Ramified Integrals Singularities And Lacunas
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Ramified Integrals Singularities And Lacunas
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Author : V.A. Vassiliev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ramified Integrals Singularities And Lacunas written by V.A. Vassiliev 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.
Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which d and n the potentials of degree d hyperbolic surfaces in [actual symbol not reproducible] are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii-Atiyah-Bott-Garding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard-Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given.
Trends In Singularities
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Author : Anatoly Libgober
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Trends In Singularities written by Anatoly Libgober and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.
Introduction To Complex Theory Of Differential Equations
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Author : Anton Savin
language : en
Publisher: Birkhäuser
Release Date : 2017-03-28
Introduction To Complex Theory Of Differential Equations written by Anton Savin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-28 with Mathematics categories.
This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.
Nonlinear Integral Equations In Abstract Spaces
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Author : Dajun Guo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22
Nonlinear Integral Equations In Abstract Spaces written by Dajun Guo 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 2013-11-22 with Mathematics categories.
Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.
Singularities
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Author : Vladimir I. Arnold
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Singularities written by Vladimir I. Arnold and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.
Integral Transformations Operational Calculus And Generalized Functions
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Author : R.G. Buschman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Integral Transformations Operational Calculus And Generalized Functions written by R.G. Buschman 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 2013-11-27 with Mathematics categories.
It is not the object of the author to present comprehensive cov erage of any particular integral transformation or of any particular development of generalized functions, for there are books available in which this is done. Rather, this consists more of an introductory survey in which various ideas are explored. The Laplace transforma tion is taken as the model type of an integral transformation and a number of its properties are developed; later, the Fourier transfor mation is introduced. The operational calculus of Mikusinski is pre sented as a method of introducing generalized functions associated with the Laplace transformation. The construction is analogous to the construction of the rational numbers from the integers. Further on, generalized functions associated with the problem of extension of the Fourier transformation are introduced. This construction is anal ogous to the construction of the reals from the rationals by means of Cauchy sequences. A chapter with sections on a variety of trans formations is adjoined. Necessary levels of sophistication start low in the first chapter, but they grow considerably in some sections of later chapters. Background needs are stated at the beginnings of each chapter. Many theorems are given without proofs, which seems appro priate for the goals in mind. A selection of references is included. Without showing many of the details of rigor it is hoped that a strong indication is given that a firm mathematical foundation does actu ally exist for such entities as the "Dirac delta-function".
Existence Theory For Nonlinear Integral And Integrodifferential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Existence Theory For Nonlinear Integral And Integrodifferential Equations written by Donal O'Regan 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 theory of integral and integrodifferential equations has ad vanced rapidly over the last twenty years. Of course the question of existence is an age-old problem of major importance. This mono graph is a collection of some of the most advanced results to date in this field. The book is organized as follows. It is divided into twelve chap ters. Each chapter surveys a major area of research. Specifically, some of the areas considered are Fredholm and Volterra integral and integrodifferential equations, resonant and nonresonant problems, in tegral inclusions, stochastic equations and periodic problems. We note that the selected topics reflect the particular interests of the authors. Donal 0 'Regan Maria Meehan CHAPTER 1 INTRODUCTION AND PRELIMINARIES 1.1. Introduction The aim of this book is firstly to provide a comprehensive existence the ory for integral and integrodifferential equations, and secondly to present some specialised topics in integral equations which we hope will inspire fur ther research in the area. To this end, the first part of the book deals with existence principles and results for nonlinear, Fredholm and Volterra inte gral and integrodifferential equations on compact and half-open intervals, while selected topics (which reflect the particular interests of the authors) such as nonresonance and resonance problems, equations in Banach spaces, inclusions, and stochastic equations are presented in the latter part.
Singularities In Geometry And Topology
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Author : Jean-Paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007
Singularities In Geometry And Topology written by Jean-Paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology. The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
Advanced Integration Theory
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Author : Corneliu Constantinescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advanced Integration Theory written by Corneliu Constantinescu 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.
Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A.
Integration On Infinite Dimensional Surfaces And Its Applications
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Author : A. V. Uglanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-31
Integration On Infinite Dimensional Surfaces And Its Applications written by A. V. Uglanov 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 2000-01-31 with Mathematics categories.
This book presents the theory of integration over surfaces in abstract topological vector space. Applications of the theory in different fields, such as infinite dimensional distributions and differential equations (including boundary value problems), stochastic processes, approximation of functions, and calculus of variation on a Banach space, are treated in detail. Audience: This book will be of interest to specialists in functional analysis, and those whose work involves measure and integration, probability theory and stochastic processes, partial differential equations and mathematical physics.