Titlebook: Advances in Analysis, Probability and Mathematical Physics; Contributions of Non Sergio A. Albeverio,Wilhelm A. J. Luxemburg,Manfre Book 19

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Two Applications of NSA in the Theory of Stochastic Dynamical Systemsthat there are analytic features which can be used to study SL and to assess whether it is at odds with market-oriented organizations from an OE perspective. I conclude that there are indications that in a Dutch context, SL meets the requirements of market-oriented organizations and can economically

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https://doi.org/10.1007/978-3-031-29973-5The methods of nonstandard analysis axe applied to the study of Navier-Stokes equations. We give a construction of weak solutions, solve general stochastic Navier-Stokes equations, and show how to obtain statistical solutions in the general stochastic case.

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https://doi.org/10.1007/BFb0092029In the paper [1] a nonstandard approach to the theory of Fourier series was based on the approximation of the group . = {. ∈ ? : |z| = 1}by the hyperfinite group . = {. ∈ ? : .. = 1} where . is an infinite large natural number. Here we prove the existence of such a hyperfinite approximation for an arbitrary LCA group with a compact open subgroup.

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Lp Theory of Pseudo-Differential Operators,We show that a classical counterexample to the spectral mapping theorem for the exponential function is not very surprising if we consider the example in a suitable nonstandard setting.

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https://doi.org/10.1007/978-3-030-48788-1C. Impens has investigated nonstandard polynomials in one variable. In this note we show that many of his results carry over to polynomials in several variables. The concept of complex and real microcontinuity of nonstandard polynomials is intimately related to polynomial approximation in function theory.

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Markov Processes and Feller SemigroupsInternal ordinary differential equations are used to construct diffusions on manifolds and nonstandard heat kernels are obtained for heat equations.

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Type-1-Diabetes

,Boundary Value Green’s Functions,In this article we investigate the ergodicity of set transformations within the Alternative Set Theory. The main result is that each ergodic transformation is homomorhic to the cycle of a suitable length.