Results 31 to 40 of about 29,433 (197)
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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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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A hypercontinuous hypersmooth Schwarzschild line element transformation
International Journal of Mathematics and Mathematical Sciences, 1997 In this paper, a new derivation for one of the black hole line elements is given since the basic derivation for this line element is flawed mathematically. This derivation postulates a transformation procedure that utilizes a transformation function that
Robert A. Herrmann
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Connectedness and compactness on standard sets
, 2010 We present a nonstandard characterization of connected compact sets. (C) 2010 WILEY-VCH Verlag GmbH & Co KGaA.
Almeida, R
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An embedding of Schwartz distributions in the algebra of asymptotic functions
International Journal of Mathematics and Mathematical Sciences, 1998 We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a differential algebra of generalized functions, called in the paper asymptotic function, similar to but different from J.
Michael Oberguggenberger +1 more
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An Introduction to Nonstandard Analysis
Irish Mathematical Society Bulletin, 1985 In the paper under review that author gives a brief introduction to axiomatic nonstandard analysis in the sense of Nelson's internal set theory. The author gives two examples of how to employ internal set theory in order to establish standard results.
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The unreasonable effectiveness of Nonstandard Analysis [PDF]
Journal of Logic and Computation, 2020 Abstract As suggested by the title, the aim of this paper is to uncover the vast computational content of classical Nonstandard Analysis. To this end, we formulate a template ${\mathfrak{C}\mathfrak{I}}$ which converts a theorem of ‘pure’ Nonstandard Analysis, i.e.
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The Relation between the Spaces L1(F ) and L1(T) with Some Applications [PDF]
Eurasian Journal of Science and Engineering, 2018 In this research we find the relation between the nonstandard space of Lebesgue integrable functions L1(F),where F={|-N⁄2|+1,|-N⁄2|+2,…,0,…,|N⁄2| is a *finite set for N > ℕ and the space of Lebesgue integrable functions L1(T), where T=[-π,π] , with some
Rashad Rashid Haji
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Dynamical and nonstandard computational analysis of heroin epidemic model
Results in Physics, 2022 Numerical modelling of real-world problems has a significant role in different disciplines like biology, physics, chemistry, economics, and many more. The numerical results are the authentication of the results of the dynamical analysis.
Ali Raza +6 more
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