Download or read book Classical and Quantic Periodic Motions of Multiply Polarized Spin Particles written by Abbas Bahri and published by CRC Press. This book was released on 1997-11-28 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: :The author of this volume defines a diffusion flow for a variational problem lacking completeness related to the geometry of a contact form a a and a vector field u in its kernel. He analyzes the ends of the flow lines and finds them to be of two types: one involving periodic orbits of the Reeb (Hamiltonian) vector field x, and the other where asymptotes occur. In the most general case these turn out to be periodic motions for x up to quantic jumps of a very special type along u. He shows that the mathematical results and the physical interpretation fit and provide new points of view useful in the foundations of quantum mechanics.
Download or read book Flow Lines and Algebraic Invariants in Contact Form Geometry written by Abbas Bahri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, it develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields. The book opens with a review of prior results and then proceeds through an examination of variational problems, non-Fredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabe-type problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized. Rich in open problems and full, detailed proofs, this work lays the foundation for new avenues of study in contact form geometry and will benefit graduate students and researchers.
Download or read book Partial Differential Equations arising from Physics and Geometry written by Mohamed Ben Ayed and published by Cambridge University Press. This book was released on 2019-05-02 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
Download or read book Progress in Partial Differential Equations written by Herbert Amann and published by CRC Press. This book was released on 1998-04-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerous applications of partial differential equations to problems in physics, mechanics, and engineering keep the subject an extremely active and vital area of research. With the number of researchers working in the field, advances-large and small-come frequently. Therefore, it is essential that mathematicians working in partial differential equations and applied mathematics keep abreast of new developments. Progress in Partial Differential Equations, presents some of the latest research in this important field. Both volumes contain the lectures and papers of top international researchers contributed at the Third European Conference on Elliptic and Parabolic Problems. In addition to the general theory of elliptic and parabolic problems, the topics covered at the conference include: applications free boundary problems fluid mechanics general evolution problems ocalculus of variations homogenization modeling numerical analysis The research notes in these volumes offer a valuable update on the state-of-the-art in this important field of mathematics.
Download or read book Real Analytic and Algebraic Singularities written by Toshisumi Fukui and published by CRC Press. This book was released on 1997-12-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. . Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.
Download or read book Linear Theory of Colombeau Generalized Functions written by M Nedeljkov and published by CRC Press. This book was released on 1998-05-20 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.
Download or read book Nonlinear Partial Differential Equations and Their Applications written by Doina Cioranescu and published by CRC Press. This book was released on 1998-08-15 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of selected lectures on recent work in the field of nonlinear partial differential equations delivered by leading international experts at the well-established weekly seminar held at the Collège de France. Emphasis is on applications to numerous areas, including control theory, theoretical physics, fluid and continuum mechanics, free boundary problems, dynamical systems, scientific computing, numerical analysis, and engineering. Proceedings of this seminar will be of particular interest to postgraduate students and specialists in the area of nonlinear partial differential equations.
Download or read book Elliptic Operators Topology and Asymptotic Methods Second Edition written by John Roe and published by CRC Press. This book was released on 1999-01-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important examples and applications, Elliptic Operators, Topology, and Asymptotic Methods, Second Edition introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. The author builds towards proof of the Lefschetz formula and the full index theorem with four chapters of geometry, five chapters of analysis, and four chapters of topology. The topics addressed include Hodge theory, Weyl's theorem on the distribution of the eigenvalues of the Laplacian, the asymptotic expansion for the heat kernel, and the index theorem for Dirac-type operators using Getzler's direct method. As a "dessert," the final two chapters offer discussion of Witten's analytic approach to the Morse inequalities and the L2-index theorem of Atiyah for Galois coverings. The text assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, Elliptic Operators, Topology, and Asymptotic Methods becomes the ideal vehicle for self-study or coursework. Mathematicians, researchers, and physicists working with index theory or supersymmetry will find it a concise but wide-ranging introduction to this important and intriguing field.
Download or read book Boundary Value Problems with Equivalued Surface and Resistivity Well Logging written by T Li and published by CRC Press. This book was released on 1998-03-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first part of this book deals with the boundary value problem with equivalued surfaces, while the second part is concerned with the mathematical model and method, including the numerical method, of the resistivity well-logging for the three-lateral well-logging.
