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{{Short description|Mathematical term}} ...very [[decreasing sequence]] of [[Ball (mathematics)|balls]] (in the sense of the metric induced by the absolute value) is nonempty:<ref>{{Cite journal | ...

...al field]]s where a more detailed analysis can be carried out with the aid of tools such as [[ramification group]]s. ...ase when <math>A, B</math> are complete; i.e., <math>L, K</math> are local fields.--> ...

...[ordered field]] that does not satisfy the [[Archimedean property]]. Such fields will contain infinitesimal and infinitely large elements, suitably defined. ...nt {{math|1}}, so that {{math|''nx''}} is the sum of {{math|''n''}} copies of {{math|''x''}}. ...

{{short description|Mathematical problem concerning limit cycles in dynamical systems}} ...und]] on [[limit cycles]] in generic finite-parameter families of [[vector fields]] on a sphere?}} ...

...ass field theory''' is the study of abelian extensions of local and global fields. * 1801 [[Carl Friedrich Gauss]] proves the [[law of quadratic reciprocity]] ...

{{Short description|Class of integral and differential operator}} ...ysis]], an '''oscillatory integral operator''' is an [[integral operator]] of the form ...

{{Short description|Mathematical concept}} ...a [[Field (mathematics)|field]] consisting of [[Germ (mathematics)|germs]] of [[real-valued function]]s at infinity that are closed under [[differentiati ...

| fields = Mathematics | workplaces = [[University of North Carolina at Chapel Hill]] ...

...Edward Kottwitz''' (born 1950 in [[Lynn, Massachusetts]])<ref>member book of IAS in 1980</ref> is an American mathematician. ...ersity of Washington]] and went in 1989 as a professor to the [[University of Chicago]]. ...

...pecializing in [[complex analysis]], [[approximation theory]], [[numerical analysis]], and [[potential theory]]. ...Approximation and was from 2004 to 2007 the Executive Dean of the College of Arts and Sciences. ...

...at [[Steklov Institute]], and also taught at the [[Independent University of Moscow]]. He became a professor at [[Cornell University]].<ref>{{Cite web|u ...02-00946-1|doi-access=free}}</ref> He proved that planar polynomial vector fields have only finitely many limit cycles. [[Jean Écalle]] independently proved ...

...on [[locally convex topological vector space]]s over [[field (mathematics)|fields]] with [[Ultrametric space|non-Archimedean]] [[Valuation (algebra)|valuatio ...Ghent University]], finished her degree with a specialty in [[mathematical analysis]] there in 1958, and took a job as a high school mathematics teacher.{{r|re ...

{{Short description|System of numbers with non-finite quantities}} ...s=1795–1815}}</ref> is a [[non-Archimedean ordered field]]; i.e., a system of numbers containing infinite and [[infinitesimal]] quantities. It is usually ...

.../erdos2011-cite.pdf|title=2011 Erdos Prize in Mathematics|publisher=Israel Mathematical Union|access-date=2015-08-02}}.</ref> | fields = [[Ergodic theory]], [[Combinatorics]], [[Number theory]] ...

...y)|degrees of freedom]], the field formulation has infinitely many degrees of freedom. ...ned from the [[Lagrangian density]] by<ref group=nb>It is a standard abuse of notation to abbreviate all the derivatives and coordinates in the Lagrangia ...

...binson]], and later a co-author with Robinson of the book ''Nonarchimedean Fields and Asymptotic Expansions''.<ref>''[[Nonarchimedean field]]s and [[asymptot ...enealogy|id=16086|name=Albert Harold Lightstone}}</ref> He was a professor of mathematics at [[Carleton University]]<ref name="trisect"/> and [[Queen's U ...

{{Short description|A analogy used to study vector fields}} [[File:ChampSelonSigneDeDiv.pdf|thumb|300x300px|Three examples of vector fields. From left to right: a field with a source, a field with a sink, a field wi ...

...ef> This valuation will show a way to count the order (at the point ''P'') of rational functions (which are natural generalizations for meromorphic funct ...deal of the local ring at a point ''P'' is actually conformed by the germs of holomorphic functions vanishing at ''P''. ...

...ansfer equation from one coordinate system to another system through scale analysis''' = ...at transfer equation in different coordinate systems and the role of scale analysis in simplifying and converting these equations. ...

...d Congress] in Stockholm simulation governance was identified as the first of eight “[https://www.nafems.org/congress/thebigissues/ big issues]” in [[num ...ication]] procedures, and (e) revision of mathematical models in the light of new information collected from physical experiments and field observations. ...