Results 1 to 10 of about 26 (26)
Infinitesimals via Cauchy sequences: Refining the classical equivalence
Open Mathematics, 2021 A refinement of the classic equivalence relation among Cauchy sequences yields a useful infinitesimal-enriched number system. Such an approach can be seen as formalizing Cauchy’s sentiment that a null sequence “becomes” an infinitesimal.
Bottazzi Emanuele, Katz Mikhail G.
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Metric completions, the Heine-Borel property, and approachability
Open Mathematics, 2020 We show that the metric universal cover of a plane with a puncture yields an example of a nonstandard hull properly containing the metric completion of a metric space.
Kanovei Vladimir +2 more
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Monotone subsequence via ultrapower
Open Mathematics, 2018 An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and ...
Błaszczyk Piotr +3 more
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Generalized solutions of variational problems and applications
Advances in Nonlinear Analysis, 2018 Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ*⊃ℝ{\mathbb{R}^{*}\supset\mathbb{R}} that allow to solve variational problems with no classical solutions.
Benci Vieri +2 more
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Courbure et Polygone de Newton [PDF]
, 2009 2000 Mathematics Subject Classification: 26E35, 14H05, 14H20.The object of this article relates to the study of the complex algebraic curves by using the concept of envelope convex.
Mezaghcha, K., Hannachi M, M.
core
Constructive Nonstandard Representations of Generalized Functions
, 1998 Using techniques of nonstandard analysis Abraham Robinson showed that it is possible to represent each Schwartz distribution T as an integral T (OE) = R f OE, where f is some nonstandard smooth function.
Erik Palmgren
core
Some of the next articles are maybe not open access.
Effective Infinitesimals in $\mathbb R$
Real Analysis Exchange, 2023Karel Hrbáček, Mikhail G Katz
exaly
Formal multiplicative root series and algorithms of their evaluation
Communications in Algebra, 2021Xiao-Xiong Gan, Dariusz Bugajewski
exaly
A ring homomorphism is enough to get nonstandard analysis
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2003Vieri Benci
exaly