id71108">F</m:ci></m:apply></m:apply><m:apply id="id71110"><m:times id="id71111"/><m:apply id="id71112"><m:csymbol id="id71113" cd="ambiguous">subscript</m:csymbol><m:ci id="id71118">p</m:ci><m:cn id="id71120">0</m:cn></m:apply><m:apply id="id71122"><m:csymbol id="id71123" cd="ambiguous">subscript</m:csymbol><m:ci id="id71128">β</m:ci><m:ci id="id71130">e</m:ci></m:apply><m:apply id="id71132"><m:csymbol id="id71134" cd="ambiguous">subscript</m:csymbol><m:ci id="id71138">γ</m:ci><m:ci id="id71141">e</m:ci></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id74990"><h4>Hit id74990</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 76</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/117/f046569.xhtml#id74990</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:322258(000047%) VariableMap:[D x 2, c, a, kappa, mu, M, ( x 2, ) x 2, ., , x 4, - x 3, 3, 2 x 3, over, 1, V, ], \ x 8, _ x 2, cal, ^, =, [] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id74990" alttext="\kappa M_{{[1]a}}\, c^{2}=-{\cal V}_{{(D-2)}}\,{(D-3)\over 2}\,\mu\,." display="block"><m:semantics id="id74996"><m:mrow id="id74998"><m:mrow id="id74999"><m:mrow id="id75000"><m:mi id="id75001">κ</m:mi><m:mo id="id75003">⁢</m:mo><m:msub id="id75006"><m:mi id="id75007">M</m:mi><m:mrow id="id75009"><m:mfenced id="id75010" open="[" close="]"><m:mn id="id75015">1</m:mn></m:mfenced><m:mo id="id75017">⁢</m:mo><m:mi id="id75019">a</m:mi></m:mrow></m:msub><m:mo id="id75022">⁢</m:mo><m:msup id="id75024"><m:mi id="id75025">c</m:mi><m:mn id="id75027">2</m:mn></m:msup></m:mrow><m:mo id="id75029">=</m:mo><m:mrow id="id75031"><m:mo id="id75032">-</m:mo><m:mrow id="id75035"><m:msub id="id75036"><m:mi id="id75037" mathvariant="script">V</m:mi><m:mfenced id="id75041" open="(" close=")"><m:mrow id="id75046"><m:mi id="id75047">D</m:mi><m:mo id="id75049">-</m:mo><m:mn id="id75052">2</m:mn></m:mrow></m:mfenced></m:msub><m:mo id="id75054">⁢</m:mo><m:mfrac id="id75056"><m:mfenced id="id75057" open="(" close=")"><m:mrow id="id75062"><m:mi id="id75063">D</m:mi><m:mo id="id75065">-</m:mo><m:mn id="id75068">3</m:mn></m:mrow></m:mfenced><m:mn id="id75070">2</m:mn></m:mfrac><m:mo id="id75072">⁢</m:mo><m:mi id="id75074">μ</m:mi></m:mrow></m:mrow></m:mrow><m:mo id="id75077">.</m:mo></m:mrow><m:annotation-xml id="id75079" encoding="MathML-Content"><m:apply id="id75082"><m:eq id="id75083"/><m:apply id="id75084"><m:times id="id75085"/><m:ci id="id75086">κ</m:ci><m:apply id="id75089"><m:csymbol id="id75090" cd="ambiguous">subscript</m:csymbol><m:ci id="id75094">M</m:ci><m:apply id="id75097"><m:times id="id75098"/><m:cn id="id75099" type="integer">1</m:cn><m:ci id="id75103">a</m:ci></m:apply></m:apply><m:apply id="id75105"><m:csymbol id="id75106" cd="ambiguous">superscript</m:csymbol><m:ci id="id75111">c</m:ci><m:cn id="id75113" type="integer">2</m:cn></m:apply></m:apply><m:apply id="id75118"><m:minus id="id75119"/><m:apply id="id75120"><m:times id="id75121"/><m:apply id="id75122"><m:csymbol id="id75123" cd="ambiguous">subscript</m:csymbol><m:ci id="id75128">V</m:ci><m:apply id="id75130"><m:minus id="id75131"/><m:ci id="id75132">D</m:ci><m:cn id="id75134" type="integer">2</m:cn></m:apply></m:apply><m:apply id="id75138"><m:divide id="id75139"/><m:apply id="id75140"><m:minus id="id75142"/><m:ci id="id75143">D</m:ci><m:cn id="id75145" type="integer">3</m:cn></m:apply><m:cn id="id75149" type="integer">2</m:cn></m:apply><m:ci id="id75154">μ</m:ci></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id75156" encoding="application/x-tex">\kappa M_{{[1]a}}\, c^{2}=-{\cal V}_{{(D-2)}}\,{(D-3)\over 2}\,\mu\,.</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id76441"><h4>Hit id76441</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 77</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/104/f041386.xhtml#id76441</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:331512(000020%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id76441" display="block"><m:semantics id="id76445"><m:mrow id="id76446"><m:mrow id="id76447"><m:msub id="id76448"><m:mi id="id76449" mathvariant="script">P</m:mi><m:mrow id="id76453"><m:mi id="id76454">K</m:mi><m:mo id="id76457">⁢</m:mo><m:mi id="id76459">J</m:mi></m:mrow></m:msub><m:mo id="id76461">⁢</m:mo><m:mfenced id="id76464" open="(" close=")"><m:mrow id="id76469"><m:mi id="id76470">t</m:mi><m:mo id="id76472">,</m:mo><m:mi id="id76474">z</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id76476">=</m:mo><m:mrow id="id76478"><m:mn id="id76479"> 2</m:mn><m:mo id="id76482">⁢</m:mo><m:msub id="id76484"><m:mi id="id76485">P</m:mi><m:mrow id="id76487"><m:mi id="id76488">K</m:mi><m:mo id="id76490">⁢</m:mo><m:mi id="id76493">J</m:mi></m:mrow></m:msub><m:mo id="id76495">⁢</m:mo><m:mfenced id="id76497" open="(" close=")"><m:mrow id="id76502"><m:mrow id="id76504"><m:msub id="id76505"><m:mi id="id76506">α</m:mi><m:mi id="id76508">s</m:mi></m:msub><m:mo id="id76510">⁢</m:mo><m:mfenced id="id76513" open="(" close=")"><m:mi id="id76518">t</m:mi></m:mfenced></m:mrow><m:mo id="id76520">,</m:mo><m:mi id="id76522">z</m:mi></m:mrow></m:mfenced></m:mrow></m:mrow><m:annotation-xml id="id76524" encoding="MathML-Content"><m:apply id="id76527"><m:eq id="id76528"/><m:apply id="id76530"><m:times id="id76531"/><m:apply id="id76532"><m:csymbol id="id76533" cd="ambiguous">subscript</m:csymbol><m:ci id="id76537">P</m:ci><m:apply id="id76540"><m:times id="id76541"/><m:ci id="id76542">K</m:ci><m:ci id="id76544">J</m:ci></m:apply></m:apply><m:apply id="id76546"><m:interval id="id76547" closure="open"/><m:ci id="id76550">t</m:ci><m:ci id="id76552">z</m:ci></m:apply></m:apply><m:apply id="id76555"><m:times id="id76556"/><m:cn id="id76557"> 2</m:cn><m:apply id="id76559"><m:csymbol id="id76560" cd="ambiguous">subscript</m:csymbol><m:ci id="id76565">P</m:ci><m:apply id="id76567"><m:times id="id76568"/><m:ci id="id76569">K</m:ci><m:ci id="id76571">J</m:ci></m:apply></m:apply><m:apply id="id76573"><m:interval id="id76574" closure="open"/><m:apply id="id76578"><m:times id="id76579"/><m:apply id="id76580"><m:csymbol id="id76581" cd="ambiguous">subscript</m:csymbol><m:ci id="id76586">α</m:ci><m:ci id="id76588">s</m:ci></m:apply><m:ci id="id76590">t</m:ci></m:apply><m:ci id="id76592">z</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id83387"><h4>Hit id83387</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 78</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/58/f023151.xhtml#id83387</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:446328(000035%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id83387" display="block"><m:semantics id="id83390"><m:mrow id="id83391"><m:mrow id="id83392"><m:msub id="id83393"><m:mi id="id83394">F</m:mi><m:mi id="id83397">p</m:mi></m:msub><m:mo id="id83399">⁢</m:mo><m:mfenced id="id83401" open="(" close=")"><m:msubsup id="id83406"><m:mi id="id83407">q</m:mi><m:mo id="id83409">⟂</m:mo><m:mn id="id83412">2</m:mn></m:msubsup></m:mfenced></m:mrow><m:mo id="id83414">=</m:mo><m:msup id="id83416"><m:mi id="id83417">e</m:mi><m:mrow id="id83419"><m:mo id="id83420">-</m:mo><m:mrow id="id83422"><m:mfrac id="id83424"><m:mi id="id83425">B</m:mi><m:mn id="id83427">4</m:mn></m:mfrac><m:mo id="id83429">⁢</m:mo><m:msubsup id="id83431"><m:mi id="id83432">q</m:mi><m:mo id="id83434">⟂</m:mo><m:mn id="id83437">2</m:mn></m:msubsup></m:mrow></m:mrow></m:msup></m:mrow><m:annotation-xml id="id83439" encoding="MathML-Content"><m:apply id="id83442"><m:eq id="id83443"/><m:apply id="id83444"><m:times id="id83446"/><m:apply id="id83447"><m:csymbol id="id83448" cd="ambiguous">subscript</m:csymbol><m:ci id="id83452">F</m:ci><m:ci id="id83454">p</m:ci></m:apply><m:apply id="id83457"><m:csymbol id="id83458" cd="ambiguous">subscript</m:csymbol><m:apply id="id83462"><m:csymbol id="id83463" cd="ambiguous">superscript</m:csymbol><m:ci id="id83468">q</m:ci><m:cn id="id83470">2</m:cn></m:apply><m:ci id="id83472">⟂</m:ci></m:apply></m:apply><m:apply id="id83475"><m:csymbol id="id83476" cd="ambiguous">superscript</m:csymbol><m:ci id="id83480">e</m:ci><m:apply id="id83483"><m:minus id="id83484"/><m:apply id="id83485"><m:times id="id83486"/><m:apply id="id83487"><m:divide id="id83488"/><m:ci id="id83489">B</m:ci><m:cn id="id83491">4</m:cn></m:apply><m:apply id="id83493"><m:csymbol id="id83494" cd="ambiguous">subscript</m:csymbol><m:apply id="id83499"><m:csymbol id="id83500" cd="ambiguous">superscript</m:csymbol><m:ci id="id83505">q</m:ci><m:cn id="id83507">2</m:cn></m:apply><m:ci id="id83509">⟂</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id83839"><h4>Hit id83839</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 79</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/26/f010029.xhtml#id83839</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:455249(000041%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id83839" display="block"><m:semantics id="id83842"><m:mrow id="id83844"><m:mrow id="id83845"><m:mrow id="id83846"><m:mi id="id83847">f</m:mi><m:mo id="id83849">⁢</m:mo><m:mfenced id="id83851" open="(" close=")"><m:mi id="id83856">b</m:mi></m:mfenced></m:mrow><m:mo id="id83858">=</m:mo><m:mrow id="id83861"><m:mfrac id="id83862"><m:mrow id="id83863"><m:mn id="id83864">1</m:mn><m:mo id="id83866">-</m:mo><m:mrow id="id83868"><m:mi id="id83869">b</m:mi><m:mo id="id83871">/</m:mo><m:mi id="id83873">a</m:mi></m:mrow></m:mrow><m:mrow id="id83876"><m:mfenced id="id83877" open="(" close=")"><m:mrow id="id83882"><m:mn id="id83883">1</m:mn><m:mo id="id83885">-</m:mo><m:mi id="id83887">b</m:mi></m:mrow></m:mfenced><m:mo id="id83889">⁢</m:mo><m:mfenced id="id83892" open="(" close=")"><m:mrow id="id83897"><m:mn id="id83898">1</m:mn><m:mo id="id83900">-</m:mo><m:mrow id="id83902"><m:mrow id="id83903"><m:mi id="id83904">b</m:mi><m:mo id="id83906">/</m:mo><m:mi id="id83908">a</m:mi></m:mrow><m:mo id="id83910">⁢</m:mo><m:mi id="id83913">z</m:mi></m:mrow></m:mrow></m:mfenced></m:mrow></m:mfrac><m:mo id="id83915">⁢</m:mo><m:mi id="id83917">f</m:mi><m:mo id="id83920">⁢</m:mo><m:mfenced id="id83922" open="(" close=")"><m:mrow id="id83927"><m:mi id="id83928">b</m:mi><m:mo id="id83930">⁢</m:mo><m:mi id="id83933">q</m:mi></m:mrow></m:mfenced></m:mrow></m:mrow><m:mo id="id83935">.</m:mo></m:mrow><m:annotation-xml id="id83937" encoding="MathML-Content"><m:apply id="id83940"><m:eq id="id83941"/><m:apply id="id83942"><m:times id="id83943"/><m:ci id="id83944">f</m:ci><m:ci id="id83947">b</m:ci></m:apply><m:apply id="id83949"><m:times id="id83950"/><m:apply id="id83951"><m:divide id="id83952"/><m:apply id="id83953"><m:minus id="id83954"/><m:cn id="id83955">1</m:cn><m:apply id="id83957"><m:divide id="id83958"/><m:ci id="id83959">b</m:ci><m:ci id="id83962">a</m:ci></m:apply></m:apply><m:apply id="id83964"><m:times id="id83965"/><m:apply id="id83966"><m:minus id="id83967"/><m:cn id="id83968">1</m:cn><m:ci id="id83970">b</m:ci></m:apply><m:apply id="id83972"><m:minus id="id83973"/><m:cn id="id83974">1</m:cn><m:apply id="id83976"><m:times id="id83978"/><m:apply id="id83979"><m:divide id="id83980"/><m:ci id="id83981">b</m:ci><m:ci id="id83983">a</m:ci></m:apply><m:ci id="id83985">z</m:ci></m:apply></m:apply></m:apply></m:apply><m:ci id="id83987">f</m:ci><m:apply id="id83989"><m:times id="id83990"/><m:ci id="id83991">b</m:ci><m:ci id="id83994">q</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id86390"><h4>Hit id86390</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 80</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/199/f079554.xhtml#id86390</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:498274(000071%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id86390" display="block"><m:semantics id="id86394"><m:mrow id="id86395"><m:mrow id="id86396"><m:mrow id="id86397"><m:mo id="id86398">-</m:mo><m:mfrac id="id86400"><m:mn id="id86401">1</m:mn><m:msubsup id="id86403"><m:mi id="id86404">N</m:mi><m:mi id="id86406">c</m:mi><m:mn id="id86408">2</m:mn></m:msubsup></m:mfrac></m:mrow><m:mo id="id86411">⟹</m:mo><m:mfrac id="id86413"><m:mrow id="id86414"><m:mrow id="id86415"><m:mn id="id86416">2</m:mn><m:mo id="id86418">⁢</m:mo><m:msub id="id86421"><m:mi id="id86422">C</m:mi><m:mi id="id86424">R</m:mi></m:msub></m:mrow><m:mo id="id86426">-</m:mo><m:msub id="id86428"><m:mi id="id86429">N</m:mi><m:mi id="id86431">c</m:mi></m:msub></m:mrow><m:msub id="id86434"><m:mi id="id86435">N</m:mi><m:mi id="id86437">c</m:mi></m:msub></m:mfrac></m:mrow><m:mo id="id86439">,</m:mo></m:mrow><m:annotation-xml id="id86441" encoding="MathML-Content"><m:apply id="id86444"><m:ci id="id86445">⟹</m:ci><m:apply id="id86448"><m:minus id="id86449"/><m:apply id="id86450"><m:divide id="id86451"/><m:cn id="id86452">1</m:cn><m:apply id="id86454"><m:csymbol id="id86455" cd="ambiguous">superscript</m:csymbol><m:apply id="id86460"><m:csymbol id="id86461" cd="ambiguous">subscript</m:csymbol><m:ci id="id86466">N</m:ci><m:ci id="id86468">c</m:ci></m:apply><m:cn id="id86470">2</m:cn></m:apply></m:apply></m:apply><m:apply id="id86472"><m:divide id="id86473"/><m:apply id="id86474"><m:minus id="id86475"/><m:apply id="id86476"><m:times id="id86477"/><m:cn id="id86478">2</m:cn><m:apply id="id86481"><m:csymbol id="id86482" cd="ambiguous">subscript</m:csymbol><m:ci id="id86486">C</m:ci><m:ci id="id86488">R</m:ci></m:apply></m:apply><m:apply id="id86491"><m:csymbol id="id86492" cd="ambiguous">subscript</m:csymbol><m:ci id="id86496">N</m:ci><m:ci id="id86498">c</m:ci></m:apply></m:apply><m:apply id="id86501"><m:csymbol