Superlens: Difference between revisions

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{{unreferenced|date=August 2012}}
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{{Expert-subject|mathematics|date=March 2011}}
[[File:Cubic with double point.svg|thumb|right|300px|A crunode at the origin of the curve defined by ''y''<sup>2</sup>−''x''<sup>2</sup>(''x''+1)=0]]
In [[mathematics]], a '''crunode''' (archaic) or '''node''' is a point where a [[curve]] intersects itself so that both branches of the curve have distinct [[tangent line]]s at the point of intersection. A crunode is also known as an ''ordinary double point''.<ref>{{cite web|last=Weisstein|first=Eric W.|title=Crunode|url=http://mathworld.wolfram.com/Crunode.html|publisher=Mathworld|accessdate=14 January 2014}}</ref>
 
For a [[plane curve]], defined as the locus of points ''f''(''x'', ''y'') = 0, where ''f''(''x'', ''y'') is a [[smooth function]] of variables ''x'' and ''y'' ranging over the real numbers, a crunode of the curve is a [[singularity theory|singularity]] of the function ''f'', where both [[partial derivative]]s <math>\partial f\over \partial x</math> and <math>\partial f\over \partial y</math> vanish. Further the [[Hessian matrix]] of second derivatives will have both positive and negative [[eigenvalues]].
 
==See also==
*[[Singular point of a curve]]
*[[Acnode]]
*[[Cusp (singularity)|Cusp]]
*[[Tacnode]]
*[[Saddle point]]
 
==References==
{{reflist}}
 
{{Algebraic curves navbox}}
 
[[Category:Curves]]
[[Category:Algebraic curves]]
 
 
{{differential-geometry-stub}}

Latest revision as of 06:29, 10 December 2014

Hi there. My name is Sophia Meagher although it is not psychic phone (http://galab-Work.cs.pusan.ac.kr/Sol09B/?document_srl=1489804) the name on my beginning certification. She functions as a journey agent but quickly she'll be on her own. Some time in the past she selected to reside in Alaska and her mothers and fathers live nearby. To climb is something I truly enjoy doing.

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