• Mathematics

Differentiable Germs and Catastrophes


Author: Th Brocker,L. Lander
Publisher: Cambridge University Press
ISBN: 0521206812
Category: Mathematics
Page: 179
View: 5053
This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.

    • Mathematics

Handbook of Global Analysis


Author: Demeter Krupka,David Saunders
Publisher: Elsevier
ISBN: 9780080556734
Category: Mathematics
Page: 1244
View: 3244
This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics. This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics - Written by world-experts in the field - Up-to-date contents

    • Mathematics

Catastrophe Theory


Author: V. I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 364296799X
Category: Mathematics
Page: 79
View: 9932
Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con troversial results from the mathematical theories of singulari ties and bifurcation. The author has tried to explain the essence of the fundamen tal results and applications to readers having minimal mathe matical background but the reader is assumed to have an in quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories ............... 1 Chapter 2. Whitney's Singularity Theory ... 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine ...... 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .


    • Mathematics

Differentiable Germs and Catastrophes


Author: Th Brocker,L. Lander
Publisher: Cambridge University Press
ISBN: 0521206812
Category: Mathematics
Page: 179
View: 3845
This book gives a fairly elementary introduction to the local theory of differentiable mappings and is suitable as a text for courses to graduates and advanced undergraduates.

    • Mathematics

London Mathematical Society lecture note series


Author: London Mathematical Society,S. Buoncristiano,Colin Patrick Rourke
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 7389

    • Technology & Engineering

Dynamics of feedback systems


Author: A. I. Mees
Publisher: John Wiley & Sons
ISBN: 9780471278221
Category: Technology & Engineering
Page: 214
View: 1389

    • Mathematics

Catastrophe theory


Author: Domenico P. L. Castrigiano,Sandra A. Hayes
Publisher: Westview Pr
ISBN: 9780813341262
Category: Mathematics
Page: 264
View: 4619
This edition contains complete proofs of Thomas classification theorems as well as the genericity and stability results assuming only elementary calculus and linear algebra. Catastrophe Theory is an intriguing beautiful theory whose striking feature is its universality. The text is self-contained and progressing in its approach. It is also unique in its treatment of genericity and stability.

    • Architecture

Environment & Planning


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Architecture
Page: N.A
View: 4111

    • Social sciences

General Systems


Author: Society for the Advancement of General Systems Theory,International Society for the Systems Sciences
Publisher: N.A
ISBN: N.A
Category: Social sciences
Page: N.A
View: 8064



    • Mathematics

Supersymmetry for Mathematicians

An Introduction
Author: V. S. Varadarajan
Publisher: American Mathematical Soc.
ISBN: 0821835742
Category: Mathematics
Page: 300
View: 7398
Supersymmetry has been the object of study by theoretical physicists since the early 1970's. In recent years it has attracted the interest of mathematicians because of its novelty, and because of significance, both in mathematics and physics, of the main issues it raises. This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles and their wave equations, such as the equations of Dirac and Weyl. It then continues the development of the theory of supermanifolds stressing the analogy with the Grothendieck theory of schemes. All the super linear algebra needed for the book is developed here and the basic theorems are established: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity.

    • Mathematics

Interaction Models


Author: Norman Biggs
Publisher: Cambridge University Press
ISBN: 0521217709
Category: Mathematics
Page: 101
View: 2104
This book is based on a set of lectures given to a mixed audience of physicists and mathematicians. The desire to be intelligible to both groups is the underlying preoccupation of the author. Physicists nowadays are particularly interested in phase transitions. The typical situation is that a system of interacting particles exhibits an abrupt change of behaviour at a certain temperature, although the local forces between the particles are thought to be smooth functions of temperature. This account discusses the theory behind a simple model of such phenomena. An important tool is the mathematical discipline known as the Theory of Graphs. There are five chapters, each subdivided into sections. The first chapter is intended as a broad introduction to the subject, and it is written in a more informal manner than the rest. Notes and references for each chapter are given at the end of the chapter.

    • Mathematics

Continuous Crossed Products and Type III Von Neumann Algebras


Author: A. van Daele
Publisher: Cambridge University Press
ISBN: 0521219752
Category: Mathematics
Page: 68
View: 2077
These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.

    • Children's literature in series

Monographic Series


Author: Library of Congress
Publisher: N.A
ISBN: N.A
Category: Children's literature in series
Page: N.A
View: 2879

    • Science

Mathematical Analysis of Evolution, Information, and Complexity


Author: Wolfgang Arendt,Wolfgang P. Schleich
Publisher: John Wiley & Sons
ISBN: 3527628037
Category: Science
Page: 502
View: 1353
Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

    • Mathematics

Robust Chaos and Its Applications


Author: Elhadj Zeraoulia,Julien C. Sprott
Publisher: World Scientific
ISBN: 9814374075
Category: Mathematics
Page: 454
View: 7922
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.

    • Mathematics

Polynomial Convexity


Author: Edgar Lee Stout
Publisher: Springer Science & Business Media
ISBN: 0817645373
Category: Mathematics
Page: 439
View: 7120
This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables. Important features of Polynomial Convexity: *Presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. *Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries. *Examines in considerable detail questions of uniform approximation, especially on totally real sets, for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. *Discusses important applications, e.g., to the study of analytic varieties and to the theory of removable singularities for CR functions. *Requires of the reader a solid background in real and complex analysis together with some previous experience with the theory of functions of several complex variables as well as the elements of functional analysis. This beautiful exposition of a rich and complex theory, which contains much material not available in other texts, is destined to be the standard reference for many years, and will appeal to all those with an interest in multivariate complex analysis.

    • Mathematics

Catastrophe Theory and Its Applications


Author: Tim Poston,Ian Stewart
Publisher: Courier Corporation
ISBN: 0486143783
Category: Mathematics
Page: 512
View: 1571
First integrated treatment of main ideas behind René Thom's theory of catastrophes stresses detailed applications in the physical sciences. Mathematics of theory explained with a minimum of technicalities. Over 200 illustrations clarify text designed for researchers and postgraduate students in engineering, mathematics, physics and biology. 1978 edition. Bibliography.