id="id86502" cd="ambiguous">subscript</m:csymbol><m:ci id="id86506">N</m:ci><m:ci id="id86508">c</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id86443"><h4>Hit id86443</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 81</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/86/f034074.xhtml#id86443</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:493609(000034%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id86443" display="inline"><m:semantics id="id86446"><m:mfenced id="id86449" open="⟨" close="⟩"><m:mrow id="id86455"><m:msup id="id86456"><m:mi id="id86457">J</m:mi><m:mi id="id86459">a</m:mi></m:msup><m:mo id="id86461">⁢</m:mo><m:mfenced id="id86464" open="(" close=")"><m:mrow id="id86467"><m:mi id="id86468">z</m:mi><m:mo id="id86470">,</m:mo><m:mover id="id86472" accent="true"><m:mi id="id86476">z</m:mi><m:mo id="id86478">¯</m:mo></m:mover></m:mrow></m:mfenced><m:mo id="id86480">⁢</m:mo><m:msup id="id86482"><m:mfenced id="id86484" open="(" close=")"><m:mrow id="id86489"><m:mi id="id86490">g</m:mi><m:mo id="id86492">⁢</m:mo><m:mover id="id86494" accent="true"><m:mi id="id86498">J</m:mi><m:mo id="id86500">¯</m:mo></m:mover><m:mo id="id86502">⁢</m:mo><m:msup id="id86504"><m:mi id="id86506">g</m:mi><m:mrow id="id86508"><m:mo id="id86509">-</m:mo><m:mn id="id86511">1</m:mn></m:mrow></m:msup></m:mrow></m:mfenced><m:mi id="id86513">b</m:mi></m:msup><m:mo id="id86515">⁢</m:mo><m:mfenced id="id86518" open="(" close=")"><m:mrow id="id86523"><m:mi id="id86524">w</m:mi><m:mo id="id86526">,</m:mo><m:mover id="id86528" accent="true"><m:mi id="id86531">w</m:mi><m:mo id="id86533">¯</m:mo></m:mover></m:mrow></m:mfenced></m:mrow></m:mfenced><m:annotation-xml id="id86536" encoding="MathML-Content"><m:apply id="id86539"><m:times id="id86540"/><m:apply id="id86541"><m:csymbol id="id86542" cd="ambiguous">superscript</m:csymbol><m:ci id="id86547">J</m:ci><m:ci id="id86549">a</m:ci></m:apply><m:apply id="id86551"><m:interval id="id86552" closure="open"/><m:ci id="id86556">z</m:ci><m:apply id="id86558"><m:ci id="id86559">¯</m:ci><m:ci id="id86561">z</m:ci></m:apply></m:apply><m:apply id="id86563"><m:csymbol id="id86564" cd="ambiguous">superscript</m:csymbol><m:apply id="id86569"><m:times id="id86570"/><m:ci id="id86571">g</m:ci><m:apply id="id86573"><m:ci id="id86574">¯</m:ci><m:ci id="id86577">J</m:ci></m:apply><m:apply id="id86579"><m:csymbol id="id86580" cd="ambiguous">superscript</m:csymbol><m:ci id="id86585">g</m:ci><m:apply id="id86587"><m:minus id="id86588"/><m:cn id="id86589">1</m:cn></m:apply></m:apply></m:apply><m:ci id="id86591">b</m:ci></m:apply><m:apply id="id86593"><m:interval id="id86594" closure="open"/><m:ci id="id86598">w</m:ci><m:apply id="id86600"><m:ci id="id86601">¯</m:ci><m:ci id="id86603">w</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id87496"><h4>Hit id87496</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 82</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/73/f029067.xhtml#id87496</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:513467(000050%) VariableMap:[prime x 3, g x 4, wp, +, \ x 4, ( x 5, ) x 5, ^ x 3, ., =, x x 5, - x 3] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 4 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id87496" alttext="-g^{{\prime}}(x)g(-x)+g^{{\prime}}(-x)g(x)=\wp^{{\prime}}(x)." display="block"><m:semantics id="id87502"><m:mrow id="id87503"><m:mrow id="id87504"><m:mrow id="id87505"><m:mo id="id87506">-</m:mo><m:mrow id="id87508"><m:msup id="id87509"><m:mi id="id87510">g</m:mi><m:mo id="id87512">′</m:mo></m:msup><m:mo id="id87515">⁢</m:mo><m:mfenced id="id87517" open="(" close=")"><m:mi id="id87522">x</m:mi></m:mfenced><m:mo id="id87524">⁢</m:mo><m:mi id="id87527">g</m:mi><m:mo id="id87529">⁢</m:mo><m:mfenced id="id87531" open="(" close=")"><m:mrow id="id87536"><m:mo id="id87538">-</m:mo><m:mi id="id87540">x</m:mi></m:mrow></m:mfenced></m:mrow><m:mo id="id87542">+</m:mo><m:mrow id="id87544"><m:msup id="id87545"><m:mi id="id87546">g</m:mi><m:mo id="id87548">′</m:mo></m:msup><m:mo id="id87551">⁢</m:mo><m:mfenced id="id87553" open="(" close=")"><m:mrow id="id87558"><m:mo id="id87559">-</m:mo><m:mi id="id87561">x</m:mi></m:mrow></m:mfenced><m:mo id="id87563">⁢</m:mo><m:mi id="id87566">g</m:mi><m:mo id="id87568">⁢</m:mo><m:mfenced id="id87570" open="(" close=")"><m:mi id="id87575">x</m:mi></m:mfenced></m:mrow></m:mrow><m:mo id="id87578">=</m:mo><m:mrow id="id87580"><m:msup id="id87581"><m:mi id="id87582" mathvariant="normal">℘</m:mi><m:mo id="id87586">′</m:mo></m:msup><m:mo id="id87589">⁢</m:mo><m:mfenced id="id87591" open="(" close=")"><m:mi id="id87596">x</m:mi></m:mfenced></m:mrow></m:mrow><m:mo id="id87598">.</m:mo></m:mrow><m:annotation-xml id="id87601" encoding="MathML-Content"><m:apply id="id87604"><m:eq id="id87605"/><m:apply id="id87606"><m:plus id="id87607"/><m:apply id="id87608"><m:minus id="id87609"/><m:apply id="id87610"><m:times id="id87611"/><m:apply id="id87612"><m:csymbol id="id87614" cd="ambiguous">superscript</m:csymbol><m:ci id="id87618">g</m:ci><m:ci id="id87620">′</m:ci></m:apply><m:ci id="id87623">x</m:ci><m:ci id="id87625">g</m:ci><m:apply id="id87627"><m:minus id="id87628"/><m:ci id="id87629">x</m:ci></m:apply></m:apply></m:apply><m:apply id="id87631"><m:times id="id87632"/><m:apply id="id87633"><m:csymbol id="id87634" cd="ambiguous">superscript</m:csymbol><m:ci id="id87639">g</m:ci><m:ci id="id87641">′</m:ci></m:apply><m:apply id="id87644"><m:minus id="id87645"/><m:ci id="id87646">x</m:ci></m:apply><m:ci id="id87648">g</m:ci><m:ci id="id87650">x</m:ci></m:apply></m:apply><m:apply id="id87652"><m:times id="id87653"/><m:apply id="id87654"><m:csymbol id="id87655" cd="ambiguous">superscript</m:csymbol><m:ci id="id87660">℘</m:ci><m:ci id="id87662">′</m:ci></m:apply><m:ci id="id87665">x</m:ci></m:apply></m:apply></m:annotation-xml><m:annotation id="id87667" encoding="application/x-tex">-g^{{\prime}}(x)g(-x)+g^{{\prime}}(-x)g(x)=\wp^{{\prime}}(x).</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id89073"><h4>Hit id89073</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 83</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/151/f060235.xhtml#id89073</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:538940(000052%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id89073" display="block"><m:semantics id="id89076"><m:mrow id="id89077"><m:mrow id="id89078"><m:mrow id="id89079"><m:mi id="id89080">ϵ</m:mi><m:mo id="id89083">⁢</m:mo><m:mfenced id="id89085" open="(" close=")"><m:msub id="id89090"><m:mi id="id89091">k</m:mi><m:mi id="id89093">b</m:mi></m:msub></m:mfenced></m:mrow><m:mo id="id89095">=</m:mo><m:mfenced id="id89098" open="(" close=")"><m:mrow id="id89103"><m:mn id="id89104">0</m:mn><m:mo id="id89106">,</m:mo><m:munder id="id89108" accent="true"><m:mi id="id89111">ϵ</m:mi><m:mo id="id89114">¯</m:mo></m:munder><m:mo id="id89116">,</m:mo><m:mrow id="id89118"><m:mo id="id89119">-</m:mo><m:mfrac id="id89121"><m:mrow id="id89122"><m:munder id="id89124" accent="true"><m:mi id="id89127">ϵ</m:mi><m:mo id="id89129">¯</m:mo></m:munder><m:mo id="id89132">⋅</m:mo><m:munder id="id89134" accent="true"><m:mi id="id89137">k</m:mi><m:mo id="id89140">¯</m:mo></m:munder></m:mrow><m:mrow id="id89142"><m:msub id="id89143"><m:mi id="id89144">x</m:mi><m:mn id="id89146">2</m:mn></m:msub><m:mo id="id89148">⁢</m:mo><m:mi id="id89151">P</m:mi></m:mrow></m:mfrac></m:mrow></m:mrow></m:mfenced></m:mrow><m:mo id="id89153">,</m:mo></m:mrow><m:annotation-xml id="id89155" encoding="MathML-Content"><m:apply id="id89158"><m:eq id="id89159"/><m:apply id="id89160"><m:times id="id89162"/><m:ci id="id89163">ϵ</m:ci><m:apply id="id89165"><m:csymbol id="id89166" cd="ambiguous">subscript</m:csymbol><m:ci id="id89171">k</m:ci><m:ci id="id89173">b</m:ci></m:apply></m:apply><m:apply id="id89175"><m:vector id="id89176"/><m:cn id="id89177">0</m:cn><m:apply id="id89179"><m:ci id="id89180">¯</m:ci><m:ci id="id89183">ϵ</m:ci></m:apply><m:apply id="id89185"><m:minus id="id89186"/><m:apply id="id89187"><m:divide id="id89188"/><m:apply id="id89189"><m:ci id="id89190">⋅</m:ci><m:apply id="id89193"><m:ci id="id89194">¯</m:ci><m:ci id="id89196">ϵ</m:ci></m:apply><m:apply id="id89199"><m:ci id="id89200">¯</m:ci><m:ci id="id89202">k</m:ci></m:apply></m:apply><m:apply id="id89204"><m:times id="id89205"/><m:apply id="id89206"><m:csymbol id="id89208" cd="ambiguous">subscript</m:csymbol><m:ci id="id89212">x</m:ci><m:cn id="id89214">2</m:cn></m:apply><m:ci id="id89216">P</m:ci></m:apply></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id89966"><h4>Hit id89966</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 84</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/70/f027885.xhtml#id89966</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:520905(000029%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id89966" display="inline"><m:semantics id="id89969"><m:mrow id="id89970"><m:msub id="id89972"><m:mover id="id89973" accent="true"><m:mi id="id89976" mathvariant="script">H</m:mi><m:mo id="id89980">~</m:mo></m:mover><m:mrow id="id89982"><m:mi id="id89984">g</m:mi><m:mo id="id89986">⁢</m:mo><m:mi id="id89988">h</m:mi></m:mrow></m:msub><m:mo id="id89990">≡</m:mo><m:mrow id="id89993"><m:msub id="id89994"><m:mi id="id89995" mathvariant="script">H</m:mi><m:mrow id="id89999"><m:mi id="id90000">g</m:mi><m:mo id="id90002">⁢</m:mo><m:mi id="id90005">h</m:mi></m:mrow></m:msub><m:mo id="id90007">⊗</m:mo><m:msub id="id90009"><m:mi id="id90010" mathvariant="script">H</m:mi><m:mrow id="id90015"><m:mi id="id90016">m</m:mi><m:mo id="id90018">⁢</m:mo><m:mi id="id90020">a</m:mi><m:mo id="id90022">⁢</m:mo><m:mi id="id90025">t</m:mi><m:mo id="id90027">⁢</m:mo><m:mi id="id90029">t</m:mi><m:mo id="id90032">⁢</m:mo><m:mi id="id90034">e</m:mi><m:mo id="id90036">⁢</m:mo><m:mi id="id90038">r</m:mi></m:mrow></m:msub></m:mrow></m:mrow><m:annotation-xml id="id90041" encoding="MathML-Content"><m:apply id="id90044"><m:ci id="id90045">≡</m:ci><m:apply id="id90047"><m:csymbol id="id90048" cd="ambiguous">subscript</m:csymbol><m:apply id="id90053"><m:ci id="id90054">~</m:ci><m:ci id="id90056">H</m:ci></m:apply><m:apply id="id90058"><m:times id="id90060"/><m:ci id="id90061">g</m:ci><m:ci id="id90063">h</m:ci></m:apply></m:apply><m:apply id="id90065"><m:ci id="id90066">⊗</m:ci><m:apply id="id90068"><m:csymbol id="id90069" cd="ambiguous">subscript</m:csymbol><m:ci id="id90074">H</m:ci><m:apply id="id90076"><m:times id="id90077"/><m:ci id="id90078">g</m:ci><m:ci id="id90080">h</m:ci></m:apply></m:apply><m:apply id="id90083"><m:csymbol id="id90084" cd="ambiguous">subscript</m:csymbol><m:ci id="id90088">H</m:ci><m:apply id="id90090"><m:times id="id90092"/><m:ci id="id90093">m</m:ci><m:ci id="id90095">a</m:ci><m:ci id="id90097">t</m:ci><m:ci id="id90099">t</m:ci><m:ci id="id90101">e</m:ci><m:ci id="id90103">r</m:ci></m:apply></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id96632"><h4>Hit id96632</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 85</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/107/f042448.xhtml#id96632</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:638413(000037%) VariableMap:[] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 0 Expects 2 occurences for '_' but has only 0 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id96632" display="inline"><m:semantics id="id96635"><m:mrow id="id96636"><m:mi id="id96637">y</m:mi><m:mo id="id96640">=</m:mo><m:mrow id="id96642"><m:mrow id="id96643"><m:msub id="id96644"><m:mi id="id96645">y</m:mi><m:mn id="id96647">1</m:mn></m:msub><m:mo id="id96649">⁢</m:mo><m:msup id="id96652"><m:mi id="id96653" mathvariant="bold">e</m:mi><m:mo id="id96657">′</m:mo></m:msup></m:mrow><m:mo id="id96659">+</m:mo><m:mrow id="id96662"><m:msub id="id96663"><m:mi id="id96664">y</m:mi><m:mn id="id96666">2</m:mn></m:msub><m:mo id="id96668">⁢</m:mo><m:mmultiscripts id="id96670"><m:mi id="id96671" mathvariant="bold">e</m:mi><m:none id="id96676"/><m:mo id="id96677">′</m:mo><m:none id="id96679"/><m:mo id="id96680">⟂</m:mo></m:mmultiscripts></m:mrow><m:mo id="id96683">+</m:mo><m:msup id="id96685"><m:mi id="id96686">y</m:mi><m:mi id="id96688">′′</m:mi></m:msup></m:mrow></m:mrow><m:annotation-xml id="id96690" encoding="MathML-Content"><m:apply id="id96694"><m:eq id="id96695"/><m:ci id="id96696">y</m:ci><m:apply id="id96698"><m:plus id="id96699"/><m:apply id="id96700"><m:times id="id96701"/><m:apply id="id96702"><m:csymbol id="id96703" cd="ambiguous">subscript</m:csymbol><m:ci id="id96708">y</m:ci><m:cn id="id96710">1</m:cn></m:apply><m:apply id="id96712"><m:csymbol id="id96713" cd="ambiguous">superscript</m:csymbol><m:ci id="id96718">e</m:ci><m:ci id="id96720">′</m:ci></m:apply></m:apply><m:apply id="id96723"><m:times id="id96724"/><m:apply id="id96725"><m:csymbol id="id96726" cd="ambiguous">subscript</m:csymbol><m:ci id="id96730">y</m:ci><m:cn id="id96733">2</m:cn></m:apply><m:apply id="id96735"><m:csymbol id="id96736" cd="ambiguous">superscript</m:csymbol><m:apply id="id96740"><m:csymbol id="id96742" cd="ambiguous">superscript</m:csymbol><m:ci id="id96746">e</m:ci><m:ci id="id96748">′</m:ci></m:apply><m:ci id="id96751">⟂</m:ci></m:apply></m:apply><m:apply id="id96753"><m:csymbol id="id96754" cd="ambiguous">superscript</m:csymbol><m:ci id="id96759">y</m:ci><m:ci id="id96761">′′</m:ci></m:apply></m:apply></m:apply></m:annotation-xml></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="id99016"><h4>Hit