Results 21 to 30 of about 25,343,404 (305)
The strength of compactness in Computability Theory and Nonstandard Analysis [PDF]
Annals of Pure and Applied Logic, 2018 The authors recently pioneered a connection between Nonstandard Analysis and Computability Theory, resulting in a number of surprising results and even more open questions.
D. Normann, Sam Sanders
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Grid functions of nonstandard analysis in the theory of distributions and in partial differential equations [PDF]
Advances in Mathematics, 2017 We introduce the space of grid functions, a space of generalized functions of nonstandard analysis that provides a coherent generalization both of the space of distributions and of the space of Young measures.
E. Bottazzi
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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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COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS [PDF]
Journal of Symbolic Logic (JSL), 2017 We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related.
D. Normann, Sam Sanders
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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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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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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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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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Axioms, 2021 Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully.
N. Ahmed +6 more
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