Download or read book Fields Medallists Lectures written by Michael Atiyah and published by World Scientific. This book was released on 1997-10-13 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.
Download or read book Early Days in Complex Dynamics written by Daniel S. Alexander and published by American Mathematical Soc.. This book was released on 2012 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.
Download or read book A History of Complex Dynamics written by Daniel S. Alexander and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon work by G. Julia (1918) and P. Fatou (1919/20). The goal of this book is to analyze this work from an historical perspective and show in detail, how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schröder (1870/71) which he made, when he studied Newton's method. In the 1880's, Gabriel Koenigs fashioned this study into a rigorous body of work and, thereby, influenced a lot the subsequent development. But only, when Fatou and Julia applied set theory as well as Paul Montel's theory of normal families, it was possible to develop a global approach to the iteration of rational maps. This book shows, how this intriguing piece of modern mathematics became reality.
Download or read book Analysis and Optimization of Systems written by Alain Bensoussan and published by . This book was released on 1986 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singularities in Boundary Value Problems written by Pierre Grisvard and published by Springer. This book was released on 1992 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Shape Design for Elliptic Systems written by O. Pironneau and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" This book is an applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most numerical simulations of physical systems are solved not to gain better understanding of the phenomena but to obtain better control and design. Problems of this type are described in Chapter 2. Traditionally, optimal shape design has been treated as a branch of the calculus of variations and more specifically of optimal control. This subject interfaces with no less than four fields: optimization, optimal control, partial differential equations (PDEs), and their numerical solutions-this is the most difficult aspect of the subject. Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).
Download or read book Nondifferentiable Optimization written by Philip Wolfe and published by . This book was released on 1975 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization of Distributed Parameter Structures written by Edward J. Haug and published by Kluwer Academic Publishers. This book was released on 1981 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Research Today and Tomorrow written by Carles Casacuberta and published by Springer. This book was released on 2006-11-15 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.
Download or read book Exploring Chaos written by Nina Hall and published by W. W. Norton & Company. This book was released on 1994 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory is giving scientists fresh insights into all sorts of unruly phenomena-from dripping faucets to swinging pendulums, from the vagaries of the weather to the movements of the planets, from heart rhythms to gold futures. In this collection of front-line reports, edited for the general reader, internationally recognized experts such as Ian Stewart, Robert M. May, and Benoit Mandelbrot draw on the latest research to trace the roots of chaos in modern science and mathematics.
Download or read book Optimal Shape Design written by B. Kawohl and published by Springer Science & Business Media. This book was released on 2000-11-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.
Download or read book Global Solutions of Reaction Diffusion Systems written by Franz Rothe and published by Springer. This book was released on 2006-12-08 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.
Download or read book Fourier Integral Operators written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a useful introduction to the subject of Fourier Integral Operators and is based on the author’s classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes application to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, rep. WKB-methods.
Download or read book Strong Rigidity of Locally Symmetric Spaces written by G. Daniel Mostow and published by Princeton University Press. This book was released on 1973-12-21 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
Download or read book Differential Games written by Avner Friedman and published by Courier Corporation. This book was released on 2013-06-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text surveys games of fixed duration, games of pursuit and evasion, the computation of saddle points, games of survival, games with restricted phase coordinates, and N-person games. 1971 edition.
Download or read book Transference Methods in Analysis written by Ronald Raphal Coifman and published by American Mathematical Soc.. This book was released on 1977-12-31 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: These ten lectures were presented by Guido Weiss at the University of Nebraska during the week of May 31 to June 4, 1976. They were a part of the Regional Conference Program sponsored by the Conference Board of the Mathematical Sciences and funded by the National Science Foundation. The topic chosen, ``the transference method'', involves a very simple idea that can be applied to several different branches of analysis. The authors have chosen familiar special cases in order to illustrate the use of transference: much that involves general locally compact abelian groups can be understood by examining the real line; the group of rotations can be used to explain what can be done with compact groups; $SL(2,\mathbf C)$ plays the same role vis-a-vis noncompact semisimple Lie groups. The main theme of these lectures is the interplay between properties of convolution operators on classical groups (such as the reals, integers, the torus) and operators associated with more general measure spaces. The basic idea behind this interplay is the notion of transferred operator; these are operators ``obtained'' from convolutions by replacing the translation by some action of the group (or, in some cases, a semigroup) and give rise, among other things, to an interaction between ergodic theory and harmonic analysis. There are illustrations of these ideas. A graduate student in analysis would be able to read most of this book. The work is partly expository, but is mostly ``self-contained''.