id99016</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 86</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/47/f018539.xhtml#id99016</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:681770(000021%) VariableMap:[Phi x 2, A, +, Sigma, -, lambda x 3, P x 3, \ x 7, _ x 3, ^ x 3, rho, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <m:math id="id99016" alttext="\Phi _{{-\lambda}}^{P}=\rho\Sigma _{{\lambda}}^{P}+A\Phi _{{\lambda}}^{P}" display="inline"><m:semantics id="id99022"><m:mrow id="id99023"><m:msubsup id="id99024"><m:mi id="id99025" mathvariant="normal">Φ</m:mi><m:mrow id="id99030"><m:mo id="id99031">-</m:mo><m:mi id="id99033">λ</m:mi></m:mrow><m:mi id="id99036">P</m:mi></m:msubsup><m:mo id="id99038">=</m:mo><m:mrow id="id99040"><m:mrow id="id99041"><m:mi id="id99042">ρ</m:mi><m:mo id="id99044">⁢</m:mo><m:msubsup id="id99047"><m:mi id="id99048" mathvariant="normal">Σ</m:mi><m:mi id="id99052">λ</m:mi><m:mi id="id99055">P</m:mi></m:msubsup></m:mrow><m:mo id="id99057">+</m:mo><m:mrow id="id99059"><m:mi id="id99060">A</m:mi><m:mo id="id99062">⁢</m:mo><m:msubsup id="id99065"><m:mi id="id99066" mathvariant="normal">Φ</m:mi><m:mi id="id99070">λ</m:mi><m:mi id="id99073">P</m:mi></m:msubsup></m:mrow></m:mrow></m:mrow><m:annotation-xml id="id99075" encoding="MathML-Content"><m:apply id="id99078"><m:eq id="id99079"/><m:apply id="id99080"><m:csymbol id="id99082" cd="ambiguous">superscript</m:csymbol><m:apply id="id99086"><m:csymbol id="id99087" cd="ambiguous">subscript</m:csymbol><m:ci id="id99092">Φ</m:ci><m:apply id="id99094"><m:minus id="id99095"/><m:ci id="id99096">λ</m:ci></m:apply></m:apply><m:ci id="id99099">P</m:ci></m:apply><m:apply id="id99101"><m:plus id="id99102"/><m:apply id="id99103"><m:times id="id99104"/><m:ci id="id99105">ρ</m:ci><m:apply id="id99108"><m:csymbol id="id99109" cd="ambiguous">superscript</m:csymbol><m:apply id="id99113"><m:csymbol id="id99114" cd="ambiguous">subscript</m:csymbol><m:ci id="id99119">Σ</m:ci><m:ci id="id99122">λ</m:ci></m:apply><m:ci id="id99124">P</m:ci></m:apply></m:apply><m:apply id="id99126"><m:times id="id99127"/><m:ci id="id99128">A</m:ci><m:apply id="id99130"><m:csymbol id="id99131" cd="ambiguous">superscript</m:csymbol><m:apply id="id99136"><m:csymbol id="id99137" cd="ambiguous">subscript</m:csymbol><m:ci id="id99142">Φ</m:ci><m:ci id="id99144">λ</m:ci></m:apply><m:ci id="id99147">P</m:ci></m:apply></m:apply></m:apply></m:apply></m:annotation-xml><m:annotation id="id99149" encoding="application/x-tex">\Phi _{{-\lambda}}^{P}=\rho\Sigma _{{\lambda}}^{P}+A\Phi _{{\lambda}}^{P}</m:annotation></m:semantics></m:math> <br /> End of MathML <br /> .</div><div id="idp14495376"><h4>Hit idp14495376</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 87</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/116/f046110.xhtml#idp14495376</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1834726(000069%) VariableMap:[dx, mathbb x 2, N x 2, beta x 2, sup, dot, T x 4, nabla x 2, \ x 13, _ x 6, ^ x 7, leq x 2, int x 3, +, (, ), ,, - x 2, 2 x 4, dxdt, u x 2, t x 4, 0 x 4, | x 4, x] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp14495376" alttext="\sup _{{0\leq t\leq T_{{0}}}}t^{{2-\beta}}\int _{{\mathbb{T}^{{N}}}}|\nabla u(t,x)|^{{2}}dx+\int^{{T_{{0}}}}_{{0}}\int _{{\mathbb{T}^{{N}}}}t^{{2-\beta}}|\nabla\dot{u}|^{{2}}dxdt" display="block"><semantics id="idp14496288"><mrow id="idp14496416"><mrow id="idp14496544"><munder id="idp14496672"><mo id="idp14496800" movablelimits="false">sup</mo><mrow id="idp14497296"><mn id="idp14497424">0</mn><mo id="idp14497680">≤</mo><mi id="idp14497936">t</mi><mo id="idp14498192">≤</mo><msub id="idp14498480"><mi id="idp14498608">T</mi><mn id="idp14498864">0</mn></msub></mrow></munder><mo id="idp14499120">⁡</mo><mrow id="idp14499408"><msup id="idp14499536"><mi id="idp14499664">t</mi><mrow id="idp14499920"><mn id="idp14500048">2</mn><mo id="idp14500304">-</mo><mi id="idp14500560">β</mi></mrow></msup><mo id="idp14500848">⁢</mo><mrow id="idp14501136"><msub id="idp14501264"><mo id="idp14501392">∫</mo><msup id="idp14501680"><mi id="idp14501808" mathvariant="double-struck">T</mi><mi id="idp14502336">N</mi></msup></msub><mrow id="idp14502592"><msup id="idp14502720"><mrow id="idp14502848"><mo id="idp14502976" fence="true">|</mo><mrow id="idp14503504"><mrow id="idp14503632"><mo id="idp14503760">∇</mo><mo id="idp14504048">⁡</mo><mi id="idp14504336">u</mi></mrow><mo id="idp14504592">⁢</mo><mrow id="idp14504880"><mo id="idp14505008">(</mo><mrow id="idp14505264"><mi id="idp14505392">t</mi><mo id="idp14505648">,</mo><mi id="idp14505904">x</mi></mrow><mo id="idp14506160">)</mo></mrow></mrow><mo id="idp14506416" fence="true">|</mo></mrow><mn id="idp14506944">2</mn></msup><mo id="idp14507200">⁢</mo><mi id="idp14507488">d</mi><mo id="idp14507744">⁢</mo><mi id="idp14508032">x</mi></mrow></mrow></mrow></mrow><mo id="idp14508288">+</mo><mrow id="idp14508544"><msubsup id="idp14508672"><mo id="idp14508800">∫</mo><mn id="idp14509088">0</mn><msub id="idp14509344"><mi id="idp14509472">T</mi><mn id="idp14509728">0</mn></msub></msubsup><mrow id="idp14509984"><msub id="idp14510112"><mo id="idp14510240">∫</mo><msup id="idp14510528"><mi id="idp14510656" mathvariant="double-struck">T</mi><mi id="idp14511184">N</mi></msup></msub><mrow id="idp14511440"><msup id="idp14511568"><mi id="idp14511696">t</mi><mrow id="idp14511952"><mn id="idp14512080">2</mn><mo id="idp14512336">-</mo><mi id="idp14512592">β</mi></mrow></msup><mo id="idp14512880">⁢</mo><msup id="idp14513168"><mrow id="idp14513296"><mo id="idp14513424" fence="true">|</mo><mrow id="idp14513952"><mo id="idp14514080">∇</mo><mo id="idp14514368">⁡</mo><mover id="idp14514656" accent="true"><mi id="idp14515056">u</mi><mo id="idp14515312">˙</mo></mover></mrow><mo id="idp14515600" fence="true">|</mo></mrow><mn id="idp14516128">2</mn></msup><mo id="idp14516384">⁢</mo><mi id="idp14516672">d</mi><mo id="idp14516928">⁢</mo><mi id="idp14517216">x</mi><mo id="idp14517472">⁢</mo><mi id="idp14517760">d</mi><mo id="idp14518016">⁢</mo><mi id="idp14518304">t</mi></mrow></mrow></mrow></mrow><annotation-xml id="idp14518560" encoding="MathML-Content"><apply id="idp14518960"><plus id="idp14519088"/><apply id="idp14519216"><apply id="idp14519344"><csymbol id="idp14519472" cd="ambiguous">subscript</csymbol><csymbol id="idp14520032" cd="latexml">supremum</csymbol><apply id="idp14520592"><and id="idp14520720"/><apply id="idp14520848"><leq id="idp14520976"/><cn id="idp14521104" type="integer">0</cn><ci id="S4.Ex61.m1.sh1.cmml">t</ci></apply><apply id="idp14522160"><leq id="idp14522288"/><share id="idp14522416" href="#S4.Ex61.m1.sh1.cmml"/><apply id="S4.Ex61.m1.sh2c.cmml"><csymbol cd="ambiguous" id="S4.Ex61.m1.sh2.cmml">subscript</csymbol><ci id="S4.Ex61.m1.sh2a.cmml">T</ci><cn type="integer" id="S4.Ex61.m1.sh2b.cmml">0</cn></apply></apply></apply></apply><apply id="idp14525376"><times id="idp14525504"/><apply id="idp14525632"><csymbol id="idp14525760" cd="ambiguous">superscript</csymbol><ci id="idp14526320">t</ci><apply id="idp14526576"><minus id="idp14526704"/><cn id="idp14526832" type="integer">2</cn><ci id="idp14527360">β</ci></apply></apply><apply id="idp14527648"><apply id="idp14527776"><csymbol id="idp14527904" cd="ambiguous">subscript</csymbol><int id="idp14528464"/><apply id="idp14528592"><csymbol id="idp14528720" cd="ambiguous">superscript</csymbol><ci id="idp14529280">T</ci><ci id="idp14529536">N</ci></apply></apply><apply id="idp14529792"><times id="idp14529920"/><apply id="idp14530048"><csymbol id="idp14530176" cd="ambiguous">superscript</csymbol><apply id="idp14530736"><abs id="idp14530864"/><apply id="idp14530992"><times id="idp14531120"/><apply id="idp14531248"><ci id="idp14531376">∇</ci><ci id="idp14531664">u</ci></apply><apply id="idp14531920"><interval id="idp14532048" closure="open"/><ci id="idp14532448">t</ci><ci id="idp14532704">x</ci></apply></apply></apply><cn id="idp14532960" type="integer">2</cn></apply><ci id="idp14533488">d</ci><ci id="idp14533744">x</ci></apply></apply></apply></apply><apply id="idp14534000"><apply id="idp14534128"><csymbol id="idp14534256" cd="ambiguous">subscript</csymbol><apply id="idp14534816"><csymbol id="idp14534944" cd="ambiguous">superscript</csymbol><int id="idp14535504"/><apply id="idp14535632"><csymbol id="idp14535760" cd="ambiguous">subscript</csymbol><ci id="idp14536320">T</ci><cn id="idp14536576" type="integer">0</cn></apply></apply><cn id="idp14537104" type="integer">0</cn></apply><apply id="idp14537632"><apply id="idp14537760"><csymbol id="idp14537888" cd="ambiguous">subscript</csymbol><int id="idp14538448"/><apply id="idp14538576"><csymbol id="idp14538704" cd="ambiguous">superscript</csymbol><ci id="idp14539264">T</ci><ci id="idp14539520">N</ci></apply></apply><apply id="idp14539776"><times id="idp14539904"/><apply id="idp14540032"><csymbol id="idp14540160" cd="ambiguous">superscript</csymbol><ci id="idp14540720">t</ci><apply id="idp14540976"><minus id="idp14541104"/><cn id="idp14541232" type="integer">2</cn><ci id="idp14541760">β</ci></apply></apply><apply id="idp14542048"><csymbol id="idp14542176" cd="ambiguous">superscript</csymbol><apply id="idp14542736"><abs id="idp14542864"/><apply id="idp14542992"><ci id="idp14543120">∇</ci><apply id="idp14543408"><ci id="idp14543536">˙</ci><ci id="idp14543824">u</ci></apply></apply></apply><cn id="idp14544080" type="integer">2</cn></apply><ci id="idp14544576">d</ci><ci id="idp14544832">x</ci><ci id="idp14545088">d</ci><ci id="idp14545344">t</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp14545600" encoding="application/x-tex">\sup _{{0\leq t\leq T_{{0}}}}t^{{2-\beta}}\int _{{\mathbb{T}^{{N}}}}|\nabla u(t,x)|^{{2}}dx+\int^{{T_{{0}}}}_{{0}}\int _{{\mathbb{T}^{{N}}}}t^{{2-\beta}}|\nabla\dot{u}|^{{2}}dxdt</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp163776"><h4>Hit idp163776</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 88</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/18/f006847.xhtml#idp163776</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:14865(000015%) VariableMap:[dx x 2, mathbb x 3, int x 2, C, n x 3, inf, ( x 3, ) x 3, neq, ., infty, in, frac x 2, 2 x 3, 0 x 2, displaystyle, nabla, R x 3, \ x 16, _ x 4, | x 6, ^ x 7, =, phi x 3, x x 3] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp163776" alttext="\displaystyle=\inf _{{0\neq\phi\in C_{0}^{{\infty}}(\mathbb{R}^{n})}}\frac{\int _{{\mathbb{R}^{n}}}|\nabla\phi(x)|^{2}dx}{\int _{{\mathbb{R}^{n}}}\frac{|\phi(x)|^{2}}{|x|^{2}}dx}." display="inline"><semantics id="idp164640"><mrow id="idp164768"><mrow id="idp164896"><none id="idp165024"/><mo id="idp165152">=</mo><mrow id="idp165408"><munder id="idp165536"><mo id="idp165664" movablelimits="false">inf</mo><mrow id="idp166160"><mn id="idp166288">0</mn><mo id="idp166544">≠</mo><mi id="idp166800">ϕ</mi><mo id="idp167088">∈</mo><mrow id="idp167376"><msubsup id="idp167504"><mi id="idp167632">C</mi><mn id="idp167888">0</mn><mi id="idp168144" mathvariant="normal">∞</mi></msubsup><mo id="idp168704">⁢</mo><mrow id="idp168992"><mo id="idp169120">(</mo><msup id="idp169376"><mi id="idp169504" mathvariant="double-struck">R</mi><mi id="idp170032">n</mi></msup><mo id="idp170288">)</mo></mrow></mrow></mrow></munder><mo id="idp170544">⁡</mo><mstyle id="idp170832" displaystyle="true"><mfrac id="idp171232"><mrow id="idp171360"><msub id="idp171488"><mo id="idp171616">∫</mo><msup id="idp171904"><mi id="idp172032" mathvariant="double-struck">R</mi><mi id="idp172560">n</mi></msup></msub><mrow id="idp172816"><msup id="idp172944"><mrow id="idp173072"><mo id="idp173200" fence="true">|</mo><mrow id="idp173728"><mrow id="idp173856"><mo id="idp173984">∇</mo><mo id="idp174272">⁡</mo><mi id="idp174560">ϕ</mi></mrow><mo id="idp174848">⁢</mo><mrow id="idp175136"><mo id="idp175264">(</mo><mi id="idp175520">x</mi><mo id="idp175776">)</mo></mrow></mrow><mo id="idp176032" fence="true">|</mo></mrow><mn id="idp176560">2</mn></msup><mo id="idp176816">⁢</mo><mi id="idp177104">d</mi><mo id="idp177360">⁢</mo><mi id="idp177648">x</mi></mrow></mrow><mrow id="idp177904"><msub id="idp178032"><mo id="idp178160">∫</mo><msup id="idp178448"><mi id="idp178576" mathvariant="double-struck">R</mi><mi id="idp179104">n</mi></msup></msub><mrow id="idp179360"><mfrac id="idp179488"><msup id="idp179616"><mrow id="idp179744"><mo id="idp179872" fence="true">|</mo><mrow id="idp180400"><mi id="idp180528">ϕ</mi><mo id="idp180816">⁢</mo><mrow id="idp181104"><mo id="idp181232">(</mo><mi id="idp181488">x</mi><mo id="idp181744">)</mo></mrow></mrow><mo id="idp182000" fence="true">|</mo></mrow><mn id="idp182528">2</mn></msup><msup id="idp182784"><mrow id="idp182912"><mo id="idp183040" fence="true">|</mo><mi id="idp183568">x</mi><mo id="idp183824" fence="true">|</mo></mrow><mn id="idp184352">2</mn></msup></mfrac><mo id="idp184608">⁢</mo><mi id="idp184896">d</mi><mo id="idp185152">⁢</mo><mi id="idp185440">x</mi></mrow></mrow></mfrac></mstyle></mrow></mrow><mo id="idp185696">.