Direct And Projective Limits Of Geometric Banach Structures
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Direct And Projective Limits Of Geometric Banach Structures
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Author : Patrick Cabau
language : en
Publisher: CRC Press
Release Date : 2023-10-06
Direct And Projective Limits Of Geometric Banach Structures written by Patrick Cabau and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Mathematics categories.
This book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced. Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics. This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.
Fractional Integrals Potentials And Radon Transforms
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Author : Boris Rubin
language : en
Publisher: CRC Press
Release Date : 2024-08-14
Fractional Integrals Potentials And Radon Transforms written by Boris Rubin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-14 with Mathematics categories.
Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud’s approach and its generalization, leading to wavelet type representations. New to this Edition Two new chapters and a new appendix, related to Radon transforms and harmonic analysis of linear operators commuting with rotations and dilations have been added. Contains new exercises and bibliographical notes along with a thoroughly expanded list of references. This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis.
Variational Hemivariational Inequalities With Applications
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Author : Mircea Sofonea
language : en
Publisher: CRC Press
Release Date : 2024-12-23
Variational Hemivariational Inequalities With Applications written by Mircea Sofonea and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-23 with Mathematics categories.
Variational-Hemivariational Inequalities with Applications, Second Edition represents the outcome of the cross-fertilization of nonlinear functional analysis and mathematical modelling, demonstrating its application to solid and contact mechanics. Based on authors’ original results, the book illustrates the use of various functional methods (including monotonicity, pseudomonotonicity, compactness, penalty and fixed-point methods) in the study of various nonlinear problems in analysis and mechanics. The classes of history-dependent operators and almost history-dependent operators are exposed in a large generality. A systematic and unified presentation contains a carefully selected collection of new results on variational-hemivariational inequalities with or without unilateral constraints. A wide spectrum of static, quasistatic, dynamic contact problems for elastic, viscoelastic and viscoplastic materials illustrates the applicability of these theoretical results. Written for mathematicians, applied mathematicians, engineers and scientists, this book is also a valuable tool for graduate students and researchers in nonlinear analysis, mathematical modelling, mechanics of solids, and contact mechanics. New to the second edition Convergence and well-posedness results for elliptic and history-dependent variational-hemivariational inequalities Existence results on various optimal control problems with applications in solid and contact mechanics Existence, uniqueness and stability results for evolutionary and differential variational-hemivariational inequalities with unilateral constraints Modelling and analysis of static and quasistatic contact problems for elastic and viscoelastic materials with looking effect Modelling and analysis of viscoelastic and viscoplastic dynamic contact problems with unilateral constraints.
Separate And Joint Continuity
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Author : Jiling Cao
language : en
Publisher: CRC Press
Release Date : 2024-07-09
Separate And Joint Continuity written by Jiling Cao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-09 with Mathematics categories.
Separate and Joint Continuity presents and summarises the main ideas and theorems that have been developed on this topic, which lies at the interface between General Topology and Functional Analysis (and the geometry of Banach spaces in particular). The book offers detailed, self-contained proofs of many of the key results. Although the development of this area has now slowed to a point where an authoritative book can be written, many important and significant problems remain open, and it is hoped that this book may serve as a springboard for future and emerging researchers into this area. Furthermore, it is the strong belief of the authors that this area of research is ripe for exploitation. That is to say, it is their belief that many of the results contained in this monograph can, and should be, applied to other areas of mathematics. It is hoped that this monograph may provide an easily accessible entry point to the main results on separate and joint continuity for mathematicians who are not directly working in this field, but who may be able to exploit some of the deep results that have been developed over the past 125 years. Features Provides detailed, self-contained proofs of many of the key results in the area Suitable for researchers and postgraduates in topology and functional analysis Is the first book to offer a detailed and up-to-date summary of the main ideas and theorems on this topic
Classical Clifford Algebras
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Author : Ilwoo Cho
language : en
Publisher: CRC Press
Release Date : 2024-04-08
Classical Clifford Algebras written by Ilwoo Cho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-08 with Mathematics categories.
Classical Clifford Algebras: Operator-Algebraic and Free-Probabilistic Approaches offers novel insights through operator-algebraic and free-probabilistic models. By employing these innovative methods, the author sheds new light on the intrinsic connections between Clifford algebras and various mathematical domains. This monograph should be an essential addition to the library of any researchers interested in Clifford Algebras or Algebraic Geometry more widely. Features Includes multiple examples and applications Suitable for postgraduates and researchers working in Algebraic Geometry Takes an innovative approach to a well-established topic
Perturbed Functional Iterations
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Author : Suhrit Dey
language : en
Publisher: CRC Press
Release Date : 2024-06-28
Perturbed Functional Iterations written by Suhrit Dey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-28 with Mathematics categories.
