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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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AppliedMath, 2022 Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green’s function.
Tohru Morita
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An operator equation and relativistic alterations in the time for radioactive decay
International Journal of Mathematics and Mathematical Sciences, 1996 In this paper, using concepts from the nonstandard physical world, the linear effect line element is derived. Previously, this line element was employed to obtain, with the exception of radioactive decay, all of the experimentally verified special theory
Robert A. Herrmann
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ON SOME NONSTANDARD DEVELOPMENTS OF INTERMEDIATE VALUE PROPERTY [PDF]
Assiut University Journal of Multidisciplinary Scientific Research, 2016 In this paper, by using the power of nonstandard analysis tools, we review some of the standard facts on the intermediate value property (IVP) and investigates some new nonstandard developments by extending the classical definition.
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On differential operators an differential equations on torus
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2018 In this paper, we consider periodic boundary value problems for a differential equation whose coefficients are trigonometric polynomials. The spaces of generalized functions are constructed, in which the problems considered have solutions, in particular,
Vladimir P Burskii
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Time averaging for functional differential equations
Journal of Applied Mathematics, 2003 We present a result on the averaging for functional differential equations on finite time intervals. The result is formulated in both classical mathematics and nonstandard analysis; its proof uses some methods of nonstandard analysis.
Mustapha Lakrib
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Solution of Euler’s Differential Equation in Terms of Distribution Theory and Fractional Calculus
Mathematics, 2020 For Euler’s differential equation of order n, a theorem is presented to give n solutions, by modifying a theorem given in a recent paper of the present authors in J. Adv. Math. Comput. Sci.
Tohru Morita, Ken-ichi Sato
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Singular perturbations and nonstandard analysis [PDF]
Transactions of the American Mathematical Society, 1979 We study by methods of nonstandard analysis second order differential operators with zero order coefficients which are too singular to be defined by standard functions. In particular we study perturbations of the Laplacian in
Albeverio, Sergio +2 more
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MagmaFlow: A desktop platform for artificial intelligence‐driven expression analysis
FEBS Open Bio, EarlyView.MagmaFlow is a free, no‐code platform for gene expression analysis. It generates interactive volcano plots, links genes to literature, pathways, and diseases, prioritizes candidates using millions of publications, identifies affected biological processes, builds network diagrams, and exports publication‐ready figures and reports for macOS and Windows ...
Carlos E. Buss +7 more
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Forcing in nonstandard analysis
Annals of Pure and Applied Logic, 1994 The results and methods in this paper could lead to a significant improvement within the discipline of nonstandard analysis. A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. Much of this paper is taken up with such a construction and showing how this construction's properties compare with those of the
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