Results 11 to 20 of about 82,468 (248)
NONSTANDARD COMPLETION OF NON-COMPLETE METRIC SPACE
Zanco Journal of Pure and Applied Sciences, 2021 Our aim in this study is to establishing nonstandard foundations, definitions and theorems for completion a noncomplete metric spaces. We have a lot of space or sets X which agree with all usual properties of complete, except at a small size subset
Ala O. Hassan, Ibrahim O. Hamad
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Categorical Nonstandard Analysis [PDF]
Symmetry, 2021 In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while we make use of an endofunctor U on a topos of sets S together with a natural transformation υ, instead of the ...
Hayato Saigo, Juzo Nohmi
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Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We propose a new model of computation based on nonstandard analysis. Intuitively, the role of "algorithm" is played by a new notion of finite procedure, called Omega-invariance and inspired by physics, from nonstandard analysis.
Sam Sanders
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Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století
Filosofický časopis, 2022 Vopěnka’s Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem’s construction of a nonstandard model of arithmetic, and its inception has been
Haniková, Zuzana
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Mathematics, 2021 Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the ...
Tohru Morita, Ken-ichi Sato
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A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits
Journal of Educational Research in Mathematics, 2021 This study investigated seven pre-service teachers’ (who studied analysis) conceptions about infinitesimals, infinite numbers, and explanation methods of limits. Some pre-service teachers thought that infinitesimals and infinite numbers existed.
Seungju Baek, Jihyun Lee
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Systems, 2023 Under the general trend of reducing leverage and strictly controlling new implicit debts of local governments, the risk of nonstandard defaults by urban investment and development companies (UIDCs) continues to be released, which will increase the credit
Xue Yan +3 more
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Examples and counterexamples regarding hyperfinite representations of real distributions
Examples and Counterexamples, 2022 We provide some examples and counterexamples regarding hyperfinite representations of real distributions. We examine some hyperfinite representatives of the null distribution and of the Dirac distribution, we discuss hyperfinite representations of an ...
Emanuele Bottazzi
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SSM: Population Health, 2021 This study investigates the link between nonstandard schedules and three psychological resources salient to working parents' parental functioning (psychological distress, work-family conflict and relationship quality).
Yixuan Zhao +4 more
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Mechanizing Nonstandard Real Analysis [PDF]
LMS Journal of Computation and Mathematics, 2000 AbstractThis paper first describes the construction and use of the hyperreals in the theorem-prover Isabelle within the framework of higher-order logic (HOL). The theory, which includes infinitesimals and infinite numbers, is based on the hyperreal number system developed by Abraham Robinson in his nonstandard analysis (NSA).
Fleuriot, Jacques D. +1 more
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