Perturbed functional iterations (PFI) is a large‐scale nonlinear system solver. Nature is abundant with events simulated mathematically by nonlinear systems of equations and inequalities. These we call nonlinear models. Often, they are ill‐conditioned, meaning small changes in data causing huge changes in the output. PFI, previously called the perturbed iterative scheme (PIS), is a numerical method to solve nonlinear systems of equations in multidimensional space. Computational results demonstrate that this numerical method has some unique features, which have made it more practical for applications in engineering and applied mathematics. This book will guide readers in the proper use of PFI, both in theoretical and practical settings. Features: Ideal resource for postgraduates and professional researchers in science and engineering working in nonlinear systems Algorithmically simple enough for engineers and applied scientists to write their own software based on the contents
Spectral Theory For Linear Operators
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Author : Bilel Krichen
language : en
Publisher: CRC Press
Release Date : 2025-08-01
Spectral Theory For Linear Operators written by Bilel Krichen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-01 with Mathematics categories.
This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators acting on Banach spaces. This class played an important rule in the theory of perturbation. More precisely, it contributed in the construction of several classes of stability of essential spectra for bounded or unbounded linear operators. We should emphasize that this book is the first one dealing with the demicompactness concept and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. Researchers, as well as graduate students in applicable analysis, will find that this book constitutes a useful survey of the fundamental principles of the subject. Nevertheless, the reader is assumed to be, at least, familiar with some related sections concerning notions like the compact, Fredholm operators, the basic tools of the weak topology, the concept of measures of weak noncompactness, etc. Otherwise, the reader is urged to consult the recommended literature in order to benefit fully from this book. Features - • First book dealing with demicompactness theory and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. • Self-contained coverage of classical and more recent classes of perturbations involving the concept of demicompactness. • Offers a useful survey of the fundamental principles of spectral theory. • Provides applications for problem arising in physics and which are modeled by integral or partial differential equations.
Completely Regular Codes In Distance Regular Graphs
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Author : Minjia Shi
language : en
Publisher: CRC Press
Release Date : 2025-03-14
Completely Regular Codes In Distance Regular Graphs written by Minjia Shi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-14 with Mathematics categories.
The concept of completely regular codes was introduced by Delsarte in his celebrated 1973 thesis, which created the field of Algebraic Combinatorics. This notion was extended by several authors from classical codes over finite fields to codes in distance-regular graphs. Half a century later, there was no book dedicated uniquely to this notion. Most of Delsarte examples were in the Hamming and Johnson graphs. In recent years, many examples were constructed in other distance regular graphs including q-analogues of the previous, and the Doob graph. Completely Regular Codes in Distance Regular Graphs provides, for the first time, a definitive source for the main theoretical notions underpinning this fascinating area of study. It also supplies several useful surveys of constructions using coding theory, design theory and finite geometry in the various families of distance regular graphs of large diameters. Features Written by pioneering experts in the domain Suitable as a research reference at the master’s level Includes extensive tables of completely regular codes in the Hamming graph Features a collection of up-to-date surveys.
Classification Of Lipschitz Mappings
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Author : Torrey M. Gallagher
language : en
Publisher: CRC Press
Release Date : 2025-03-06
Classification Of Lipschitz Mappings written by Torrey M. Gallagher and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-06 with Mathematics categories.
Classification of Lipschitz Mappings, Second Edition presents a systematic, self-contained treatment of a new classification of Lipschitz mappings and its applications, particularly to metric fixed point theory. Suitable for readers interested in nonlinear analysis, metric fixed point theory, differential equations, ergodic theory, and dynamical systems, the book requires only a basic background in functional analysis and topology, and should therefore be accessible to graduate students or advanced undergraduates, as well as to professionals looking for new topics in metric fixed point theory. In particular, the second edition contains results related to: Regulating the growth of the sequence of Lipschitz constants k(Tn) Ensuring good estimates for k0(T) and k∞(T) Studying moving harmonic and geometric averages as well as generalized Fibonacci-type sequences and their application to provide a new algorithm for solving polynomials in the real case and in Banach algebras Classifying mean isometries and mean contractions Generalizing Browder’s famous Demiclosedness Principle Providing some new results in metric fixed point theory Minimal displacement and optimal retraction problems
Non Newtonian Sequence Spaces With Applications
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Author : Feyzi Başar
language : en
Publisher: CRC Press
Release Date : 2025-06-25
Non Newtonian Sequence Spaces With Applications written by Feyzi Başar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-25 with Mathematics categories.
Non-Newtonian Sequence Spaces with Applications presents an alternative to the usual calculus based on multiplication instead of addition. The book is intended for graduate students and researchers with a special interest in non-Newtonian calculus, its applications and related topics. Features · Valuable material for postgraduate researchers studying non-Newtonian calculus · Suitable as supplementary reading to a Computational Physics course