Results 1 to 10 of about 22,057,611 (283)
Theory of hypernumbers and extrafunctions: Functional spaces and differentiation
Discrete Dynamics in Nature and Society, 2002 The theory of hypernumbers and extrafunctions is a novel approach in functional analysis aimed at problems of mathematical and computational physics.
Mark Burgin
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Journal of Family Research, 2020 Many children live in households where either one or both parents work nonstandard schedules in the evening, night or weekend. Using a mixed methods design, this study examined whether nonstandard work schedules were linked to lower social and emotional ...
Jianghong Li +3 more
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Time averaging for ordinary differential equations and retarded functional differential equations
Electronic Journal of Differential Equations, 2010 We prove averaging theorems for non-autonomous ordinary differential equations and retarded functional differential equations in the case where the vector fields are continuous in the spatial variable uniformly with respect to the time and the ...
Mustapha Lakrib, Tewfik Sari
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Calculus using proximities: a mathematical approach in which students can actually prove theorems
Open Mathematics, 2017 Teaching and learning calculus are notoriously difficult and the didactic solutions may involve resorting to intuitive but vague definitions or informal gestures offered as proofs.
O’Donovan Richard
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Advances in Difference Equations, 2020 The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus.
Wasfi Shatanawi +5 more
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The Caccioppoli ultrafunctions
Advances in Nonlinear Analysis, 2017 Ultrafunctions are a particular class of functions defined on a hyperreal field ℝ∗⊃ℝ{\mathbb{R}^{\ast}\supset\mathbb{R}}. They have been introduced and studied in some previous works [2, 6, 7].
Benci Vieri +2 more
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Generalized solutions of variational problems and applications
Advances in Nonlinear Analysis, 2018 Ultrafunctions are a particular class of generalized functions defined on a hyperreal field ℝ*⊃ℝ{\mathbb{R}^{*}\supset\mathbb{R}} that allow to solve variational problems with no classical solutions.
Benci Vieri +2 more
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On the Plausibility of Nonstandard Proofs in Analysis
Dialectica, 1984 In the paper the authors emphasize one aspect of nonstandard considerations. Namely, that the usage of new nonstandard predicates (e.g., to be infinitely small) makes some standard notions and some proofs of standard theorems clearer and easier. They give examples of the simplification of the formal description of some definitions (the number of ...
Farkas, E. J., Szabo, M. E.
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On the averaging method for differential equations with delay
Electronic Journal of Differential Equations, 2002 In this paper, we present averaging results for delay differential equations under weak conditions. The main result is formulated in both classical mathematics and nonstandard analysis.
Mustapha Lakrib
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SPθ-TOPOLOGICAL GROUPS IN NONSTANDARD ANALYSIS [PDF]
Assiut University Journal of Multidisciplinary Scientific Research, 2016 The aim of this paper is to introduce and study a new class of topological groups called SPθ-topological group. By using some nonstandard techniques given by A., Robison and axiomatized by E., Nelson.
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