Download or read book Recent Advances in Differential Equations written by H-H Dai and published by CRC Press. This book was released on 2020-01-30 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First Pan-China Conference on Differential Equations was held in Kunming, China in June of 1997. Researchers from around the world attended-including representatives from the US, Canada, and the Netherlands-but the majority of the speakers hailed from China and Hong Kong. This volume contains the plenary lectures and invited talks presented at that conference, and provides an excellent view of the research on differential equations being carried out in China. Most of the subjects addressed arose from actual applications and cover ordinary and partial differential equations. Topics include:
Download or read book Progress in Holomorphic Dynamics written by Hartje Kriete and published by CRC Press. This book was released on 1998-05-20 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few decades, complex dynamical systems have received widespread public attention and emerged as one of the most active fields of mathematical research. Starting where other monographs in the subject end, Progress in Holomorphic Dynamics advances the theoretical aspects and recent results in complex dynamical systems, with particular emphasis on Siegel discs. Organized into four parts, the papers in this volume grew out of three workshops: two hosted by the Georg-August-Universität Göttingen and one at the "Mathematisches Forschungsinstitut Oberwolfach." Part I addresses linearization. The authors review Yoccoz's proof that the Brjuno condition is the optimal condition for linearizability of indifferent fixed points and offer a treatment of Perez-Marco's refinement of Yoccoz's work. Part II discusses the conditions necessary for the boundary of a Siegel disc to contain a critical point, builds upon Herman's work, and offers a survey of the state-of-the-art regarding the boundaries of Siegel discs. Part III deals with the topology of Julia sets with Siegel discs and contains a remarkable highlight: C.L. Petersen establishes the existence of Siegel discs of quadratic polynomials with a locally connected boundary. Keller, taking a different approach, explains the relations between locally connected "real Julia sets" with Siegel discs and the abstract concepts of kneading sequences and itineraries. Part IV closes the volume with four papers that review the different directions of present research in iteration theory. It includes discussions on the relations between commuting rational functions and their Julia sets, interactions between the iteration of polynomials and the iteration theory of entire transcendental functions, a deep analysis of the topology of the limbs of the Mandelbrot set, and an overview of complex dynamics in higher dimensions.
Download or read book Topics in Random Polynomials written by K Farahmand and published by CRC Press. This book was released on 1998-08-15 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Random Polynomials presents a rigorous and comprehensive treatment of the mathematical behavior of different types of random polynomials. These polynomials-the subject of extensive recent research-have many applications in physics, economics, and statistics. The main results are presented in such a fashion that they can be understood and used by readers whose knowledge of probability incorporates little more than basic probability theory and stochastic processes.
Download or read book Elliptic Operators Topology and Asymptotic Methods written by John Roe and published by CRC Press. This book was released on 2013-12-19 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl
Download or read book Dirac Operators in Analysis written by John Ryan and published by CRC Press. This book was released on 1999-01-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent developments in the field of Clifford analysis with contributions by many of the field's leading researchers.
Download or read book Strongly Irreducible Operators on Hilbert Space written by ChunLan Jiang and published by Taylor & Francis. This book was released on 2023-02-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive treatment of strongly irreducible operators acting on a complex separable infinite dimensional Hilbert space, and to expose and reflect the internal structure of operators by analyzing and studying irreducibility of operators. Much of the material presented here appears in book form for the first time.
Download or read book Navier Stokes Equations written by Rodolfo Salvi and published by CRC Press. This book was released on 1998-05-20 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the texts of selected lectures delivered at the "International Conference on Navier-Stokes Equations: Theory and Numerical Methods," held during 1997 in Varenna, Lecco (Italy). In recent years, the interest in mathematical theory of phenomena in fluid mechanics has increased, particularly from the point of view of numerical analysis. The book surveys recent developments in Navier-Stokes equations and their applications, and contains contributions from leading experts in the field. It will be a valuable resource for all researchers in fluid dynamics.
Download or read book Numerical Analysis 1997 written by D.F. Griffiths and published by CRC Press. This book was released on 1997-12-05 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book forms a valuable guide to the direction in which current numerical analysis research is heading. It will be of particular interest to graduate students and researchers concerned with the theoretical and practical issues associated with scientific computation. The main topics include ordinary and partial differential equations, fluid flow, optimization, linear algebra, and approximation theory. Two recurring themes are the need for adaptive and structure preserving numerical methods. The work presented here has a list of direct applications that include colliding black holes, molecular dynamics, blow-up problems, and card shuffling.
