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		<title>en&gt;K9re11: /* See also */</title>
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		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;See also&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 14:02, 21 November 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{underlinked|date=November 2012}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1 tool which can make or break you in a survival predicament is a great knife. And despite the fact that it really is said that the ideal knife &lt;/ins&gt;is the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one you have with you, and a lot can be accomplished with &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;correct capabilities and any knife, there are attributes which make some survival knives much better &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://dore.Gia.Ncnu.edu.tw/88ipart/node/3028898 choices&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;than others&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;&amp;lt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In case you adored this informative article and also you desire to acquire more information concerning [http://www.thebestpocketknifereviews.com/zero-tolerance-knives-review/ Zero Tolerance Knives Review] kindly go to our web site. There are also two holes in the handle at the hilt, which in theory can be made use of to convert the knife into a spear in a survival circumstance. Actually, I&#039;m not confident why any one would want to convert their major cutting tool into a spear when 1 can basically use the knife to [http://sss.chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&amp;amp;summary&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&amp;amp;description=If+I+am+being+honest%2C+I+am+not+as+significantly+into+knives+as+I+am+into+bags+but+I+do+stick+to+Gibb%27s+Rule+%239+Thus%2C+I+do+like+to+carry+a+top+quality+folder.+I%27ve+not+however+ventured+into+custom+knife+territory+due+to+price+and+I+normally+don%27t+get+cheap+knifes+unless+I+am+going+to+beat+the+hell+out+&lt;/ins&gt;of&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+them.%0D%0A%0D%0A%5B%5Biframe+%2F%2Fwww.youtube.com%2Fembed%2FuUnnRzWTzuQ+height%3D%22360%22+width%3D%22640%22%5D%5DThe+Zero+Tolerance+350+Series+is+anything+you+would+want+in+&lt;/ins&gt;a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+folding+duty-grade+knife.+It+is+also+worth+noting+that+it+really+is+entirely+produced+in+the+U.S.%E2%80%94something+worth+supporting.+With+no+a+doubt%2C+Zero+Tolerance+has+built+a+robust%2C+hard-use+knife+that+will+surely+stand+up+to+the+rigors+&lt;/ins&gt;of&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+law+enforcement+&lt;/ins&gt;and&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+military+use.+It+seems+to+me+that+Zero+Tolerance+just+has+a+zero+tolerance+for+officer+failure%E2%80%94and+that%27s+good+&lt;/ins&gt;to&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+know.+Kershaw+Zero+Tolerance+Ranger+Knife+0121+Was+this+evaluation+helpful%3F+Yes+just+what+&lt;/ins&gt;I&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+required+Assessment+by+Pete+Steelman+Kershaw+Zero+Tolerance+Bayonet+ZT-9+Kershaw+Zero+Tolerance+Shifter+Fixed+Blade+Knife+0160+%24260&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;00+Zero+Tolerance+Rick+Hinderer+Folder+Elmax+Steel+Zero+Tolerance+0350+Stonewashed+Carbon+Fiber+Zero+Tolerance+Model+0301ST+SpeedSafe+Folder%0D%0A%0D%0AThis+knife+certainly+floors+me+for+value.++If+you+loved+this+post+in+addition+to+you+would+like+to+get+more+information+regarding+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fzero-tolerance-knives-review%2F+The+Best+Pocket+Knife+Reviews%5D+i+implore+you+to+visit+the+webpage.+Its+produced+really+nicely%2C+and+has+quite+nicely+machined+particulars+such+as+the+textured+scales+and+framelock&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hinderer+lockbar+stabilizer+and+ultra-thick+handles+&lt;/ins&gt;and&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+a+complete+black+G&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ten+backspacer.+There+is+also+a+scale+&lt;/ins&gt;on&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+the+G-10+deal+with+side+that+homes+the+speed+protected+mechanism%2C+I+think.+The+Kershaw+Cryo+won+%E2%80%9CBest+Obtain+of+the+Year%E2%80%9D+at+the+2012+Blade+Show%2C+&lt;/ins&gt;and&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+now+it+is+offered+with+a+G-10+front+scale.+This+Cryo+features+SpeedSafe+assisted+opening+%2C+a+stainless+steel+back%2C+a+strong+frame+lock%2C+a+Hinderer+lockbar+stabilizer%2C+&lt;/ins&gt;a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+completely&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reversible+pocket+clip%2C+and+an+8Cr13MoV+blade.+It+was+a+small+slow+receiving+in%2C+but+it+fits+my+knife+just+ideal+and+performs+well+with+my+ACU.+%28Posted+on+five%2F26%2F2014%29+ZT+0620+Tanto+Emerson%0D%0A%0D%0ACreated+from+stainless+steel%2C+the+blade+discovered+on+the%C2%A0ZT0301%C2%A0is+extremely+powerful+and+put+&lt;/ins&gt;on&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+resistant+and+also+the+ergonomic+design+&lt;/ins&gt;and&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+style+makes+it+comfy+to+grip.+I+could+hardly+noticed+any+pain+&lt;/ins&gt;on&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+my+hand+even+just+after+worked+with+this+knife+for+hours.+There+is+an+adequately+jimped+thumb+ramp+and+a+thumb+groove+along+the+spine.%C2%A0Made+from%C2%A0Titanium+metal%2C+the%C2%A0blade+is+genuinely+lightweight+and+challenging&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;%C2%A0The+shape+of+&lt;/ins&gt;the+&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blade+is+developed+for+delivering+far+more+cutting+power%2C+it+is+helpful+for+cutting+by+means+of+just+about+something+and+possesses+wonderful+edge+retention.%0D%0A%0D%0AS30V+&lt;/ins&gt;is&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+&lt;/ins&gt;a&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+premium+knife+steel+that+is+being+jointly+created+by+the+Crucible+Supplies+Corporation+and+the+popular+Chris+Reeve.