Tag: Approximations

Free Download Introduction to Diophantine Approximations: New Expanded Edition By Serge Lang (auth.)
1995 | 130 Pages | ISBN: 1461287006 | PDF | 4 MB
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere.Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.

Free Download Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms (Lecture Notes in Mathematics) by Chuchu Chen, Jialin Hong, Lihai Ji
English | January 5, 2024 | ISBN: 981996685X | 304 pages | MOBI | 66 Mb
The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.

Free Download Green’s Kernels and Meso-Scale Approximations in Perforated Domains By Vladimir Maz’ya, Alexander Movchan, Michael Nieves
2013 | 272 Pages | ISBN: 3319003569 | PDF | 4 MB
There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions.The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables.This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.

Free Download Introduction to Diophantine Approximations: New Expanded Edition by Serge Lang
English | PDF | 1995 | 137 Pages | ISBN : 0387944567 | 7.8 MB
The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere.

Free Download Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms by Chuchu Chen , Jialin Hong , Lihai Ji
English | PDF EPUB (True) | 2024 | 293 Pages | ISBN : 981996685X | 40.8 MB
The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.