This book reflects the progress made in the forty years since the appearance of Abraham Robinson’s revolutionary book Nonstandard Analysis in the foundations of mathematics and logic, number theory, statistics and probability, in ordinary, partial and stochastic differential equations and in education. The contributions are clear and essentially self-contained.
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Foundations.- The strength of nonstandard analysis.- The virtue of simplicity.- Analysis of various practices of referring in classical or non standard mathematics.- Stratified analysis?.- ERNA at work.- The Sousa Pinto approach to nonstandard generalised functions.- Neutrices in more dimensions.- Number theory.- Nonstandard methods for additive and combinatorial number theory. A survey.- Nonstandard methods and the Erd?s-Turán conjecture.- Statistics, probability and measures.- Nonstandard likelihood ratio test in exponential families.- A finitary approach for the representation of the infinitesimal generator of a markovian semigroup.- On two recent applications of nonstandard analysis to the theory of financial markets.- Quantum Bernoulli experiments and quantum stochastic processes.- Applications of rich measure spaces formed from nonstandard models.- More on S-measures.- A Radon-Nikodým theorem for a vector-valued reference measure.- Differentiability of Loeb measures.- Differential systems and equations.- The power of Gâteaux differentiability.- Nonstandard Palais-Smale conditions.- Averaging for ordinary differential equations and functional differential equations.- Path-space measure for stochastic differential equation with a coefficient of polynomial growth.- Optimal control for Navier-Stokes equations.- Local-in-time existence of strong solutions of the n-dimensional Burgers equation via discretizations.- Infinitesimals and education.- Calculus with infinitesimals.- Pre-University Analysis.
Ngôn ngữ Anh ● định dạng PDF ● Trang 401 ● ISBN 9783211499054 ● Kích thước tập tin 18.8 MB ● Biên tập viên Imme van den Berg & Vitor Neves ● Nhà xuất bản Springer Wien ● Thành phố Vienna ● Quốc gia AT ● Được phát hành 2007 ● Có thể tải xuống 24 tháng ● Tiền tệ EUR ● TÔI 2155088 ● Sao chép bảo vệ DRM xã hội
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