</mo></mrow><annotation-xml id="idp185952" encoding="MathML-Content"><apply id="idp186352"><eq id="idp186480"/><csymbol id="idp186608" cd="latexml">absent</csymbol><apply id="idp187168"><apply id="idp187296"><csymbol id="idp187424" cd="ambiguous">subscript</csymbol><csymbol id="idp187984" cd="latexml">infimum</csymbol><apply id="idp188544"><and id="idp188672"/><apply id="idp188800"><neq id="idp188928"/><cn id="idp189056" type="integer">0</cn><ci id="S1.Ex1X.m3.sh1.cmml">ϕ</ci></apply><apply id="idp190144"><in id="idp190272"/><share id="idp190400" href="#S1.Ex1X.m3.sh1.cmml"/><apply id="S1.Ex1X.m3.sh2l.cmml"><times id="S1.Ex1X.m3.sh2.cmml"/><apply id="S1.Ex1X.m3.sh2g.cmml"><csymbol cd="ambiguous" id="S1.Ex1X.m3.sh2a.cmml">superscript</csymbol><apply id="S1.Ex1X.m3.sh2e.cmml"><csymbol cd="ambiguous" id="S1.Ex1X.m3.sh2b.cmml">subscript</csymbol><ci id="S1.Ex1X.m3.sh2c.cmml">C</ci><cn type="integer" id="S1.Ex1X.m3.sh2d.cmml">0</cn></apply><infinity id="S1.Ex1X.m3.sh2f.cmml"/></apply><apply id="S1.Ex1X.m3.sh2k.cmml"><csymbol cd="ambiguous" id="S1.Ex1X.m3.sh2h.cmml">superscript</csymbol><ci id="S1.Ex1X.m3.sh2i.cmml">R</ci><ci id="S1.Ex1X.m3.sh2j.cmml">n</ci></apply></apply></apply></apply></apply><apply id="idp198080"><divide id="idp198208"/><apply id="idp198336"><apply id="idp198464"><csymbol id="idp198592" cd="ambiguous">subscript</csymbol><int id="idp199152"/><apply id="idp199280"><csymbol id="idp199408" cd="ambiguous">superscript</csymbol><ci id="idp199968">R</ci><ci id="idp200224">n</ci></apply></apply><apply id="idp200480"><times id="idp200608"/><apply id="idp200736"><csymbol id="idp200864" cd="ambiguous">superscript</csymbol><apply id="idp201424"><abs id="idp201552"/><apply id="idp201680"><times id="idp201808"/><apply id="idp201936"><ci id="idp202064">∇</ci><ci id="idp202352">ϕ</ci></apply><ci id="idp202640">x</ci></apply></apply><cn id="idp202896" type="integer">2</cn></apply><ci id="idp203424">d</ci><ci id="idp203680">x</ci></apply></apply><apply id="idp203936"><apply id="idp204064"><csymbol id="idp204192" cd="ambiguous">subscript</csymbol><int id="idp204752"/><apply id="idp204880"><csymbol id="idp205008" cd="ambiguous">superscript</csymbol><ci id="idp205568">R</ci><ci id="idp205824">n</ci></apply></apply><apply id="idp206080"><times id="idp206208"/><apply id="idp206336"><divide id="idp206464"/><apply id="idp206592"><csymbol id="idp206720" cd="ambiguous">superscript</csymbol><apply id="idp207280"><abs id="idp207408"/><apply id="idp207536"><times id="idp207664"/><ci id="idp207792">ϕ</ci><ci id="idp208080">x</ci></apply></apply><cn id="idp208336" type="integer">2</cn></apply><apply id="idp208864"><csymbol id="idp208992" cd="ambiguous">superscript</csymbol><apply id="idp209552"><abs id="idp209680"/><ci id="idp209808">x</ci></apply><cn id="idp210064" type="integer">2</cn></apply></apply><ci id="idp210592">d</ci><ci id="idp210848">x</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp211104" encoding="application/x-tex">\displaystyle=\inf _{{0\neq\phi\in C_{0}^{{\infty}}(\mathbb{R}^{n})}}\frac{\int _{{\mathbb{R}^{n}}}|\nabla\phi(x)|^{2}dx}{\int _{{\mathbb{R}^{n}}}\frac{|\phi(x)|^{2}}{|x|^{2}}dx}.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp18333472"><h4>Hit idp18333472</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 89</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/18/f007142.xhtml#idp18333472</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:2334150(000083%) VariableMap:[dx x 2, int x 2, B x 2, delta x 2, M, o, ( x 3, ) x 3, k, /, hat, backslash, 2 x 3, 1, u x 2, 0 x 2, nabla x 2, alpha x 2, \ x 10, _ x 6, ^ x 3, | x 4, =] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp18333472" alttext="\int _{{B_{0}(\delta)\backslash B_{0}(\delta/2)}}|\nabla^{k}\hat{u}_{\alpha}|^{2}dx=o(1)\int _{M}|\nabla u_{\alpha}|^{2}dx" display="block"><semantics id="idp18334336"><mrow id="idp18334464"><mrow id="idp18334592"><msub id="idp18334720"><mo id="idp18334848">∫</mo><mrow id="idp18335104"><mrow id="idp18335232"><mrow id="idp18335360"><msub id="idp18335488"><mi id="idp18335616">B</mi><mn id="idp18335872">0</mn></msub><mo id="idp18336128">⁢</mo><mrow id="idp18336384"><mo id="idp18336512">(</mo><mi id="idp18336768">δ</mi><mo id="idp18337056">)</mo></mrow></mrow><mo id="idp18337312">\</mo><msub id="idp18337568"><mi id="idp18337696">B</mi><mn id="idp18337952">0</mn></msub></mrow><mo id="idp18338208">⁢</mo><mrow id="idp18338496"><mo id="idp18338624">(</mo><mrow id="idp18338880"><mi id="idp18339008">δ</mi><mo id="idp18339296">/</mo><mn id="idp18339552">2</mn></mrow><mo id="idp18339808">)</mo></mrow></mrow></msub><mrow id="idp18340064"><msup id="idp18340192"><mrow id="idp18340320"><mo id="idp18340448" fence="true">|</mo><mrow id="idp18340976"><msup id="idp18341104"><mo id="idp18341232">∇</mo><mi id="idp18341520">k</mi></msup><mo id="idp18341776">⁡</mo><msub id="idp18342064"><mover id="idp18342192" accent="true"><mi id="idp18342592">u</mi><mo id="idp18342848">^</mo></mover><mi id="idp18343104">α</mi></msub></mrow><mo id="idp18343392" fence="true">|</mo></mrow><mn id="idp18343920">2</mn></msup><mo id="idp18344176">⁢</mo><mi id="idp18344464">d</mi><mo id="idp18344720">⁢</mo><mi id="idp18345008">x</mi></mrow></mrow><mo id="idp18345264">=</mo><mrow id="idp18345520"><mi id="idp18345648">o</mi><mo id="idp18345904">⁢</mo><mrow id="idp18346160"><mo id="idp18346288">(</mo><mn id="idp18346544">1</mn><mo id="idp18346800">)</mo></mrow><mo id="idp18347056">⁢</mo><mrow id="idp18347312"><msub id="idp18347440"><mo id="idp18347568">∫</mo><mi id="idp18347824">M</mi></msub><mrow id="idp18348080"><msup id="idp18348208"><mrow id="idp18348336"><mo id="idp18348464" fence="true">|</mo><mrow id="idp18348992"><mo id="idp18349120">∇</mo><mo id="idp18349408">⁡</mo><msub id="idp18349696"><mi id="idp18349824">u</mi><mi id="idp18350080">α</mi></msub></mrow><mo id="idp18350368" fence="true">|</mo></mrow><mn id="idp18350896">2</mn></msup><mo id="idp18351152">⁢</mo><mi id="idp18351440">d</mi><mo id="idp18351696">⁢</mo><mi id="idp18351984">x</mi></mrow></mrow></mrow></mrow><annotation-xml id="idp18352240" encoding="MathML-Content"><apply id="idp18352640"><eq id="idp18352768"/><apply id="idp18352896"><apply id="idp18353024"><csymbol id="idp18353152" cd="ambiguous">subscript</csymbol><int id="idp18353712"/><apply id="idp18353840"><times id="idp18353968"/><apply id="idp18354096"><ci id="idp18354224">\</ci><apply id="idp18354480"><times id="idp18354608"/><apply id="idp18354736"><csymbol id="idp18354864" cd="ambiguous">subscript</csymbol><ci id="idp18355424">B</ci><cn id="idp18355680" type="integer">0</cn></apply><ci id="idp18356208">δ</ci></apply><apply id="idp18356496"><csymbol id="idp18356624" cd="ambiguous">subscript</csymbol><ci id="idp18357184">B</ci><cn id="idp18357440" type="integer">0</cn></apply></apply><apply id="idp18357968"><divide id="idp18358096"/><ci id="idp18358224">δ</ci><cn id="idp18358512" type="integer">2</cn></apply></apply></apply><apply id="idp18359040"><times id="idp18359168"/><apply id="idp18359296"><csymbol id="idp18359424" cd="ambiguous">superscript</csymbol><apply id="idp18359984"><abs id="idp18360112"/><apply id="idp18360240"><apply id="idp18360368"><csymbol id="idp18360496" cd="ambiguous">superscript</csymbol><ci id="idp18361056">∇</ci><ci id="idp18361344">k</ci></apply><apply id="idp18361600"><csymbol id="idp18361728" cd="ambiguous">subscript</csymbol><apply id="idp18362288"><ci id="idp18362416">^</ci><ci id="idp18362672">u</ci></apply><ci id="idp18362928">α</ci></apply></apply></apply><cn id="idp18363216" type="integer">2</cn></apply><ci id="idp18363744">d</ci><ci id="idp18364000">x</ci></apply></apply><apply id="idp18364256"><times id="idp18364384"/><ci id="idp18364512">o</ci><cn id="idp18364768" type="integer">1</cn><apply id="idp18365296"><apply id="idp18365424"><csymbol id="idp18365552" cd="ambiguous">subscript</csymbol><int id="idp18366112"/><ci id="idp18366240">M</ci></apply><apply id="idp18366496"><times id="idp18366624"/><apply id="idp18366752"><csymbol id="idp18366880" cd="ambiguous">superscript</csymbol><apply id="idp18367440"><abs id="idp18367568"/><apply id="idp18367696"><ci id="idp18367824">∇</ci><apply id="idp18368112"><csymbol id="idp18368240" cd="ambiguous">subscript</csymbol><ci id="idp18368800">u</ci><ci id="idp18369056">α</ci></apply></apply></apply><cn id="idp18369344" type="integer">2</cn></apply><ci id="idp18369872">d</ci><ci id="idp18370128">x</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp18370384" encoding="application/x-tex">\int _{{B_{0}(\delta)\backslash B_{0}(\delta/2)}}|\nabla^{k}\hat{u}_{\alpha}|^{2}dx=o(1)\int _{M}|\nabla u_{\alpha}|^{2}dx</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp21309088"><h4>Hit idp21309088</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 90</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/206/f082087.xhtml#idp21309088</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:214536(000023%) VariableMap:[dx x 5, B x 5, N, , nabla, ] x 2, \ x 25, left, _ x 14, ^ x 6, right, rho x 6, [ x 2, leq, int x 5, + x 2, ( x 7, ) x 7, ., , x 12, frac, -, 2 x 5, u x 7, 0 x 7, 6, r x 4, | x 14, big x 2, =, x x 7] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp21309088" alttext="\int _{{B(x_{0},r)}}|u|^{2}\, dx=\int _{{B(x_{0},r)}}\big(|u|^{2}-[|u|^{2}]_{{x_{0},\rho}}\big)\, dx+\int _{{B(x_{0},r)}}[|u|^{2}]_{{x_{0},\rho}}\, dx\\ \leq N\rho\int _{{B(x_{0},\rho)}}|\nabla u||u|\, dx+\left(\frac{r}{\rho}\right)^{6}\int _{{B(x_{0},\rho)}}|u|^{2}\, dx." display="block"><semantics id="idp21308640"><mrow id="idp21308768"><mrow id="idp21308896"><mrow id="idp21310096"><msub id="idp21310224"><mo id="idp21310352">∫</mo><mrow id="idp21310608"><mi id="idp21310736">B</mi><mo id="idp21310992">⁢</mo><mrow id="idp21311248"><mo id="idp21311376">(</mo><mrow id="idp21311632"><msub id="idp21311760"><mi id="idp21311888">x</mi><mn id="idp21312144">0</mn></msub><mo id="idp21312400">,</mo><mi id="idp21312656">r</mi></mrow><mo id="idp21312912">)</mo></mrow></mrow></msub><mrow id="idp21313168"><msup id="idp21313296"><mrow id="idp21313424"><mo id="idp21313552" fence="true">|</mo><mi id="idp21314048">u</mi><mo id="idp21314304" fence="true">|</mo></mrow><mn id="idp21314800">2</mn></msup><mo id="idp21315056">⁢</mo><mi id="idp21315344">d</mi><mo id="idp21315600">⁢</mo><mi id="idp21315888">x</mi></mrow></mrow><mo id="idp21316144">=</mo><mrow id="idp21316400"><mrow id="idp21316528"><msub id="idp21316656"><mo id="idp21316784">∫</mo><mrow id="idp21317072"><mi id="idp21317200">B</mi><mo id="idp21317456">⁢</mo><mrow id="idp21317744"><mo id="idp21317872">(</mo><mrow id="idp21318128"><msub id="idp21318256"><mi id="idp21318384">x</mi><mn id="idp21318640">0</mn></msub><mo id="idp21318896">,</mo><mi id="idp21319152">r</mi></mrow><mo id="idp21319408">)</mo></mrow></mrow></msub><mrow id="idp21319664"><mrow id="idp21319792"><mo id="idp21319920">(</mo><mrow id="idp21320176"><msup id="idp21320304"><mrow id="idp21320432"><mo id="idp21320560" fence="true">|</mo><mi id="idp21321088">u</mi><mo id="idp21321344" fence="true">|</mo></mrow><mn id="idp21321872">2</mn></msup><mo id="idp21322128">-</mo><msub id="idp21322384"><mrow id="idp21322512"><mo id="idp21322640">[</mo><msup id="idp21322896"><mrow id="idp21323024"><mo id="idp21323152" fence="true">|</mo><mi id="idp21323680">u</mi><mo id="idp21323936" fence="true">|</mo></mrow><mn id="idp21324464">2</mn></msup><mo id="idp21324720">]</mo></mrow><mrow id="idp21324976"><msub id="idp21325104"><mi id="idp21325232">x</mi><mn id="idp21325488">0</mn></msub><mo id="idp21325744">,</mo><mi id="idp21326000">ρ</mi></mrow></msub></mrow><mo id="idp21326288">)</mo></mrow><mo id="idp21326544">⁢</mo><mi id="idp21326832">d</mi><mo id="idp21327088">⁢</mo><mi id="idp21327376">x</mi></mrow></mrow><mo id="idp21327632">+</mo><mrow id="idp21327888"><msub id="idp21328016"><mo id="idp21328144">∫</mo><mrow id="idp21328432"><mi id="idp21328560">B</mi><mo id="idp21328816">⁢</mo><mrow id="idp21329104"><mo id="idp21329232">(</mo><mrow id="idp21329488"><msub id="idp21329616"><mi id="idp21329744">x</mi><mn id="idp21330000">0</mn></msub><mo id="idp21330256">,</mo><mi id="idp21330512">r</mi></mrow><mo id="idp21330768">)</mo></mrow></mrow></msub><mrow id="idp21331024"><msub id="idp21331152"><mrow id="idp21331280"><mo id="idp21331408">[</mo><msup id="idp21331664"><mrow id="idp21331792"><mo 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id="S3.SS1.p2.m2.sh1ab.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1w.cmml">superscript</csymbol><apply id="S3.SS1.p2.m2.sh1z.cmml"><abs id="S3.SS1.p2.m2.sh1x.cmml"/><ci id="S3.SS1.p2.m2.sh1y.cmml">u</ci></apply><cn type="integer" id="S3.SS1.p2.m2.sh1aa.cmml">2</cn></apply><apply id="S3.SS1.p2.m2.sh1ai.cmml"><list id="S3.SS1.p2.m2.sh1ac.cmml"/><apply id="S3.SS1.p2.m2.sh1ag.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1ad.cmml">subscript</csymbol><ci id="S3.SS1.p2.m2.sh1ae.cmml">x</ci><cn type="integer" id="S3.SS1.p2.m2.sh1af.cmml">0</cn></apply><ci id="S3.SS1.p2.m2.sh1ah.cmml">ρ</ci></apply></apply></apply><ci id="S3.SS1.p2.m2.sh1al.cmml">d</ci><ci id="S3.SS1.p2.m2.sh1am.cmml">x</ci></apply></apply><apply id="S3.SS1.p2.m2.sh1bv.cmml"><apply id="S3.SS1.p2.m2.sh1bb.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1ap.cmml">subscript</csymbol><int id="S3.SS1.p2.m2.sh1aq.cmml"/><apply id="S3.SS1.p2.m2.sh1ba.cmml"><times id="S3.SS1.p2.m2.sh1ar.cmml"/><ci id="S3.SS1.p2.m2.sh1as.cmml">B</ci><apply id="S3.SS1.p2.m2.sh1az.cmml"><interval closure="open" id="S3.SS1.p2.m2.sh1at.cmml"/><apply id="S3.SS1.p2.m2.sh1ax.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1au.cmml">subscript</csymbol><ci id="S3.SS1.p2.m2.sh1av.cmml">x</ci><cn type="integer" id="S3.SS1.p2.m2.sh1aw.cmml">0</cn></apply><ci id="S3.SS1.p2.m2.sh1ay.cmml">r</ci></apply></apply></apply><apply id="S3.SS1.p2.m2.sh1bu.cmml"><times id="S3.SS1.p2.m2.sh1bc.cmml"/><apply id="S3.SS1.p2.m2.sh1br.