Nonstandard Analysis
A note on Brouwer’s weak continuity principle and the transfer principle in nonstandard analysis
... A well-known approach to nonstandard analysis is obtained by extending the structure of real numbers using an ultrapower construction (see [4]). There is also a constructive approach, originating with ...
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Proof of Ito’s Formula for Ito’s Process in Nonstandard Analysis
... In our previous paper [1], we proposed a non-standardization of the concept of convolution in order to construct an extended Wiener measure using non- standard analysis by E. Nelson [2]. In this paper, we consider ...
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Extended Wiener Measure by Nonstandard Analysis for Financial Time Series
... DOI: 10.4236/am.2018.98066 980 Applied Mathematics A rigorous treatment, which would agree with nonstandard analysis (see, e.g., [4] [5] [6]), may be deduced from some infinitesimal time-sampling of ...
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Axiomatics for the external numbers of nonstandard analysis
... build nonstandard real numbers in which, unlike Nelson’s approaches [23], [24] the infinitesimals are not postulated through a new undefined symbol, but by the existence of ...
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Boundary Value Problems for Burgers Equations, through Nonstandard Analysis
... In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane x ∈ R T , > 0 . First we consider the Burgers equations with initial conditions admitting two and three shocks and ...
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Nonstandard analysis based calculus
... than every negative Real number. Infinitesimal if is either positive infinitesimal, negative infinitesimal, or 0.. Then we do the same for the infinite numbers. Definition: A Hyperrea[r] ...
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Complex spaces and nonstandard schemes
... of nonstandard mathematics - its most powerful tool - does not work directly ...on nonstandard analysis, we always use in this paper the expres- sion “bounded” point instead of a “limited” one and ...
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Ends of groups: a nonstandard perspective
... Nonstandard analysis made its first serious impact on geometric group theory via the work of van den Dries and Wilkie [7] on Gromov’s theorem on polynomial ...used nonstandard methods to settle the ...
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Near equivalence on metric spaces and a nonstandard central limit theorem
... elementary analysis no new objects, such as hyperreals, are ...bit” analysis [11, Preface]) without any heavy apparatus from nonstandard analysis, whether from IST [10] or from Robinson’s ...
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Nonstandard hulls of locally exponential Lie algebras
... elementary nonstandard analysis; other- wise, consult Davis [3] or Henson [6] for a friendly ...all nonstandard arguments take place in a sufficiently saturated nonstandard ...
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Nonstandard Models in Measure Theory and in functional Analysis
... of nonstandard analysis and by polynomi- als of a hyperfinite degree ...Another nonstandard approach to the theory of generalized functions has been proposed by Oberbuggenberg and Todorov in [67] and ...
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Nonstandard explicit third-order Runge-Kutta method with positivity property
... In the second section, general positivity results are presented for standard RK3 method. In the third section, the main positivity results are obtained for nonstandard RK3 method. The numerical results obtained ...
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A dynamically consistent nonstandard finite difference scheme for a predator–prey model
... He and Lai [6] investigated stability, period-doubling bifurcation, Neimark–Sacker bi- furcation and chaos control for a discrete counterpart of (1) with application of Euler forward approximation. Consequently, their ...
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Study of weak solutions for parabolic variational inequalities with nonstandard growth conditions
... The aim of this paper is to study the existence and uniqueness of solutions for a degenerate parabolic variational inequality problem.. The outline of this paper is as follows.[r] ...
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ISSN Review. Nonstandard Approach to Gravity for the Dark Sector of the Universe
... In this paper we review some ongoing research on a model which is a first building block for a new theory describing the dark sector of the Universe. This model, introduced in [15] and further developed in [16,17], ...
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Deliberately casual? Workers' agency, health, and nonstandard employment relations in Australia
... Our analysis uncovered the underlying structural factors that constrained or enabled the agency represented by participants’ ...of nonstandard employment on worker health,(2, 8, 47) with those workers ...
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Description of locally finite families from a nonstandard point of view
... To apply these results about locally finite families, we now turn to paracompact spaces. First, we recall the traditional definition in standard terms, which can be found as first definition in Chapter 6.4 of Munkres ...
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Existence and Uniqueness Results for a Nonstandard Variational-Hemivariational Inequalities with Application
... Monotone and generalized monotone play cru- cial role in several branches of mathematics such as variational analysis, engineering, optimization, and differentiability theory of convex functions, etc (see [2, 15, ...
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Nonstandard finite difference variational integrators for nonlinear Schrödinger equation with variable coefficients
... The nonstandard finite difference schemes developed by Mickens et ...solutions, nonstandard finite difference schemes also have a better perfor- mance than standard finite difference ...a nonstandard finite ...
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A new total variation diminishing implicit nonstandard finite difference scheme for conservation laws
... For problems with smooth solutions, usually a linear stability analysis is adequate. For problems with discontinuous solutions, however, such as solutions to (1.1), a stronger measure of stability is usually ...
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