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Author : Michael Grosser,Michael Kunzinger,Michael Oberguggenberger
Publisher : Unknown
Page : 524 pages
File Size : 53,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401598460
Author : M. Grosser,M. Kunzinger,Michael Oberguggenberger,R. Steinbauer
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 51,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401598453
Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. F. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving singularities, the theory has undergone a change both in in ternal structure and scope of applicability, due to a growing number of applications to questions of a more geometric nature. The present book is intended to provide an in-depth presentation of these develop ments comprising its structural aspects within the theory of generalized functions as well as a (selective but, as we hope, representative) set of applications. This main purpose of the book is accompanied by a number of sub ordinate goals which we were aiming at when arranging the material included here. First, despite the fact that by now several excellent mono graphs on Colombeau algebras are available, we have decided to give a self-contained introduction to the field in Chapter 1. Our motivation for this decision derives from two main features of our approach. On the one hand, in contrast to other treatments of the subject we base our intro duction to the field on the so-called special variant of the algebras, which makes many of the fundamental ideas of the field particularly transpar ent and at the same time facilitates and motivates the introduction of the more involved concepts treated later in the chapter.
Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 490 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681746
Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises
Author : Giampiero Esposito
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 53,7 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471186
This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research papers, for pedagogical r- sons. Familiarity with fibre-bundle theory is certainly helpful, but in many cases I only rely on two-spinor calculus and conformally invariant concepts in gravitational physics. The key concepts the book is devoted to are complex manifolds, spinor techniques, conformal gravity, ?-planes, ?-surfaces, Penrose transform, complex 3 1 – – space-time models with non-vanishing torsion, spin- fields and spin- potentials. 2 2 Problems have been inserted at the end, to help the reader to check his und- standing of these topics. Thus, I can find at least four reasons for writing yet another book on spinor and twistor methods in general relativity: (i) to write a textbook useful to - ginning graduate students and research workers, where two-component spinor c- culus is the unifying mathematical language.
Author : Vladimir Dobrev
Publisher : Springer
Page : 614 pages
File Size : 53,7 Mb
Release : 2016-12-10
Category : Science
ISBN : 9789811026362
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Author : Taylor & Francis Group
Publisher : CRC Press
Page : 128 pages
File Size : 43,6 Mb
Release : 2020-12-18
Category : Electronic
ISBN : 1138417742
Covers the research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this work provides a compilation of approaches to the problem of singularities in nonlinear models.
Author : El Hassan Zerrik,Said Melliani,Oscar Castillo
Publisher : Springer Nature
Page : 275 pages
File Size : 42,6 Mb
Release : 2019-08-26
Category : Technology & Engineering
ISBN : 9783030261498
This book describes recent developments in a wide range of areas, including the modeling, analysis and control of dynamical systems, and explores related applications. The book provided a forum where researchers have shared their ideas, results on theory, and experiments in application problems. The current literature devoted to dynamical systems is quite large, and the authors’ choice for the considered topics was motivated by the following considerations. Firstly, the mathematical jargon for systems theory remains quite complex and the authors feel strongly that they have to maintain connections between the people of this research field. Secondly, dynamical systems cover a wider range of applications, including engineering, life sciences and environment. The authors consider that the book is an important contribution to the state of the art in the fuzzy and dynamical systems areas.
Author : Claus Beisbart,Tilman Sauer,Christian Wüthrich
Publisher : Springer Nature
Page : 277 pages
File Size : 50,5 Mb
Release : 2020-09-25
Category : Mathematics
ISBN : 9783030477820
This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity (e.g., to cosmology) and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativity Mach's Principle The structure of Einstein's theory Cosmology and the Einstein world Stability of cosmological models The metaphysical nature of spacetime The relationship between spacetime and dynamics The Geodesic Principle Symmetries Thinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the (early and later) uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory.
Author : Michael Reissig,Michael Ruzhansky
Publisher : Springer Science & Business Media
Page : 448 pages
File Size : 42,6 Mb
Release : 2013-03-30
Category : Mathematics
ISBN : 9783319001258
Progress in Partial Differential Equations is devoted to modern topics in the theory of partial differential equations. It consists of both original articles and survey papers covering a wide scope of research topics in partial differential equations and their applications. The contributors were participants of the 8th ISAAC congress in Moscow in 2011 or are members of the PDE interest group of the ISAAC society. This volume is addressed to graduate students at various levels as well as researchers in partial differential equations and related fields. The readers will find this an excellent resource of both introductory and advanced material. The key topics are: • Linear hyperbolic equations and systems (scattering, symmetrisers) • Non-linear wave models (global existence, decay estimates, blow-up) • Evolution equations (control theory, well-posedness, smoothing) • Elliptic equations (uniqueness, non-uniqueness, positive solutions) • Special models from applications (Kirchhoff equation, Zakharov-Kuznetsov equation, thermoelasticity)
Author : Vladimir Dobrev
Publisher : Springer
Page : 427 pages
File Size : 52,5 Mb
Release : 2018-11-28
Category : Mathematics
ISBN : 9789811327155
This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.
Author : Vladimir Georgiev,Alessandro Michelangeli,Raffaele Scandone
Publisher : Springer Nature
Page : 246 pages
File Size : 55,6 Mb
Release : 2022-12-02
Category : Mathematics
ISBN : 9789811964343
This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.
Author : Shahla Molahajloo,Stevan Pilipović,Joachim Toft,M. W. Wong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 50,8 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9783034805858
This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.
Author : Said Melliani,Oscar Castillo
Publisher : Springer Nature
Page : 496 pages
File Size : 42,9 Mb
Release : 2022-08-10
Category : Technology & Engineering
ISBN : 9783031124167
We describe in this book recent advances in fuzzy sets theory, fractional calculus, dynamic systems, and optimization. The book provides a setting for the discussion of recent developments in a wide variety of topics including partial differential equations, dynamic systems, optimization, numerical analysis, fuzzy sets theory, fractional calculus, and its applications. The book is aimed at bringing together contributions from leading academic scientists, researchers, and research scholars to exchange and share their experiences and research results on all aspects of applied mathematics, modeling, algebra, economics, finance, and applications. It also provides an interdisciplinary platform for researchers, practitioners, and educators to present the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of applied mathematics. The published chapters address various aspects of academic scientists, researchers, and research scholars in many variety mathematical topics.
Author : Karl‐Olof Lindahl,Torsten Lindström,Luigi G. Rodino,Joachim Toft,Patrik Wahlberg
Publisher : Springer
Page : 568 pages
File Size : 55,5 Mb
Release : 2019-04-29
Category : Mathematics
ISBN : 9783030044596
This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on the current research in mathematical analysis and its various interdisciplinary applications.
Author : Reuven Segev,Marcelo Epstein
Publisher : Springer Nature
Page : 416 pages
File Size : 40,9 Mb
Release : 2020-05-13
Category : Mathematics
ISBN : 9783030426835
This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.