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1bd.cmml">subscript</csymbol><apply id="S3.SS1.p2.m2.sh1bj.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1be.cmml">superscript</csymbol><apply id="S3.SS1.p2.m2.sh1bh.cmml"><abs id="S3.SS1.p2.m2.sh1bf.cmml"/><ci id="S3.SS1.p2.m2.sh1bg.cmml">u</ci></apply><cn type="integer" id="S3.SS1.p2.m2.sh1bi.cmml">2</cn></apply><apply id="S3.SS1.p2.m2.sh1bq.cmml"><list id="S3.SS1.p2.m2.sh1bk.cmml"/><apply id="S3.SS1.p2.m2.sh1bo.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh1bl.cmml">subscript</csymbol><ci id="S3.SS1.p2.m2.sh1bm.cmml">x</ci><cn type="integer" id="S3.SS1.p2.m2.sh1bn.cmml">0</cn></apply><ci id="S3.SS1.p2.m2.sh1bp.cmml">ρ</ci></apply></apply><ci id="S3.SS1.p2.m2.sh1bs.cmml">d</ci><ci id="S3.SS1.p2.m2.sh1bt.cmml">x</ci></apply></apply></apply></apply><apply id="idp21402752"><leq id="idp21402880"/><share id="idp21403008" href="#S3.SS1.p2.m2.sh1.cmml"/><apply id="S3.SS1.p2.m2.sh2bl.cmml"><plus id="S3.SS1.p2.m2.sh2.cmml"/><apply id="S3.SS1.p2.m2.sh2ad.cmml"><times id="S3.SS1.p2.m2.sh2a.cmml"/><ci id="S3.SS1.p2.m2.sh2b.cmml">N</ci><ci id="S3.SS1.p2.m2.sh2c.cmml">ρ</ci><apply id="S3.SS1.p2.m2.sh2ac.cmml"><apply id="S3.SS1.p2.m2.sh2p.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh2d.cmml">subscript</csymbol><int id="S3.SS1.p2.m2.sh2e.cmml"/><apply id="S3.SS1.p2.m2.sh2o.cmml"><times id="S3.SS1.p2.m2.sh2f.cmml"/><ci id="S3.SS1.p2.m2.sh2g.cmml">B</ci><apply id="S3.SS1.p2.m2.sh2n.cmml"><interval closure="open" id="S3.SS1.p2.m2.sh2h.cmml"/><apply id="S3.SS1.p2.m2.sh2l.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh2i.cmml">subscript</csymbol><ci id="S3.SS1.p2.m2.sh2j.cmml">x</ci><cn type="integer" id="S3.SS1.p2.m2.sh2k.cmml">0</cn></apply><ci id="S3.SS1.p2.m2.sh2m.cmml">ρ</ci></apply></apply></apply><apply id="S3.SS1.p2.m2.sh2ab.cmml"><times id="S3.SS1.p2.m2.sh2q.cmml"/><apply id="S3.SS1.p2.m2.sh2v.cmml"><abs id="S3.SS1.p2.m2.sh2r.cmml"/><apply id="S3.SS1.p2.m2.sh2u.cmml"><ci id="S3.SS1.p2.m2.sh2s.cmml">∇</ci><ci id="S3.SS1.p2.m2.sh2t.cmml">u</ci></apply></apply><apply id="S3.SS1.p2.m2.sh2y.cmml"><abs id="S3.SS1.p2.m2.sh2w.cmml"/><ci id="S3.SS1.p2.m2.sh2x.cmml">u</ci></apply><ci id="S3.SS1.p2.m2.sh2z.cmml">d</ci><ci id="S3.SS1.p2.m2.sh2aa.cmml">x</ci></apply></apply></apply><apply id="S3.SS1.p2.m2.sh2bk.cmml"><times id="S3.SS1.p2.m2.sh2ae.cmml"/><apply id="S3.SS1.p2.m2.sh2al.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh2af.cmml">superscript</csymbol><apply id="S3.SS1.p2.m2.sh2aj.cmml"><divide id="S3.SS1.p2.m2.sh2ag.cmml"/><ci id="S3.SS1.p2.m2.sh2ah.cmml">r</ci><ci id="S3.SS1.p2.m2.sh2ai.cmml">ρ</ci></apply><cn type="integer" id="S3.SS1.p2.m2.sh2ak.cmml">6</cn></apply><apply id="S3.SS1.p2.m2.sh2bj.cmml"><apply id="S3.SS1.p2.m2.sh2ay.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh2am.cmml">subscript</csymbol><int id="S3.SS1.p2.m2.sh2an.cmml"/><apply id="S3.SS1.p2.m2.sh2ax.cmml"><times id="S3.SS1.p2.m2.sh2ao.cmml"/><ci id="S3.SS1.p2.m2.sh2ap.cmml">B</ci><apply id="S3.SS1.p2.m2.sh2aw.cmml"><interval closure="open" id="S3.SS1.p2.m2.sh2aq.cmml"/><apply id="S3.SS1.p2.m2.sh2au.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh2ar.cmml">subscript</csymbol><ci id="S3.SS1.p2.m2.sh2as.cmml">x</ci><cn type="integer" id="S3.SS1.p2.m2.sh2at.cmml">0</cn></apply><ci id="S3.SS1.p2.m2.sh2av.cmml">ρ</ci></apply></apply></apply><apply id="S3.SS1.p2.m2.sh2bi.cmml"><times id="S3.SS1.p2.m2.sh2az.cmml"/><apply id="S3.SS1.p2.m2.sh2bf.cmml"><csymbol cd="ambiguous" id="S3.SS1.p2.m2.sh2ba.cmml">superscript</csymbol><apply id="S3.SS1.p2.m2.sh2bd.cmml"><abs id="S3.SS1.p2.m2.sh2bb.cmml"/><ci id="S3.SS1.p2.m2.sh2bc.cmml">u</ci></apply><cn type="integer" id="S3.SS1.p2.m2.sh2be.cmml">2</cn></apply><ci id="S3.SS1.p2.m2.sh2bg.cmml">d</ci><ci id="S3.SS1.p2.m2.sh2bh.cmml">x</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp21436608" encoding="application/x-tex">\int _{{B(x_{0},r)}}|u|^{2}\, dx=\int _{{B(x_{0},r)}}\big(|u|^{2}-[|u|^{2}]_{{x_{0},\rho}}\big)\, dx+\int _{{B(x_{0},r)}}[|u|^{2}]_{{x_{0},\rho}}\, dx\\ \leq N\rho\int _{{B(x_{0},\rho)}}|\nabla u||u|\, dx+\left(\frac{r}{\rho}\right)^{6}\int _{{B(x_{0},\rho)}}|u|^{2}\, dx.</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp21578768"><h4>Hit idp21578768</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 91</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/17/f006403.xhtml#idp21578768</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:248516(000003%) VariableMap:[dx, int, Omega, ,, 2, u, 0, nabla, alpha, \ x 7, _ x 2, left, | x 2, ^, right, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Expects 2 occurences for '^' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp21578768" alttext="\int _{{\Omega}}\left|\nabla u_{\alpha}\right|^{2}\, dx=0" display="inline"><semantics id="idp21579568"><mrow id="idp21579696"><mrow id="idp21579824"><msub id="idp21579952"><mo id="idp21580080">∫</mo><mi id="idp21580336" mathvariant="normal">Ω</mi></msub><mrow id="idp21580864"><msup id="idp21580992"><mrow id="idp21581120"><mo id="idp21581248" fence="true">|</mo><mrow id="idp21581776"><mo id="idp21581904">∇</mo><mo id="idp21582192">⁡</mo><msub id="idp21582480"><mi id="idp21582608">u</mi><mi id="idp21582864">α</mi></msub></mrow><mo id="idp21583152" fence="true">|</mo></mrow><mn id="idp21583680">2</mn></msup><mo id="idp21583936">⁢</mo><mi id="idp21584224">d</mi><mo id="idp21584480">⁢</mo><mi id="idp21584768">x</mi></mrow></mrow><mo id="idp21585024">=</mo><mn id="idp21585280">0</mn></mrow><annotation-xml id="idp21585536" encoding="MathML-Content"><apply id="idp21585936"><eq id="idp21586064"/><apply id="idp21586192"><apply id="idp21586320"><csymbol id="idp21586448" cd="ambiguous">subscript</csymbol><int id="idp21587008"/><ci id="idp21587136">Ω</ci></apply><apply id="idp21587424"><times id="idp21587552"/><apply id="idp21587680"><csymbol id="idp21587808" cd="ambiguous">superscript</csymbol><apply id="idp21588368"><abs id="idp21588496"/><apply id="idp21588624"><ci id="idp21588752">∇</ci><apply id="idp21589040"><csymbol id="idp21589168" cd="ambiguous">subscript</csymbol><ci id="idp21589728">u</ci><ci id="idp21589984">α</ci></apply></apply></apply><cn id="idp21590272" type="integer">2</cn></apply><ci id="idp21590800">d</ci><ci id="idp21591056">x</ci></apply></apply><cn id="idp21591312" type="integer">0</cn></apply></annotation-xml><annotation id="idp21591840" encoding="application/x-tex">\int _{{\Omega}}\left|\nabla u_{\alpha}\right|^{2}\, dx=0</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp24874944"><h4>Hit idp24874944</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 92</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/62/f024503.xhtml#idp24874944</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:696397(000065%) VariableMap:[to, H, nabla, R x 2, \ x 11, _ x 5, cal, ^ x 3, d, int, lim, (, l x 4, ), ., partial, /, ,, frac, 3, 2, 1, u, 0 x 2, displaystyle, tau, 4, | x 2, =] Expects 2 occurences for 'd' but has only 1 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp24874944" alttext="\lim _{{l\to 0}}\frac{\tau(R_{l})^{{3/4}}}{\displaystyle\int _{{\partial R_{l}}}|\nabla u_{l}|^{2}\, d{\cal H}^{1}}=0\ ." display="block"><semantics id="idp24875808"><mrow id="idp24875936"><mrow id="idp24876064"><munder id="idp24876192"><mo id="idp24876320" movablelimits="false">lim</mo><mrow id="idp24876816"><mi id="idp24876944">l</mi><mo id="idp24877200">→</mo><mn id="idp24877456">0</mn></mrow></munder><mo id="idp24877712">⁡</mo><mfrac id="idp24878000"><mrow id="idp24878128"><mi id="idp24878256">τ</mi><mo id="idp24878544">⁢</mo><msup id="idp24878832"><mrow id="idp24878960"><mo id="idp24879088">(</mo><msub id="idp24879344"><mi id="idp24879472">R</mi><mi id="idp24879728">l</mi></msub><mo id="idp24879984">)</mo></mrow><mrow id="idp24880240"><mn id="idp24880368">3</mn><mo id="idp24880624">/</mo><mn id="idp24880880">4</mn></mrow></msup></mrow><mrow id="idp24881136"><mstyle id="idp24881360" displaystyle="true"><msub id="idp24881760"><mo id="idp24881888">∫</mo><mrow id="idp24882176"><mo id="idp24882304">∂</mo><mo id="idp24882592">⁡</mo><msub id="idp24882880"><mi id="idp24883008">R</mi><mi id="idp24883264">l</mi></msub></mrow></msub></mstyle><mrow id="idp24883520"><msup id="idp24883648"><mrow id="idp24883776"><mo id="idp24883904" fence="true">|</mo><mrow id="idp24884432"><mo id="idp24884560">∇</mo><mo id="idp24884848">⁡</mo><msub id="idp24885136"><mi id="idp24885264">u</mi><mi id="idp24885520">l</mi></msub></mrow><mo id="idp24885776" fence="true">|</mo></mrow><mn id="idp24886304">2</mn></msup><mo id="idp24886560">⁢</mo><mi id="idp24886848">d</mi><mo id="idp24887104">⁢</mo><msup id="idp24887392"><mi id="idp24887520" mathvariant="script">H</mi><mn id="idp24888048">1</mn></msup></mrow></mrow></mfrac></mrow><mo id="idp24888304">=</mo><mn id="idp24888560">0 .</mn></mrow><annotation-xml id="idp24888848" encoding="MathML-Content"><apply id="idp24889248"><eq id="idp24889376"/><apply id="idp24889504"><apply id="idp24889632"><csymbol id="idp24889760" cd="ambiguous">subscript</csymbol><limit id="idp24890368"/><apply id="idp24890496"><ci id="idp24890624">→</ci><ci id="idp24890912">l</ci><cn id="idp24891168" type="integer">0</cn></apply></apply><apply id="idp24891696"><divide id="idp24891824"/><apply id="idp24891952"><times id="idp24892080"/><ci id="idp24892208">τ</ci><apply id="idp24892496"><csymbol id="idp24892624" cd="ambiguous">superscript</csymbol><apply id="idp24893184"><csymbol id="idp24893312" cd="ambiguous">subscript</csymbol><ci id="idp24893872">R</ci><ci id="idp24894128">l</ci></apply><apply id="idp24894384"><divide id="idp24894512"/><cn id="idp24894640" type="integer">3</cn><cn id="idp24895168" type="integer">4</cn></apply></apply></apply><apply id="idp24895696"><apply id="idp24895824"><csymbol id="idp24895952" cd="ambiguous">subscript</csymbol><int id="idp24896512"/><apply id="idp24896640"><partialdiff id="idp24896768"/><apply id="idp24896896"><csymbol id="idp24897024" cd="ambiguous">subscript</csymbol><ci id="idp24897584">R</ci><ci id="idp24897840">l</ci></apply></apply></apply><apply id="idp24898096"><times id="idp24898224"/><apply id="idp24898352"><csymbol id="idp24898480" cd="ambiguous">superscript</csymbol><apply id="idp24899040"><abs id="idp24899168"/><apply id="idp24899296"><ci id="idp24899424">∇</ci><apply id="idp24899712"><csymbol id="idp24899840" cd="ambiguous">subscript</csymbol><ci id="idp24900400">u</ci><ci id="idp24900656">l</ci></apply></apply></apply><cn id="idp24900912" type="integer">2</cn></apply><ci id="idp24901440">d</ci><apply id="idp24901696"><csymbol id="idp24901824" cd="ambiguous">superscript</csymbol><ci id="idp24902384">H</ci><cn id="idp24902640" type="integer">1</cn></apply></apply></apply></apply></apply><cn id="idp24903168" type="float">0 .</cn></apply></annotation-xml><annotation id="idp24903728" encoding="application/x-tex">\lim _{{l\to 0}}\frac{\tau(R_{l})^{{3/4}}}{\displaystyle\int _{{\partial R_{l}}}|\nabla u_{l}|^{2}\, d{\cal H}^{1}}=0\ .</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp24982064"><h4>Hit idp24982064</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 93</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/62/f024503.xhtml#idp24982064</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:710405(000067%) VariableMap:[H, K x 5, lambda, nabla, \ x 11, _ x 5, cal, ^ x 4, d, int, inf, (, ), partial, in, /, ,, frac, 3, 2 x 3, 1 x 2, u, 0, mathcal, displaystyle, | x 2] Expects 2 occurences for 'd' but has only 1 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp24982064" alttext="\inf _{{K\in\mathcal{K}_{0}^{2}}}\frac{\lambda _{1}(K)^{{3/2}}}{\displaystyle\int _{{\partial K}}|\nabla u_{K}|^{2}\, d{\cal H}^{1}}" display="block"><semantics id="idp24982928"><mrow id="idp24983056"><munder id="idp24983184"><mo id="idp24983312" movablelimits="false">inf</mo><mrow id="idp24983808"><mi id="idp24983936">K</mi><mo id="idp24984192">∈</mo><msubsup id="idp24984448"><mi id="idp24984576" mathvariant="script">K</mi><mn id="idp24985104">0</mn><mn id="idp24985360">2</mn></msubsup></mrow></munder><mo id="idp24985616">⁡</mo><mfrac id="idp24985904"><mrow id="idp24986032"><msub id="idp24986160"><mi id="idp24986288">λ</mi><mn id="idp24986576">1</mn></msub><mo id="idp24986832">⁢</mo><msup id="idp24987120"><mrow id="idp24987248"><mo id="idp24987376">(</mo><mi id="idp24987632">K</mi><mo id="idp24987888">)</mo></mrow><mrow id="idp24988144"><mn id="idp24988272">3</mn><mo id="idp24988528">/</mo><mn id="idp24988784">2</mn></mrow></msup></mrow><mrow id="idp24989040"><mstyle id="idp24989168" displaystyle="true"><msub id="idp24989568"><mo id="idp24989696">∫</mo><mrow id="idp24989984"><mo id="idp24990112">∂</mo><mo id="idp24990400">⁡</mo><mi id="idp24990688">K</mi></mrow></msub></mstyle><mrow id="idp24990944"><msup id="idp24991072"><mrow id="idp24991200"><mo id="idp24991328" fence="true">|</mo><mrow id="idp24991856"><mo id="idp24991984">∇</mo><mo id="idp24992272">⁡</mo><msub id="idp24992560"><mi id="idp24992688">u</mi><mi id="idp24992944">K</mi></msub></mrow><mo id="idp24993200" fence="true">|</mo></mrow><mn id="idp24993728">2</mn></msup><mo id="idp24993984">⁢</mo><mi id="idp24994272">d</mi><mo id="idp24994528">⁢</mo><msup id="idp24994816"><mi id="idp24994944" mathvariant="script">H</mi><mn id="idp24995472">1</mn></msup></mrow></mrow></mfrac></mrow><annotation-xml id="idp24995728" encoding="MathML-Content"><apply id="idp24996128"><apply id="idp24996256"><csymbol id="idp24996384" cd="ambiguous">subscript</csymbol><csymbol