Convergence Problems
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Convergence Problems Of Orthogonal Series
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Author : G. Alexits
language : en
Publisher: Elsevier
Release Date : 2014-07-23
Convergence Problems Of Orthogonal Series written by G. Alexits and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.
Convergence Problems Of Orthogonal Series
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Author : György Alexits
language : en
Publisher: Pergamon
Release Date : 1961
Convergence Problems Of Orthogonal Series written by György Alexits and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Convergence categories.
Some Convergence Problems Involving The Smarandache Function
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Author : E. Burton
language : en
Publisher: Infinite Study
Release Date :
Some Convergence Problems Involving The Smarandache Function written by E. Burton and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
In this paper we consider same series attached to the Smarandache Function series.
Convergence Problems
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Author : Wole Talabi
language : en
Publisher: Astra Publishing House
Release Date : 2024-02-13
Convergence Problems written by Wole Talabi and has been published by Astra Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-13 with Fiction categories.
"A jaw-dropping collection....Beautiful, vibrant, and electrifying, this has the makings of a modern classic." —Publishers Weekly (starred review), and a Publishers Weekly Top Ten Spring 2024 Roundup pick "Deftly entwining his Nigerian culture with sf and Afrofuturism, Talabi uses each story to analyze Africa’s rapidly evolving relationship with technology. For fans of Margaret Atwood’s dystopian works and P. Djèlí Clark’s speculative fiction, Convergence Problems provides an Afrocentric sf narrative that is sure to captivate." — Raychel Bennet, Booklist (starred review) "Written with an emotional economy few storytellers can master....A fascinating and riveting exploration of what the future may hold—for better or worse." —Kirkus From the Hugo, Nebula, Locus and Nommo award nominated author of Shigidi and The Brass Head Of Obalufon comes a stunning new collection of stories that investigate the rapidly changing role of technology and belief in our lives as we search for meaning, for knowledge, for justice; constantly converging on our future selves. In “An Arc of Electric Skin,” a roadside mechanic seeking justice volunteers to undergo a procedure that will increase the electrical conductivity of his skin by orders of magnitude. In “Blowout,” a woman races against time and a previously undocumented geological phenomenon to save her brother on the surface of Mars. In “Ganger,” a young woman trapped in a city run by machines must transfer her consciousness into an artificial body and find a way to give her life purpose. In “Debut,” Nairobi-based technical support engineer tries to understand what is happening when an AI art system begins malfunctioning in ways that could change the world. The sixteen stories of Convergence Problems, which include work published for the first time in this collection, rare stories, and recently acclaimed work, showcase Talabi at his creative best: playful and profound, exciting and experimental, always interesting.
Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems
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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Weak Convergence Methods And Singularly Perturbed Stochastic Control And Filtering Problems written by Harold Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).
The Master Equation And The Convergence Problem In Mean Field Games
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Author : Pierre Cardaliaguet
language : en
Publisher: Princeton University Press
Release Date : 2019-08-13
The Master Equation And The Convergence Problem In Mean Field Games written by Pierre Cardaliaguet and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-13 with Mathematics categories.
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
Approximate Global Convergence And Adaptivity For Coefficient Inverse Problems
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Author : Larisa Beilina
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-09
Approximate Global Convergence And Adaptivity For Coefficient Inverse Problems written by Larisa Beilina and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-09 with Mathematics categories.
Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.
Convergence Analysis Of Proximal Like Methods For Variational Inequalities And Fixed Point Problems
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Author : Nils Langenberg
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2011
Convergence Analysis Of Proximal Like Methods For Variational Inequalities And Fixed Point Problems written by Nils Langenberg and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Business & Economics categories.
Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions may be considered as rather restrictive e.g. in the framework of Nash equilibrium problems. This motivates the development of convergence results under weaker hypotheses which constitute the major subject of the present book. Studied methods include the Bregman-function-based Proximal Point Algorithm (BPPA), Cohen's Auxiliary Problem Principle and an extragradient algorithm.Moreover, this work also contains the first numerical comparison of stopping criteria in the framework of the BPPA. Although such conditions are the subject of theoretical investigations frequently, their numerical effectiveness and a deducible preference were still unknown. This gives rise to the necessity of the presented numerical experiments.
Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction Diffusion Problems
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Author : Omar Anza Hafsa
language : en
Publisher: World Scientific
Release Date : 2022-06-21
Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction Diffusion Problems written by Omar Anza Hafsa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-21 with Mathematics categories.
A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
On Estimating Rates Of Convergence In Multigroup Diffusion Problems
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Author : Richard S. Varga
language : en
Publisher:
Release Date : 1957
On Estimating Rates Of Convergence In Multigroup Diffusion Problems written by Richard S. Varga and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Diffusion categories.