Results 151 to 160 of about 29,433 (197)
Developments in Constructive Nonstandard Analysis
Bulletin of Symbolic Logic, 1998 AbstractWe develop a constructive version of nonstandard analysis, extending Bishop's constructive analysis with infinitesimal methods. A full transfer principle and a strong idealisation principle are obtained by using a sheaf-theoretic construction due to I. Moerdijk.
Palmgren, E,
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Retroreflecting Curves in Nonstandard Analysis
, 2011 We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1.
Almeida, R, Neves, V, Plakhov, A
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Extended Nonstandard Neutrosophic Logic, Set, and Probability Based on Extended Nonstandard Analysis [PDF]
Symmetry, 2019 We extend for the second time the nonstandard analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad—all these in order to close ...
Florentin Smarandache
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Journal of Automated Reasoning, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruben Gamboa, Matt Kaufmann
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ruben Gamboa, Matt Kaufmann
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On the strength of nonstandard analysis
The Journal of Symbolic Logic, 1986It is often asserted in the literature that any theorem which can be proved using nonstandard analysis can also be proved without it. The purpose of this paper is to show that this assertion is wrong, and in fact there are theorems which can be proved with nonstandard analysis but cannot be proved without it.
C. Ward Henson, H. Jerome Keisler
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Standard foundations for nonstandard analysis
Journal of Symbolic Logic, 1992In the thirty years since its invention by Abraham Robinson, nonstandard analysis has become a useful tool for research in many areas of mathematics. It seems fair to say, however, that the search for practically satisfactory foundations for the subject is not yet completed.
David Ballard, Karel Hrbacek
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Nonstandard analysis of global attractors
Mathematical Logic Quarterly, 2015Key concepts of the theory of abstract dynamical systems are formulated in the language of nonstandard analysis (NSA). We are then able to provide simple and intuitive proofs of the basic facts. In particular, we use the NSA to give an alternative proof of the characterization of global attractors due to Ball. We also address the issue of connectedness.
Dalibor Prazák, Jakub Slavík
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Singular Traces and Nonstandard Analysis
1995We discuss non trivial singular traces on the compact operators, extending some results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states using tools of non standard analysis.
Albeverio, S +3 more
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2018
Nonstandard analysis is an important application of mathematical logic to the rest of mathematics. Invented in 1960, it provided a long-sought-for rigorous justification for the use of infinitely large and infinitely small (infinitesimal) quantities in the differential and integral calculus, and the first sound canon for manipulating such quantities.
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Nonstandard analysis is an important application of mathematical logic to the rest of mathematics. Invented in 1960, it provided a long-sought-for rigorous justification for the use of infinitely large and infinitely small (infinitesimal) quantities in the differential and integral calculus, and the first sound canon for manipulating such quantities.
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The eightfold path to nonstandard analysis
2017This paper consists of a quick introduction to the “hyper-methods” of nonstandard analysis, and of a review of eight different approaches to the subject, which have been recently elaborated by the authors.
BENCI, VIERI +2 more
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