id="idp24996944" cd="latexml">infimum</csymbol><apply id="idp24997504"><in id="idp24997632"/><ci id="idp24997760">K</ci><apply id="idp24998016"><csymbol id="idp24998144" cd="ambiguous">superscript</csymbol><apply id="idp24998704"><csymbol id="idp24998832" cd="ambiguous">subscript</csymbol><ci id="idp24999392">K</ci><cn id="idp24999648" type="integer">0</cn></apply><cn id="idp25000176" type="integer">2</cn></apply></apply></apply><apply id="idp25000704"><divide id="idp25000832"/><apply id="idp25000960"><times id="idp25001088"/><apply id="idp25001216"><csymbol id="idp25001344" cd="ambiguous">subscript</csymbol><ci id="idp25001904">λ</ci><cn id="idp25002192" type="integer">1</cn></apply><apply id="idp25002720"><csymbol id="idp25002848" cd="ambiguous">superscript</csymbol><ci id="idp25003408">K</ci><apply id="idp25003664"><divide id="idp25003792"/><cn id="idp25003920" type="integer">3</cn><cn id="idp25004448" type="integer">2</cn></apply></apply></apply><apply id="idp25004976"><apply id="idp25005104"><csymbol id="idp25005232" cd="ambiguous">subscript</csymbol><int id="idp25005792"/><apply id="idp25005920"><partialdiff id="idp25006048"/><ci id="idp25006176">K</ci></apply></apply><apply id="idp25006432"><times id="idp25006560"/><apply id="idp25006688"><csymbol id="idp25006816" cd="ambiguous">superscript</csymbol><apply id="idp25007376"><abs id="idp25007504"/><apply id="idp25007632"><ci id="idp25007760">∇</ci><apply id="idp25008048"><csymbol id="idp25008176" cd="ambiguous">subscript</csymbol><ci id="idp25008736">u</ci><ci id="idp25008992">K</ci></apply></apply></apply><cn id="idp25009248" type="integer">2</cn></apply><ci id="idp25009776">d</ci><apply id="idp25010032"><csymbol id="idp25010160" cd="ambiguous">superscript</csymbol><ci id="idp25010720">H</ci><cn id="idp25010976" type="integer">1</cn></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp25011504" encoding="application/x-tex">\inf _{{K\in\mathcal{K}_{0}^{2}}}\frac{\lambda _{1}(K)^{{3/2}}}{\displaystyle\int _{{\partial K}}|\nabla u_{K}|^{2}\, d{\cal H}^{1}}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp25115664"><h4>Hit idp25115664</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 94</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/62/f024503.xhtml#idp25115664</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:727177(000068%) VariableMap:[to, H, lambda, nabla, R x 2, \ x 14, _ x 6, cal, ^ x 4, d, int, lim, (, l x 4, ), . x 2, partial, /, ,, frac x 2, 3, 2 x 4, 1 x 2, u, 0, 6, displaystyle, 4 x 2, sim, | x 2, pi, =] Expects 2 occurences for 'd' but has only 1 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp25115664" alttext="\lim _{{l\to 0}}\frac{\lambda _{1}(R_{l})^{{3/2}}}{\displaystyle\int _{{\partial R_{l}}}|\nabla u_{l}|^{2}\, d{\cal H}^{1}}=\frac{\pi^{2}}{4}\sim 2.46\ ." display="block"><semantics id="idp25116560"><mrow id="idp25116688"><mrow id="idp25116816"><munder id="idp25116944"><mo id="idp25117072" movablelimits="false">lim</mo><mrow id="idp25117568"><mi id="idp25117696">l</mi><mo id="idp25117952">→</mo><mn id="idp25118208">0</mn></mrow></munder><mo id="idp25118464">⁡</mo><mfrac id="idp25118752"><mrow id="idp25118880"><msub id="idp25119008"><mi id="idp25119136">λ</mi><mn id="idp25119424">1</mn></msub><mo id="idp25119680">⁢</mo><msup id="idp25119968"><mrow id="idp25120096"><mo id="idp25120224">(</mo><msub id="idp25120480"><mi id="idp25120608">R</mi><mi id="idp25120864">l</mi></msub><mo id="idp25121120">)</mo></mrow><mrow id="idp25121376"><mn id="idp25121504">3</mn><mo id="idp25121760">/</mo><mn id="idp25122016">2</mn></mrow></msup></mrow><mrow id="idp25122272"><mstyle id="idp25122400" displaystyle="true"><msub id="idp25122800"><mo id="idp25122928">∫</mo><mrow id="idp25123216"><mo id="idp25123344">∂</mo><mo id="idp25123632">⁡</mo><msub id="idp25123920"><mi id="idp25124048">R</mi><mi id="idp25124304">l</mi></msub></mrow></msub></mstyle><mrow id="idp25124560"><msup id="idp25124688"><mrow id="idp25124816"><mo id="idp25124944" fence="true">|</mo><mrow id="idp25125472"><mo id="idp25125600">∇</mo><mo id="idp25125888">⁡</mo><msub id="idp25126176"><mi id="idp25126304">u</mi><mi id="idp25126560">l</mi></msub></mrow><mo id="idp25126816" fence="true">|</mo></mrow><mn id="idp25127344">2</mn></msup><mo id="idp25127600">⁢</mo><mi id="idp25127888">d</mi><mo id="idp25128144">⁢</mo><msup id="idp25128432"><mi id="idp25128560" mathvariant="script">H</mi><mn id="idp25129088">1</mn></msup></mrow></mrow></mfrac></mrow><mo id="idp25129344">=</mo><mfrac id="idp25129600"><msup id="idp25129728"><mi id="idp25129856">π</mi><mn id="idp25130144">2</mn></msup><mn id="idp25130400">4</mn></mfrac><mo id="idp25130656">∼</mo><mn id="idp25130944">2.46 .</mn></mrow><annotation-xml id="idp25131232" encoding="MathML-Content"><apply id="idp25131632"><and id="idp25131760"/><apply id="idp25131888"><eq id="idp25132016"/><apply id="idp25132144"><apply id="idp25132272"><csymbol id="idp25132400" cd="ambiguous">subscript</csymbol><limit id="idp25132960"/><apply id="idp25133088"><ci id="idp25133216">→</ci><ci id="idp25133504">l</ci><cn id="idp25133760" type="integer">0</cn></apply></apply><apply id="idp25134288"><divide id="idp25134416"/><apply id="idp25134544"><times id="idp25134672"/><apply id="idp25134800"><csymbol id="idp25134928" cd="ambiguous">subscript</csymbol><ci id="idp25135488">λ</ci><cn id="idp25135776" type="integer">1</cn></apply><apply id="idp25136304"><csymbol id="idp25136432" cd="ambiguous">superscript</csymbol><apply id="idp25136992"><csymbol id="idp25137120" cd="ambiguous">subscript</csymbol><ci id="idp25137680">R</ci><ci id="idp25137936">l</ci></apply><apply id="idp25138192"><divide id="idp25138320"/><cn id="idp25138448" type="integer">3</cn><cn id="idp25138976" type="integer">2</cn></apply></apply></apply><apply id="idp25139504"><apply id="idp25139632"><csymbol id="idp25139760" cd="ambiguous">subscript</csymbol><int id="idp25140320"/><apply id="idp25140448"><partialdiff id="idp25140576"/><apply id="idp25140704"><csymbol id="idp25140832" cd="ambiguous">subscript</csymbol><ci id="idp25141392">R</ci><ci id="idp25141648">l</ci></apply></apply></apply><apply id="idp25141904"><times id="idp25142032"/><apply id="idp25142160"><csymbol id="idp25142288" cd="ambiguous">superscript</csymbol><apply id="idp25142848"><abs id="idp25142976"/><apply id="idp25143104"><ci id="idp25143232">∇</ci><apply id="idp25143520"><csymbol id="idp25143648" cd="ambiguous">subscript</csymbol><ci id="idp25144208">u</ci><ci id="idp25144464">l</ci></apply></apply></apply><cn id="idp25144720" type="integer">2</cn></apply><ci id="idp25145248">d</ci><apply id="idp25145504"><csymbol id="idp25145632" cd="ambiguous">superscript</csymbol><ci id="idp25146192">H</ci><cn id="idp25146448" type="integer">1</cn></apply></apply></apply></apply></apply><apply id="S3.Ex27.m1.sh1f.cmml"><divide id="S3.Ex27.m1.sh1.cmml"/><apply id="S3.Ex27.m1.sh1d.cmml"><csymbol cd="ambiguous" id="S3.Ex27.m1.sh1a.cmml">superscript</csymbol><ci id="S3.Ex27.m1.sh1b.cmml">π</ci><cn type="integer" id="S3.Ex27.m1.sh1c.cmml">2</cn></apply><cn type="integer" id="S3.Ex27.m1.sh1e.cmml">4</cn></apply></apply><apply id="idp25151168"><csymbol id="idp25151296" cd="latexml">similar-to</csymbol><share id="idp25151856" href="#S3.Ex27.m1.sh1.cmml"/><cn type="float" id="S3.Ex27.m1.sh2.cmml">2.46 .</cn></apply></apply></annotation-xml><annotation id="idp25153088" encoding="application/x-tex">\lim _{{l\to 0}}\frac{\lambda _{1}(R_{l})^{{3/2}}}{\displaystyle\int _{{\partial R_{l}}}|\nabla u_{l}|^{2}\, d{\cal H}^{1}}=\frac{\pi^{2}}{4}\sim 2.46\ .</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp2688720"><h4>Hit idp2688720</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 95</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/115/f045858.xhtml#idp2688720</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:335556(000027%) VariableMap:[dx, B x 3, H, nabla x 2, R x 3, \ x 18, _ x 9, ^ x 4, cal, d, int x 5, delta, + x 2, ( x 3, ) x 3, , x 3, -, frac, 2 x 2, u x 5, dxdt x 2, t x 3, 0 x 3, displaystyle x 5, | x 4] Expects 2 occurences for 'd' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 1 occurences for 'q' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp2688720" alttext="\displaystyle\delta\displaystyle\int _{0}^{t}\displaystyle\int _{{B_{R}}}\frac{|\nabla u|^{2}}{d(u)}\, dxdt+\displaystyle\int _{0}^{t}\displaystyle\int _{{B_{R}}}|\nabla{\cal H}u|^{2}\, dxdt+\int _{{B_{R}}}(u_{0}-u(t))\, dx" display="inline"><semantics id="idp2689680"><mrow id="idp2689808"><mrow id="idp2689936"><mi id="idp2690064">δ</mi><mo id="idp2690320">⁢</mo><mrow id="idp2690576"><mstyle id="idp2690704" displaystyle="true"><msubsup id="idp2691104"><mo id="idp2691232">∫</mo><mn id="idp2691520">0</mn><mi id="idp2691776">t</mi></msubsup></mstyle><mrow id="idp2692032"><mstyle id="idp2692160" displaystyle="true"><msub id="idp2692560"><mo id="idp2692688">∫</mo><msub id="idp2692976"><mi id="idp2693104">B</mi><mi id="idp2693360">R</mi></msub></msub></mstyle><mrow id="idp2693616"><mpadded id="idp2693744" width="+1.666667pt"><mstyle id="idp2694144" displaystyle="true"><mfrac id="idp2694544"><msup id="idp2694672"><mrow id="idp2694800"><mo id="idp2694928" fence="true">|</mo><mrow id="idp2695456"><mo id="idp2695584">∇</mo><mo id="idp2695872">⁡</mo><mi id="idp2696160">u</mi></mrow><mo id="idp2696416" fence="true">|</mo></mrow><mn id="idp2696944">2</mn></msup><mrow id="idp2697200"><mi id="idp2697328">d</mi><mo id="idp2697584">⁢</mo><mrow id="idp2697872"><mo id="idp2698000">(</mo><mi id="idp2698256">u</mi><mo id="idp2698512">)</mo></mrow></mrow></mfrac></mstyle></mpadded><mo id="idp2698768">⁢</mo><mi id="idp2699056">d</mi><mo id="idp2699312">⁢</mo><mi id="idp2699600">x</mi><mo id="idp2699856">⁢</mo><mi id="idp2700144">d</mi><mo id="idp2700400">⁢</mo><mi id="idp2700688">t</mi></mrow></mrow></mrow></mrow><mo id="idp2700944">+</mo><mrow id="idp2701200"><mstyle id="idp2701328" displaystyle="true"><msubsup id="idp2701728"><mo id="idp2701856">∫</mo><mn id="idp2702144">0</mn><mi id="idp2702400">t</mi></msubsup></mstyle><mrow id="idp2702656"><mstyle id="idp2702784" displaystyle="true"><msub id="idp2703184"><mo id="idp2703312">∫</mo><msub id="idp2703600"><mi id="idp2703728">B</mi><mi id="idp2703984">R</mi></msub></msub></mstyle><mrow id="idp2704240"><msup id="idp2704368"><mrow id="idp2704496"><mo id="idp2704624" fence="true">|</mo><mrow id="idp2705152"><mo id="idp2705280">∇</mo><mo id="idp2705568">⁡</mo><mrow id="idp2705856"><mi id="idp2705984" mathvariant="script">H</mi><mo id="idp2706512">⁢</mo><mi id="idp2706800">u</mi></mrow></mrow><mo id="idp2707056" fence="true">|</mo></mrow><mn id="idp2707584">2</mn></msup><mo id="idp2707840">⁢</mo><mi id="idp2708128">d</mi><mo id="idp2708384">⁢</mo><mi id="idp2708672">x</mi><mo id="idp2708928">⁢</mo><mi id="idp2709216">d</mi><mo id="idp2709472">⁢</mo><mi id="idp2709760">t</mi></mrow></mrow></mrow><mo id="idp2710016">+</mo><mrow id="idp2710272"><mstyle id="idp2710400" displaystyle="true"><msub id="idp2710800"><mo id="idp2710928">∫</mo><msub id="idp2711216"><mi id="idp2711344">B</mi><mi id="idp2711600">R</mi></msub></msub></mstyle><mrow id="idp2711856"><mrow id="idp2711984"><mo id="idp2712112">(</mo><mrow id="idp2712368"><msub id="idp2712496"><mi id="idp2712624">u</mi><mn id="idp2712880">0</mn></msub><mo id="idp2713136">-</mo><mrow id="idp2713392"><mi id="idp2713520">u</mi><mo id="idp2713776">⁢</mo><mrow id="idp2714064"><mo id="idp2714192">(</mo><mi id="idp2714448">t</mi><mo id="idp2714704">)</mo></mrow></mrow></mrow><mo id="idp2714960">)</mo></mrow><mo id="idp2715216">⁢</mo><mi id="idp2715504">d</mi><mo id="idp2715760">⁢</mo><mi id="idp2716048">x</mi></mrow></mrow></mrow><annotation-xml id="idp2716304" encoding="MathML-Content"><apply id="idp2716704"><plus id="idp2716832"/><apply id="idp2716960"><times id="idp2717088"/><ci id="idp2717216">δ</ci><apply id="idp2717504"><apply id="idp2717632"><csymbol id="idp2717760" cd="ambiguous">superscript</csymbol><apply id="idp2718320"><csymbol id="idp2718448" cd="ambiguous">subscript</csymbol><int id="idp2719008"/><cn id="idp2719136" type="integer">0</cn></apply><ci id="idp2719664">t</ci></apply><apply id="idp2719920"><apply id="idp2720048"><csymbol id="idp2720176" cd="ambiguous">subscript</csymbol><int id="idp2720736"/><apply id="idp2720864"><csymbol id="idp2720992" cd="ambiguous">subscript</csymbol><ci id="idp2721552">B</ci><ci id="idp2721808">R</ci></apply></apply><apply id="idp2722064"><times id="idp2722192"/><apply id="idp2722320"><divide id="idp2722448"/><apply id="idp2722576"><csymbol id="idp2722704" cd="ambiguous">superscript</csymbol><apply id="idp2723264"><abs id="idp2723392"/><apply id="idp2723520"><ci id="idp2723648">∇</ci><ci id="idp2723936">u</ci></apply></apply><cn id="idp2724192" type="integer">2</cn></apply><apply id="idp2724720"><times id="idp2724848"/><ci id="idp2724976">d</ci><ci id="idp2725232">u</ci></apply></apply><ci id="idp2725488">d</ci><ci id="idp2725744">x</ci><ci id="idp2726000">d</ci><ci id="idp2726256">t</ci></apply></apply></apply></apply><apply id="idp2726512"><apply id="idp2726640"><csymbol id="idp2726768" cd="ambiguous">superscript</csymbol><apply id="idp2727328"><csymbol id="idp2727456" cd="ambiguous">subscript</csymbol><int id="idp2728016"/><cn id="idp2728144" type="integer">0</cn></apply><ci id="idp2728672">t</ci></apply><apply id="idp2728928"><apply id="idp2729056"><csymbol id="idp2729184" cd="ambiguous">subscript</csymbol><int id="idp2729744"/><apply id="idp2729872"><csymbol