+Chris+Reeve+is+one+of+the+most+well&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;known+knife+makers+who+has+wonderful+information+and+ability+concerning+this+art.+Thus%2C+his+collaboration+with+%5Bhttp%3A%2F%2Fmondediplo.com%2Fspip.php%3Fpage%3Drecherche%26recherche%3DCrucible%2BMaterials+Crucible+Materials%5D+offers+the+steel+a+lot+of+credibility.+And+all+this+credibility+is+incredibly+effectively+%5Bhttp%3A%2F%2Fsearch.un.org%2Fsearch%3Fie%3Dutf8%26site%3Dun_org%26output%3Dxml_no_dtd%26client%3DUN_Website_en%26num%3D10%26lr%3Dlang_en%26proxystylesheet%3DUN_Website_en%26oe%3Dutf8%26q%3Ddeserved%26Submit%3DGo+deserved%5D+by+S30V.+It+is+an+really+sharp%2C+challenging+and+wear+resistant+material.+It+is+one+particular+of+the+finest+powdered+steels+made+use+of+to+make+combat+knives.+If+you+are+preparing+to+invest+in+a+knife+from+Zero+Tolerance+&lt;/ins&gt;then&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+you+could+get+1+created+with+S30V+steel.+This+is+the+kind+of+steel+that+is+utilised+to+make+of+the+knives+by+Zero+Tolerance.%0D%0A%0D%0AThe+ZT++represents+18+months+of+collaborative+efforts+between+SKD+and+Zero+Tolerance+that+started+back+in+August+of+2008.+Initially+primarily+based+on+the+ZT+0300+series+knives%2C+the+notion+morphed+and+gained+momentum+with+the+release+of+the+ZT+0350%2C+and+ultimately+migrating+to+the+0350+platform+as+the+foundation+for+this+new+model.+In+technical+parlance%2C+we+took+a+kick&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ass+knife%2C+and+created+it+KICK+More+ASS.+Considering+the+fact+that+our+initial+brief+production+run+back+in+2010%2C+there+have+been+key+personnel+changes+at+ZT+and+increases&lt;/ins&gt;+in&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;+minimum+order+requirements+that+created+a+stick+to-on+production+run+somewhat+elusive.&amp;amp;create=Create sharpen&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a stick into a spear. That getting mentioned&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it really is an added function at no loss to the general usability of &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;knife. This knife &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;capable of [http&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;//Dore.Gia.Ncnu.Edu.tw/88ipart/node/3008428 handling] chopping&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;splitting&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;carving&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hammering&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sawing and even engraving. Its design is various from the standard survival knives. It has a wide blade created from 1095 higher carbon alloy &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is serrated on  Micarta handle is hard but slightly heavy. six. Cold Steel Leatherneck 39LSF Ferro rod striking location on the Bear Grylls Ultimate Knife&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;My initially impression of the knife was that it &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a sturdy, nicely-developed piece of equipment. I used it for a couple of weeks, for each job I would commonly use a knife for. This includes use in &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;kitchen for meals preparation, and in the field as an all-around knife. Utilizes will range from slicing potatoes and meat to whittling weiner sticks and fuzz-sticks for firemaking. I do not baton wood as a knife test, or purposely abuse a knife as element &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;testing.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Knives are more than just tools to assistance when you uncover your self in a dire life preserving state They come in handy on a day to day basis &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;are most probably component of your each day carry collection. The greatest daily carry knife &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one particular &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you can rely upon to handle a range of survival tasks and are not just specialized for 1 technique &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;particular. If you locate yourself hunting&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;skinning&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cutting or batoning &lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a high-quality survival knife should really be capable to take a beating&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Right here are the Standard Points Which Should Shape Your Selection&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Bihari&#039;s inequality&#039;&#039;&#039;, proved by Hungarian mathematician Imre Bihari (1915–1998), &lt;/del&gt;is the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;following nonlinear generalization of &lt;/del&gt;the [&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[Grönwall&#039;s lemma]&lt;/del&gt;].&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cite journal | title &lt;/del&gt;= &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A generalization &lt;/del&gt;of a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lemma &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Bellman &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;its application &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;uniqueness problems of differential equations | author = &lt;/del&gt;I. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Bihari | journal = Acta Mathematica Hungarica | year = 1956 | volume = 7 | number = 1 | month = March | pages = 81–94 | doi = 10&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1007/BF02022967}}&amp;lt;/ref&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Let &#039;&#039;u&#039;&#039; &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&amp;amp;fnof;&#039;&#039; be non&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;negative continuous functions defined &lt;/del&gt;on &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[0,&amp;amp;nbsp;∞), &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;let &#039;&#039;w&#039;&#039; be &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;continuous non&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;decreasing function defined &lt;/del&gt;on &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[0,&amp;amp;nbsp;∞) &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;w&#039;&#039;(&#039;&#039;u&#039;&#039;)&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 &lt;/del&gt;on &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(0,&amp;amp;nbsp;∞)&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If &#039;&#039;u&#039;&#039; satisfies &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;following integral inequality,&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;: &amp;lt;math&amp;gt;u(t)\leq \alpha&lt;/del&gt;+ &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\int_0^t f(s)\,w(u(s))\,ds,\qquad t\in[0,\infty),&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where &#039;&#039;α&#039;&#039; &lt;/del&gt;is a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;non&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;negative constant, &lt;/del&gt;then&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;: &amp;lt;math&amp;gt;u(t)\leq G^{&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1}\left(G(\alpha)&lt;/del&gt;+&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\int_0^t\,f(s) \, ds\right),\qquad t\&lt;/del&gt;in&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[0,T&lt;/del&gt;],&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;function &#039;&#039;G&#039;&#039; &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;defined by&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;: &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;G(x)=\int_{x_0}^x \frac{dy}{w(y)}&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\qquad x \geq 0&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;x_0&amp;gt;0&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;G&#039;&#039;&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sup&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;−1&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/sup&lt;/del&gt;&amp;gt; is the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;inverse function &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;G&#039;&#039; &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;T&#039;&#039; &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;chosen so &lt;/del&gt;that&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;: &amp;lt;math&amp;gt;G(\alpha)+\int_0^t\,f(s)\,ds\&lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\text{Dom}(G^{-1})&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\qquad \forall \&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;t \in [0&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;T]&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{reflist}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Differential equations]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Inequalities]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;K9re11</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Local_Tate_duality&amp;diff=25427&amp;oldid=prev</id>
		<title>en&gt;RobHar: /* Case of p-adic representations */ make prime more prominent</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Local_Tate_duality&amp;diff=25427&amp;oldid=prev"/>
		<updated>2011-09-07T22:55:50Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Case of p-adic representations: &lt;/span&gt; make prime more prominent&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{underlinked|date=November 2012}}&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Bihari&amp;#039;s inequality&amp;#039;&amp;#039;&amp;#039;, proved by Hungarian mathematician Imre Bihari (1915–1998), is the following nonlinear generalization of the [[Grönwall&amp;#039;s lemma]].&amp;lt;ref&amp;gt;{{cite journal | title = A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations | author = I. Bihari | journal = Acta Mathematica Hungarica | year = 1956 | volume = 7 | number = 1 | month = March | pages = 81–94 | doi = 10.1007/BF02022967}}&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Let &amp;#039;&amp;#039;u&amp;#039;&amp;#039; and &amp;#039;&amp;#039;&amp;amp;fnof;&amp;#039;&amp;#039; be non-negative continuous functions defined on [0,&amp;amp;nbsp;∞), and let &amp;#039;&amp;#039;w&amp;#039;&amp;#039; be a continuous non-decreasing function defined on [0,&amp;amp;nbsp;∞) and &amp;#039;&amp;#039;w&amp;#039;&amp;#039;(&amp;#039;&amp;#039;u&amp;#039;&amp;#039;)&amp;amp;nbsp;&amp;gt;&amp;amp;nbsp;0 on (0,&amp;amp;nbsp;∞). If &amp;#039;&amp;#039;u&amp;#039;&amp;#039; satisfies the following integral inequality,&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;u(t)\leq \alpha+ \int_0^t f(s)\,w(u(s))\,ds,\qquad t\in[0,\infty),&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;#039;&amp;#039;α&amp;#039;&amp;#039; is a non-negative constant, then&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;u(t)\leq G^{-1}\left(G(\alpha)+\int_0^t\,f(s) \, ds\right),\qquad t\in[0,T],&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where the function &amp;#039;&amp;#039;G&amp;#039;&amp;#039; is defined by&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;G(x)=\int_{x_0}^x \frac{dy}{w(y)},\qquad x \geq 0,\,x_0&amp;gt;0, &amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and &amp;#039;&amp;#039;G&amp;#039;&amp;#039;&amp;lt;sup&amp;gt;−1&amp;lt;/sup&amp;gt; is the inverse function of &amp;#039;&amp;#039;G&amp;#039;&amp;#039; and &amp;#039;&amp;#039;T&amp;#039;&amp;#039; is chosen so that&lt;br /&gt;
&lt;br /&gt;
: &amp;lt;math&amp;gt;G(\alpha)+\int_0^t\,f(s)\,ds\in \text{Dom}(G^{-1}),\qquad \forall \, t \in [0,T].&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Differential equations]]&lt;br /&gt;
[[Category:Inequalities]]&lt;/div&gt;</summary>
		<author><name>en&gt;RobHar</name></author>
	</entry>
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