Search results

...s lemma''' is a lemma used by [[Kurt Heegner]] in his paper on the [[class number problem]]. His lemma states that if ...'a''₄ not a square, then it has a solution if it has a solution in an [[field extension|extension]] of odd degree. ...

...g and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. * [[Digital Morse theory]] ...

In [[mathematics]], '''Cartan's lemma''' refers to a number of results named after either [[Élie Cartan]] or his son [[Henri Cartan]]: * In [[exterior algebra]]:<ref>*{{cite book | last = Sternberg | first = S. | ye ...

..., where n=2, the red 1-simplex has vertices which are labelled by the same number with opposite signs. Tucker's lemma states that for such a triangulation at In [[mathematics]], '''Tucker's lemma''' is a [[combinatorics|combinatorial]] ...

...the [[Stability theory|stability]] of delayed differential equations, and in particular, the stability of industrial processes with dead-time<ref>{{Cite ...math>t_{0}</math> be a real number and <math>\tau</math> be a non-negative number. If <math>v: [t_{0}-\tau, \infty) \rightarrow \mathbb{R}^{+}</math> satisfi ...

...lemma provides a similar yet more general notion on the space of graphons, in which a scalar of the cut distance between two graphs is correlated to the ...ty <math>d(U,V)</math>, is ''close'' ''to being'' a random bipartite graph in which every edge appears with probability <math>d(U,V)</math>, with some <m ...

{{short description|Field theory result}} ...rYuAUC&pg=PA120}}.</ref><ref>This theorem, for [[Minimal polynomial (field theory)|minimal polynomials]] rather than irreducible polynomials more generally, ...

...sis of a [[function space]]. The result was originally proved by Stechkin in the case <math>q = 2</math>. ...math>N</math> largest terms of the sequence <math>(a_{i})_{i \in I}</math> in [[absolute value]]. Then ...

...king lemma''' is any of a number of related [[lemma (mathematics)|lemmas]] in [[cryptography]] research. The lemma states that if an adversary (typicall ...ry Neven, "[http://portal.acm.org/citation.cfm?id=1180453 Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma]", Proceedings of th ...

{{Short description|Technique for reducing number of solutions}} ...'''isolating lemma''') refers to [[randomized algorithm]]s that reduce the number of solutions to a problem to one, should a solution exist. ...

...m the commutations required by the [[Poincaré–Birkhoff–Witt theorem]] used in the construction of a [[universal enveloping algebra]]. As such, this gener ...ng process]] was described first, in 1934, by [[Philip Hall]] and explored in 1937 by [[Wilhelm Magnus]].<ref> ...

In [[number theory]], more specifically in [[p-adic analysis|''p''-adic analysis]], '''Krasner's lemma''' is a basic r ...{{overline|''K''}} be a [[separable closure]] of ''K''. Given an element α in {{overline|''K''}}, denote its [[Galois conjugate]]s by ''α''₂,& ...

...ng edge disjoint paths in [[expander graphs]], and exploring [[anti-Ramsey theory]] and the stability of [[routing algorithms]]. |number =1 ...

{{Short description|Type of graph in mathematics}} In [[graph theory]], a branch of [[mathematics]], a '''half graph''' is a special type of [[b ...

...te-[[Dimension (vector space)|dimensional]] [[vector space]] have the same number of elements. The result is named after the German mathematician [[Ernst Ste ...ac Lane|year=1936|title=Some interpretations of abstract linear dependence in terms of projective geometry|journal=American Journal of Mathematics|volume ...

...in ergodic theory, for example in [[Ornstein isomorphism theorem|Ornstein theory]] and has many generalizations. ...is which are traditionally called lemmas despite the fact that their roles in their respective fields are fundamental. ...

{{Short description|Method in combinatorics}} ...], and [[Ramsey theory]]; they include some of the most classical problems in the associated fields. ...

{{Short description|Number theoretic lemma}} ...it describes the steps necessary to "lift" the exponent of <math>p</math> in such expressions. It is related to [[Hensel's lemma]]. ...

{{Short description|Mathematical method in extremal graph theory}} ...use of [[Szemerédi regularity lemma|Szemerédi's regularity]] and counting lemmas. ...

...'''ring lemma''' gives a [[lower bound]] on the sizes of adjacent circles in a circle packing.{{r|s}} ...s in the ring tangent to each other. Then the minimum radius of any circle in the ring is at least the [[unit fraction]] ...