id="idp2730000" cd="ambiguous">subscript</csymbol><ci id="idp2730560">B</ci><ci id="idp2730816">R</ci></apply></apply><apply id="idp2731072"><times id="idp2731200"/><apply id="idp2731328"><csymbol id="idp2731456" cd="ambiguous">superscript</csymbol><apply id="idp2732016"><abs id="idp2732144"/><apply id="idp2732272"><ci id="idp2732400">∇</ci><apply id="idp2732688"><times id="idp2732816"/><ci id="idp2732944">H</ci><ci id="idp2733200">u</ci></apply></apply></apply><cn id="idp2733456" type="integer">2</cn></apply><ci id="idp2733984">d</ci><ci id="idp2734240">x</ci><ci id="idp2734496">d</ci><ci id="idp2734752">t</ci></apply></apply></apply><apply id="idp2735008"><apply id="idp2735136"><csymbol id="idp2735264" cd="ambiguous">subscript</csymbol><int id="idp2735824"/><apply id="idp2735952"><csymbol id="idp2736080" cd="ambiguous">subscript</csymbol><ci id="idp2736640">B</ci><ci id="idp2736896">R</ci></apply></apply><apply id="idp2737152"><times id="idp2737280"/><apply id="idp2737408"><minus id="idp2737536"/><apply id="idp2737664"><csymbol id="idp2737792" cd="ambiguous">subscript</csymbol><ci id="idp2738352">u</ci><cn id="idp2738608" type="integer">0</cn></apply><apply id="idp2739136"><times id="idp2739264"/><ci id="idp2739392">u</ci><ci id="idp2739648">t</ci></apply></apply><ci id="idp2739904">d</ci><ci id="idp2740160">x</ci></apply></apply></apply></annotation-xml><annotation id="idp2740416" encoding="application/x-tex">\displaystyle\delta\displaystyle\int _{0}^{t}\displaystyle\int _{{B_{R}}}\frac{|\nabla u|^{2}}{d(u)}\, dxdt+\displaystyle\int _{0}^{t}\displaystyle\int _{{B_{R}}}|\nabla{\cal H}u|^{2}\, dxdt+\int _{{B_{R}}}(u_{0}-u(t))\, dx</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp275712"><h4>Hit idp275712</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 96</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/206/f082102.xhtml#idp275712</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:347108(000037%) VariableMap:[v x 2, circ, C, ], \ x 3, _, =, [, phi x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 0 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 3 Expects 2 occurences for '_' but has only 1 Expects 4 occurences for '|' but has only 0 Expects 2 occurences for '^' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp2754688" alttext="C_{{\phi}}[v]=v\circ\phi" display="inline"><semantics id="idp2755456"><mrow id="idp2755584"><mrow id="idp2755712"><msub id="idp2755840"><mi id="idp2755968">C</mi><mi id="idp2756224">ϕ</mi></msub><mo id="idp2756480">⁢</mo><mrow id="idp2756736"><mo id="idp2756864">[</mo><mi id="idp2757120">v</mi><mo id="idp2757376">]</mo></mrow></mrow><mo id="idp2757632">=</mo><mrow id="idp2757888"><mi id="idp2758016">v</mi><mo id="idp2758272">∘</mo><mi id="idp2758560">ϕ</mi></mrow></mrow><annotation-xml id="idp2758848" encoding="MathML-Content"><apply id="idp2759248"><eq id="idp2759376"/><apply id="idp2759504"><times id="idp2759632"/><apply id="idp2759760"><csymbol id="idp2759888" cd="ambiguous">subscript</csymbol><ci id="idp2760448">C</ci><ci id="idp2760704">ϕ</ci></apply><ci id="idp2760992">v</ci></apply><apply id="idp2761248"><compose id="idp2761376"/><ci id="idp2761504">v</ci><ci id="idp2761760">ϕ</ci></apply></apply></annotation-xml><annotation id="idp2762048" encoding="application/x-tex">C_{{\phi}}[v]=v\circ\phi</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp31639936"><h4>Hit idp31639936</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 97</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/61/f024342.xhtml#idp31639936</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:1613560(000093%) VariableMap:[dv, mathbb, nabla, R, \ x 9, _ x 2, ^ x 4, limits, e, int, (, ), m, h, frac, prime x 2, 3, 2 x 2, 1 x 2, 0, 6, ;, | x 2, pi, TT, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp31639936" alttext="16\pi m^{{\prime\prime}}(0)=\frac{1}{2}\int\limits _{{\mathbb{R}^{3}}}|\nabla h^{{TT}}|^{2}\; dv_{e}" display="inline"><semantics id="idp31640768"><mrow id="idp31640896"><mrow id="idp31641024"><mn id="idp31641152">16</mn><mo id="idp31641408">⁢</mo><mi id="idp31641664">π</mi><mo id="idp31641920">⁢</mo><msup id="idp31642208"><mi id="idp31642336">m</mi><mi id="idp31642592">′′</mi></msup><mo id="idp31642880">⁢</mo><mrow id="idp31643168"><mo id="idp31643296">(</mo><mn id="idp31643552">0</mn><mo id="idp31643808">)</mo></mrow></mrow><mo id="idp31644064">=</mo><mrow id="idp31644320"><mfrac id="idp31644448"><mn id="idp31644576">1</mn><mn id="idp31644832">2</mn></mfrac><mo id="idp31645088">⁢</mo><mrow id="idp31645376"><munder id="idp31645504"><mo id="idp31645632" movablelimits="false">∫</mo><msup id="idp31646192"><mi id="idp31646320" mathvariant="double-struck">R</mi><mn id="idp31646848">3</mn></msup></munder><mrow id="idp31647104"><msup id="idp31647232"><mrow id="idp31647360"><mo id="idp31647488" fence="true">|</mo><mrow id="idp31648016"><mo id="idp31648144">∇</mo><mo id="idp31648432">⁡</mo><msup id="idp31648720"><mi id="idp31648848">h</mi><mrow id="idp31649104"><mi id="idp31649232">T</mi><mo id="idp31649488">⁢</mo><mi id="idp31649776">T</mi></mrow></msup></mrow><mo id="idp31650032" fence="true">|</mo></mrow><mn id="idp31650560">2</mn></msup><mo id="idp31650816">⁢</mo><mi id="idp31651104">d</mi><mo id="idp31651360">⁢</mo><msub id="idp31651648"><mi id="idp31651776">v</mi><mi id="idp31652032">e</mi></msub></mrow></mrow></mrow></mrow><annotation-xml id="idp31652288" encoding="MathML-Content"><apply id="idp31652688"><eq id="idp31652816"/><apply id="idp31652944"><times id="idp31653072"/><cn id="idp31653200" type="integer">16</cn><ci id="idp31653728">π</ci><apply id="idp31654016"><csymbol id="idp31654144" cd="ambiguous">superscript</csymbol><ci id="idp31654704">m</ci><ci id="idp31654960">′′</ci></apply><cn id="idp31655248" type="integer">0</cn></apply><apply id="idp31655776"><times id="idp31655904"/><apply id="idp31656032"><divide id="idp31656160"/><cn id="idp31656288" type="integer">1</cn><cn id="idp31656816" type="integer">2</cn></apply><apply id="idp31657344"><apply id="idp31657472"><csymbol id="idp31657600" cd="ambiguous">subscript</csymbol><int id="idp31658160"/><apply id="idp31658288"><csymbol id="idp31658416" cd="ambiguous">superscript</csymbol><ci id="idp31658976">R</ci><cn id="idp31659232" type="integer">3</cn></apply></apply><apply id="idp31659760"><times id="idp31659888"/><apply id="idp31660016"><csymbol id="idp31660144" cd="ambiguous">superscript</csymbol><apply id="idp31660704"><abs id="idp31660832"/><apply id="idp31660960"><ci id="idp31661088">∇</ci><apply id="idp31661376"><csymbol id="idp31661504" cd="ambiguous">superscript</csymbol><ci id="idp31662064">h</ci><apply id="idp31662320"><times id="idp31662448"/><ci id="idp31662576">T</ci><ci id="idp31662832">T</ci></apply></apply></apply></apply><cn id="idp31663088" type="integer">2</cn></apply><ci id="idp31663616">d</ci><apply id="idp31663872"><csymbol id="idp31664000" cd="ambiguous">subscript</csymbol><ci id="idp31664560">v</ci><ci id="idp31664816">e</ci></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp31665072" encoding="application/x-tex">16\pi m^{{\prime\prime}}(0)=\frac{1}{2}\int\limits _{{\mathbb{R}^{3}}}|\nabla h^{{TT}}|^{2}\; dv_{e}</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp36087904"><h4>Hit idp36087904</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 98</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/203/f081144.xhtml#idp36087904</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:2081808(000086%) VariableMap:[leq, widetilde x 3, C, + x 6, ( x 2, ) x 2, , x 3, -, ty, 2 x 7, u x 6, 0, t x 2, nabla x 2, alpha x 2, ] x 2, \ x 8, _, | x 12, ^ x 6, [ x 2, x x 2] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 2 occurences for '_' but has only 1 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp36087904" alttext="[|\nabla\widetilde{u}|^{2}+|\widetilde{u}|^{{{\alpha+2}}}+|\widetilde{u}|^{2}](t,x)\leq C[|\nabla u|^{2}+|u|^{{{\alpha+2}}}+|u|^{2}](t,x-2ty_{0})," display="block"><semantics id="idp36088784"><mrow id="idp36088912"><mrow id="idp36089040"><mrow id="idp36089168"><mrow id="idp36089296"><mo id="idp36089424">[</mo><mrow id="idp36089680"><msup id="idp36089808"><mrow id="idp36089936"><mo id="idp36090064" fence="true">|</mo><mrow id="idp36090560"><mo id="idp36090688">∇</mo><mo id="idp36090944">⁡</mo><mover id="idp36091232" accent="true"><mi id="idp36091632">u</mi><mo id="idp36091888">~</mo></mover></mrow><mo id="idp36092144" fence="true">|</mo></mrow><mn id="idp36092672">2</mn></msup><mo id="idp36092928">+</mo><msup id="idp36093184"><mrow id="idp36093312"><mo id="idp36093440" fence="true">|</mo><mover id="idp36093968" accent="true"><mi id="idp36094368">u</mi><mo id="idp36094624">~</mo></mover><mo id="idp36094880" fence="true">|</mo></mrow><mrow id="idp36095408"><mi id="idp36095536">α</mi><mo id="idp36095824">+</mo><mn id="idp36096080">2</mn></mrow></msup><mo id="idp36096336">+</mo><msup id="idp36096592"><mrow id="idp36096720"><mo id="idp36096848" fence="true">|</mo><mover id="idp36097376" accent="true"><mi id="idp36097776">u</mi><mo id="idp36098032">~</mo></mover><mo id="idp36098288" fence="true">|</mo></mrow><mn id="idp36098816">2</mn></msup></mrow><mo id="idp36099072">]</mo></mrow><mo id="idp36099328">⁢</mo><mrow id="idp36099616"><mo id="idp36099744">(</mo><mrow id="idp36100000"><mi id="idp36100128">t</mi><mo id="idp36100384">,</mo><mi id="idp36100640">x</mi></mrow><mo id="idp36100896">)</mo></mrow></mrow><mo id="idp36101152">≤</mo><mrow id="idp36101440"><mi id="idp36101568">C</mi><mo id="idp36101824">⁢</mo><mrow id="idp36102112"><mo id="idp36102240">[</mo><mrow id="idp36102496"><msup id="idp36102624"><mrow id="idp36102752"><mo id="idp36102880" fence="true">|</mo><mrow id="idp36103408"><mo id="idp36103536">∇</mo><mo id="idp36103824">⁡</mo><mi id="idp36104112">u</mi></mrow><mo id="idp36104368" fence="true">|</mo></mrow><mn id="idp36104896">2</mn></msup><mo id="idp36105152">+</mo><msup id="idp36105408"><mrow id="idp36105536"><mo id="idp36105664" fence="true">|</mo><mi id="idp36106192">u</mi><mo id="idp36106448" fence="true">|</mo></mrow><mrow id="idp36106976"><mi id="idp36107104">α</mi><mo id="idp36107392">+</mo><mn id="idp36107648">2</mn></mrow></msup><mo id="idp36107904">+</mo><msup id="idp36108160"><mrow id="idp36108288"><mo id="idp36108416" fence="true">|</mo><mi id="idp36108944">u</mi><mo id="idp36109200" fence="true">|</mo></mrow><mn id="idp36109728">2</mn></msup></mrow><mo id="idp36109984">]</mo></mrow><mo id="idp36110240">⁢</mo><mrow id="idp36110528"><mo id="idp36110656">(</mo><mrow id="idp36110912"><mi id="idp36111040">t</mi><mo id="idp36111296">,</mo><mrow id="idp36111552"><mi id="idp36111680">x</mi><mo id="idp36111936">-</mo><mrow id="idp36112192"><mn id="idp36112320">2</mn><mo id="idp36112576">⁢</mo><mi id="idp36112864">t</mi><mo id="idp36113120">⁢</mo><msub id="idp36113408"><mi id="idp36113536">y</mi><mn id="idp36113792">0</mn></msub></mrow></mrow></mrow><mo id="idp36114048">)</mo></mrow></mrow></mrow><mo id="idp36114304">,</mo></mrow><annotation-xml id="idp36114560" encoding="MathML-Content"><apply id="idp36114960"><leq id="idp36115088"/><apply id="idp36115216"><times id="idp36115344"/><apply id="idp36115472"><plus id="idp36115600"/><apply id="idp36115728"><csymbol id="idp36115856" cd="ambiguous">superscript</csymbol><apply id="idp36116416"><abs id="idp36116544"/><apply id="idp36116672"><ci id="idp36116800">∇</ci><apply id="idp36117088"><ci id="idp36117216">~</ci><ci id="idp36117472">u</ci></apply></apply></apply><cn id="idp36117728" type="integer">2</cn></apply><apply id="idp36118256"><csymbol id="idp36118384" cd="ambiguous">superscript</csymbol><apply id="idp36118944"><abs id="idp36119072"/><apply id="idp36119200"><ci id="idp36119328">~</ci><ci id="idp36119584">u</ci></apply></apply><apply id="idp36119840"><plus id="idp36119968"/><ci id="idp36120096">α</ci><cn id="idp36120384" type="integer">2</cn></apply></apply><apply id="idp36120912"><csymbol id="idp36121040" cd="ambiguous">superscript</csymbol><apply id="idp36121600"><abs id="idp36121728"/><apply id="idp36121856"><ci id="idp36121984">~</ci><ci id="idp36122240">u</ci></apply></apply><cn id="idp36122496" type="integer">2</cn></apply></apply><apply id="idp36123024"><interval id="idp36123152" closure="open"/><ci id="idp36123552">t</ci><ci id="idp36123808">x</ci></apply></apply><apply id="idp36124064"><times id="idp36124192"/><ci id="idp36124320">C</ci><apply id="idp36124576"><plus id="idp36124704"/><apply id="idp36124832"><csymbol id="idp36124960" cd="ambiguous">superscript</csymbol><apply id="idp36125520"><abs id="idp36125648"/><apply id="idp36125776"><ci id="idp36125904">∇</ci><ci id="idp36126192">u</ci></apply></apply><cn id="idp36126448" type="integer">2</cn></apply><apply id="idp36126976"><csymbol id="idp36127104" cd="ambiguous">superscript</csymbol><apply id="idp36127664"><abs id="idp36127792"/><ci id="idp36127920">u</ci></apply><apply id="idp36128176"><plus id="idp36128304"/><ci id="idp36128432">α</ci><cn id="idp36128720" type="integer">2</cn></apply></apply><apply id="idp36129248"><csymbol id="idp36129376" cd="ambiguous">superscript</csymbol><apply id="idp36129936"><abs id="idp36130064"/><ci id="idp36130192">u</ci></apply><cn id="idp36130448" type="integer">2</cn></apply></apply><apply id="idp36130976"><interval id="idp36131104" closure="open"/><ci id="idp36131504">t</ci><apply id="idp36131760"><minus id="idp36131888"/><ci id="idp36132016">x</ci><apply id="idp36132272"><times id="idp36132400"/><cn id="idp36132528" type="integer">2</cn><ci id="idp36133056">t</ci><apply id="idp36133312"><csymbol id="idp36133440" cd="ambiguous">subscript</csymbol><ci id="idp36134000">y</ci><cn id="idp36134256" type="integer">0</cn></apply></apply></apply></apply></apply></apply></annotation-xml><annotation id="idp36134784" encoding="application/x-tex">[|\nabla\widetilde{u}|^{2}+|\widetilde{u}|^{{{\alpha+2}}}+|\widetilde{u}|^{2}](t,x)\leq C[|\nabla u|^{2}+|u|^{{{\alpha+2}}}+|u|^{2}](t,x-2ty_{0}),</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp58080"><h4>Hit idp58080</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 99</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/132/f052703.xhtml#idp58080</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:65173(000004%) VariableMap:[eta x 9, varphi x 4, int x 4, +, rvert, cdot x 4, Omega x 4, H x 2, , x 4, - x 2, 2 x 3, lvert, u x 7, 0, displaystyle, nabla x 3, ] x 2, \ x 35, :, _ x 11, ^ x 3, =, [ x 2] Expects 2 occurences for 'd' but has only 0 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 4 occurences for '|' but has only 0 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp548896" alttext="\displaystyle\int _{\Omega}\nabla u_{\eta}:\nabla\varphi-\int _{\Omega}\lvert{\nabla u_{\eta}}\rvert^{2}\,\,\, u_{\eta}\cdot\varphi+\eta^{2}\int _{{\Omega}}u_{\eta}\cdot H[u_{\eta}]\, u_{\eta}\cdot\varphi-\eta^{2}\int _{\Omega}H[u_{\eta}]\cdot\varphi=0" display="inline"><semantics id="idp549888"><mrow id="idp550016"><mrow id="idp550144"><mstyle id="idp550272" displaystyle="true"><msub id="idp550640"><mo id="idp550768">∫</mo><mi id="idp551024" mathvariant="normal">Ω</mi></msub></mstyle><mrow id="idp551584"><mo id="idp551712">∇</mo><mo id="idp552000">⁡</mo><msub id="idp552288"><mi id="idp552416">u</mi><mi id="idp552672">η</mi></msub></mrow></mrow><mo id="idp552960">:</mo><mrow id="idp553216"><mrow id="idp553344"><mrow id="idp553472"><mo id="idp553600">∇</mo><mo id="idp553888">⁡</mo><mi id="idp554176">φ</mi></mrow><mo id="idp554464">-</mo><mrow id="idp554720"><mstyle id="idp554848" displaystyle="true"><msub id="idp555248"><mo id="idp555376">∫</mo><mi id="idp555664" mathvariant="normal">Ω</mi></msub></mstyle><mrow id="idp556224"><mrow id="idp556352"><msup id="idp556480"><mrow id="idp556608"><mo id="idp556736" fence="true">|</mo><mrow id="idp557264"><mo id="idp557392">∇</mo><mo id="idp557680">⁡</mo><msub id="idp557968"><mi id="idp558096">u</mi><mi id="idp558352">η</mi></msub></mrow><mo id="idp558640" fence="true">|</mo></mrow><mn id="idp559168">2</mn></msup><mo id="idp559424">⁢</mo><msub id="idp559712"><mi id="idp559840">u</mi><mi id="idp560096">η</mi></msub></mrow><mo id="idp560384">⋅</mo><mi id="idp560672">φ</mi></mrow></mrow><mo id="idp560960">+</mo><mrow id="idp561216"><msup id="idp561344"><mi id="idp561472">η</mi><mn id="idp561760">2</mn></msup><mo id="idp562016">⁢</mo><mrow id="idp562304"><mstyle id="idp562432" displaystyle="true"><msub id="idp562832"><mo id="idp562960">∫</mo><mi id="idp563248" mathvariant="normal">Ω</mi></msub></mstyle><mrow id="idp563808"><mrow id="idp563936"><mrow id="idp564064"><msub id="idp564192"><mi id="idp564320">u</mi><mi id="idp564576">η</mi></msub><mo id="idp564864">⋅</mo><mi id="idp565152">H</mi></mrow><mo id="idp565408">⁢</mo><mrow id="idp565696"><mo id="idp565824">[</mo><msub id="idp566080"><mi id="idp566208">u</mi><mi id="idp566464">η</mi></msub><mo id="idp566752">]</mo></mrow><mo id="idp567008">⁢</mo><msub id="idp567296"><mi id="idp567424">u</mi><mi id="idp567680">η</mi></msub></mrow><mo id="idp567968">⋅</mo><mi id="idp568256">φ</mi></mrow></mrow></mrow><mo id="idp568544">-</mo><mrow id="idp568800"><msup id="idp568928"><mi id="idp569056">η</mi><mn id="idp569344">2</mn></msup><mo id="idp569600">⁢</mo><mrow id="idp569888"><mstyle id="idp570016" displaystyle="true"><msub id="idp570416"><mo id="idp570544">∫</mo><mi id="idp570832" mathvariant="normal">Ω</mi></msub></mstyle><mrow id="idp571392"><mrow id="idp571520"><mi id="idp571648">H</mi><mo id="idp571904">⁢</mo><mrow id="idp572192"><mo id="idp572320">[</mo><msub id="idp572576"><mi id="idp572704">u</mi><mi id="idp572960">η</mi></msub><mo id="idp573248">]</mo></mrow></mrow><mo id="idp573504">⋅</mo><mi id="idp573792">φ</mi></mrow></mrow></mrow></mrow><mo id="idp574080">=</mo><mn id="idp574336">0</mn></mrow></mrow><annotation-xml id="idp574592" encoding="MathML-Content"><apply id="idp574992"><ci id="idp575120">:</ci><apply id="idp575376"><apply id="idp575504"><csymbol id="idp575632" cd="ambiguous">subscript</csymbol><int id="idp576192"/><ci id="idp576320">Ω</ci></apply><apply id="idp576608"><ci id="idp576736">∇</ci><apply id="idp577024"><csymbol id="idp577152" cd="ambiguous">subscript</csymbol><ci id="idp577712">u</ci><ci id="idp577968">η</ci></apply></apply></apply><apply id="idp578256"><eq id="idp578384"/><apply id="idp578512"><minus id="idp578640"/><apply id="idp578768"><plus id="idp578896"/><apply id="idp579024"><minus id="idp579152"/><apply id="idp579280"><ci id="idp579408">∇</ci><ci id="idp579696">φ</ci></apply><apply id="idp579984"><apply id="idp580112"><csymbol id="idp580240" cd="ambiguous">subscript</csymbol><int id="idp580800"/><ci id="idp580928">Ω</ci></apply><apply id="idp581216"><ci id="idp581344">⋅</ci><apply id="idp581632"><times id="idp581760"/><apply id="idp581888"><csymbol id="idp582016" cd="ambiguous">superscript</csymbol><apply id="idp582576"><abs id="idp582704"/><apply id="idp582832"><ci id="idp582960">∇</ci><apply id="idp583248"><csymbol id="idp583376" cd="ambiguous">subscript</csymbol><ci id="idp583936">u</ci><ci id="idp584192">η</ci></apply></apply></apply><cn id="idp584480" type="integer">2</cn></apply><apply id="idp585008"><csymbol id="idp585136" cd="ambiguous">subscript</csymbol><ci id="idp585696">u</ci><ci id="idp585952">η</ci></apply></apply><ci id="idp586240">φ</ci></apply></apply></apply><apply id="idp586528"><times id="idp586656"/><apply id="idp586784"><csymbol id="idp586912" cd="ambiguous">superscript</csymbol><ci id="idp587472">η</ci><cn id="idp587760" type="integer">2</cn></apply><apply id="idp588288"><apply id="idp588416"><csymbol id="idp588544" cd="ambiguous">subscript</csymbol><int id="idp589104"/><ci id="idp589232">Ω</ci></apply><apply id="idp589520"><ci id="idp589648">⋅</ci><apply id="idp589936"><times id="idp590064"/><apply id="idp590192"><ci id="idp590320">⋅</ci><apply id="idp590608"><csymbol id="idp590736" cd="ambiguous">subscript</csymbol><ci id="idp591296">u</ci><ci id="idp591552">η</ci></apply><ci id="idp591840">H</ci></apply><apply id="idp592096"><csymbol id="idp592224" cd="ambiguous">subscript</csymbol><ci id="idp592784">u</ci><ci id="idp593040">η</ci></apply><apply id="idp593328"><csymbol id="idp593456" cd="ambiguous">subscript</csymbol><ci id="idp594016">u</ci><ci id="idp594272">η</ci></apply></apply><ci id="idp594560">φ</ci></apply></apply></apply></apply><apply id="idp594848"><times id="idp594976"/><apply id="idp595104"><csymbol id="idp595232" cd="ambiguous">superscript</csymbol><ci id="idp595792">η</ci><cn id="idp596080" type="integer">2</cn></apply><apply id="idp596608"><apply id="idp596736"><csymbol id="idp596864" cd="ambiguous">subscript</csymbol><int id="idp597424"/><ci id="idp597552">Ω</ci></apply><apply id="idp597840"><ci id="idp597968">⋅</ci><apply id="idp598256"><times id="idp598384"/><ci id="idp598512">H</ci><apply id="idp598768"><csymbol id="idp598896" cd="ambiguous">subscript</csymbol><ci id="idp599456">u</ci><ci id="idp599712">η</ci></apply></apply><ci id="idp600000">φ</ci></apply></apply></apply></apply><cn id="idp600288" type="integer">0</cn></apply></apply></annotation-xml><annotation id="idp600816" encoding="application/x-tex">\displaystyle\int _{\Omega}\nabla u_{\eta}:\nabla\varphi-\int _{\Omega}\lvert{\nabla u_{\eta}}\rvert^{2}\,\,\, u_{\eta}\cdot\varphi+\eta^{2}\int _{{\Omega}}u_{\eta}\cdot H[u_{\eta}]\, u_{\eta}\cdot\varphi-\eta^{2}\int _{\Omega}H[u_{\eta}]\cdot\varphi=0</annotation></semantics></math> <br /> End of MathML <br /> .</div><div id="idp618880"><h4>Hit idp618880</h4> <ul> <li>Reviwer: xxx</li> <li>Reviwer score: 0</li> <li>Formulasearchengine rank: 100</li> <li>Formulasearchengine score: 0</li> <li>Reference to collection: _PREFIX_/204/f081547.xhtml#idp618880</li> </ul><blockcode linenumbers="off" title="justification"> no match at pos:74133(000057%) VariableMap:[dA, A, int, mu, ., H, frac, w, 2 x 3, 1, nabla, p, \ x 4, _, | x 2, ^ x 2, =] Expects 2 occurences for 'd' but has only 0 Expects 2 occurences for 'int' but has only 1 Expects 1 occurences for 'leq' but has only 0 Expects 1 occurences for '+' but has only 0 Expects 1 occurences for '(' but has only 0 Expects 1 occurences for ')' but has only 0 Expects 2 occurences for 'neq' but has only 0 Expects 2 occurences for '0' but has only 0 Expects 2 occurences for 'nabla' but has only 1 Expects 1 occurences for 'q' but has only 0 Expects 7 occurences for '\' but has only 4 Expects 2 occurences for '_' but has only 1 Expects 4 occurences for '|' but has only 2 Scoringfunction: ' + NO_SCORE =+0.0 = 0.0' final score ~ 0 reviewer: xxx gave 0</blockcode><br /> Rendered MathML: <br /> <math xmlns="http://www.w3.org/1998/Math/MathML" id="idp618880" alttext="w=\frac{H^{2}}{12\mu}\int _{A}|\nabla p|^{2}dA." display="block"><semantics id="idp619664"><mrow id="idp619792"><mrow id="idp619920"><mi id="idp620048">w</mi><mo id="idp620304">=</mo><mrow id="idp620560"><mfrac id="idp620688"><msup id="idp620816"><mi id="idp620944">H</mi><mn id="idp621200">2</mn></msup><mrow id="idp621456"><mn id="idp621584">12</mn><mo id="idp621840">⁢</mo><mi id="idp622096">μ</mi></mrow></mfrac><mo id="idp622352">⁢</mo><mrow id="idp622640"><msub id="idp622768"><mo id="idp622896">∫</mo><mi id="idp623184">A</mi></msub><mrow id="idp623488"><msup id="idp623616"><mrow id="idp623744"><mo id="idp623920" fence="true">|</mo><mrow id="idp624448"><mo id="idp624576">∇</mo><mo id="idp624864">⁡</mo><mi id="idp625152">p</mi></mrow><mo id="idp625408" fence="true">|</mo></mrow><mn id="idp625936">2</mn></msup><mo id="idp626192">⁢</mo><mi id="idp626448">d</mi><mo id="idp626704">⁢</mo><mi id="idp626960">A</mi></mrow></mrow></mrow></mrow><mo id="idp627216">.</mo></mrow><annotation-xml id="idp627472" encoding="MathML-Content"><apply id="idp627840"><eq id="idp627968"/><ci id="idp628096">w</ci><apply id="idp628352"><times id="idp628480"/><apply id="idp628608"><divide id="idp628736"/><apply id="idp628864"><csymbol id="idp628992" cd="ambiguous">superscript</csymbol><ci id="idp629552">H</ci><cn id="idp629808" type="integer">2</cn></apply><apply id="idp630336"><times id="idp630464"/><cn id="idp630592" type="integer">12</cn><ci id="idp631120">μ</ci></apply></apply><apply id="idp631408"><apply id="idp631536"><csymbol id="idp631664" cd="ambiguous">subscript</csymbol><int id="idp632224"/><ci id="idp632352">A</ci></apply><apply id="idp632608"><times id="idp632736"/><apply id="idp632864"><csymbol id="idp632992" cd="ambiguous">superscript</csymbol><apply id="idp633552"><abs id="idp633680"/><apply id="idp633808"><ci id="idp633936">∇</ci><ci id="idp634224">p</ci></apply></apply><cn id="idp634480" type="integer">2</cn></apply><ci id="idp635008">d</ci><ci id="idp635264">A</ci></apply></apply></apply></apply></annotation-xml><annotation id="idp635520" encoding="application/x-tex">w=\frac{H^{2}}{12\mu}\int _{A}|\nabla p|^{2}dA.</annotation></semantics></math> <br /> End of MathML <br /> .</div></div></div></div><section class="field field-name-field-tags field-type-taxonomy-term-reference field-label-above view-mode-full view-mode-full"><h2 class="field-label">Tags: </h2><ul class="field-items"><li class="field-item even" rel="dc:subject"><a href="/ntcir10-math/results/FS" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">NTCIR Formulae (only) Search</a></li></ul></section> </div> <nav class="clearfix"><ul class="links"><li class="comment_forbidden first last"><span><a href="/user/login?destination=node/103%23comment-form">Log in</a> to post comments</span></li></ul></nav> </div> </article> </div></div> </section> </div></div> </div></div> </div></div> <div id="page-footer"> <div id="footer-panels-wrapper"><div class="container clearfix"> <div class="four-4x25 gpanel clearfix"> <div class="region region-four-fourth"><div class="region-inner clearfix"><div id="block-block-1" class="block block-block no-title odd first last block-count-3 block-region-four-fourth block-1" ><div class="block-inner clearfix"> <div class="block-content content no-title"><p>By <a href="mailto:info@formulasearchengine.com">Moritz Schubotz</a>, Berlin 2012 (<a href="https://plus.google.com/u/0/104541687836095789339?<br /> rel=author">g+</a>)</p> </div> </div></div></div></div> </div> </div></div> <div id="footer-wrapper"><div class="container clearfix"> <footer class="clearfix"> <div class="region region-footer"><div class="region-inner clearfix"><nav id="block-superfish-2" class="block block-superfish no-title odd first last block-count-4 block-region-footer block-2" ><div class="block-inner clearfix"> <div class="block-content content clearfix no-title"><ul id="superfish-2" class="menu sf-menu sf-menu-administration sf-horizontal sf-style-none sf-total-items-1 sf-parent-items-0 sf-single-items-1"><li id="menu-450-2" class="firstandlast odd sf-item-1 sf-depth-1 sf-no-children"><a href="/Impressum" title="Legeal notices" class="sf-depth-1">Impressum</a></li></ul></div> 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