Download or read book Stable Mappings and Their Singularities written by M. Golubitsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.
Download or read book Stable Mappings and Their Singularities written by Martin Golubitsky and published by . This book was released on 1974 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stable Mappings and Their Singularities By M Golubitsky And V Guillemin written by Martin Golubitsky and published by . This book was released on 1973 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singularities of Mappings written by David Mond and published by Springer Nature. This book was released on 2020-01-23 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Download or read book The Impact of Applications on Mathematics written by Masato Wakayama and published by Springer. This book was released on 2014-07-18 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented at the Forum “The Impact of Applications on Mathematics” in October 2013. It describes an appropriate framework in which to highlight how real-world problems, over the centuries and today, have influenced and are influencing the development of mathematics and thereby, how mathematics is reshaped, in order to advance mathematics and its application. The contents of this book address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.
Download or read book Singular Configurations of Mechanisms and Manipulators written by Andreas Müller and published by Springer. This book was released on 2019-02-19 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces the main problems, key methods, and milestone results in singularity analysis of mechanisms. It provides a comprehensive and concise overview of basic results while also addressing a few advanced topics of singularities in mechanical systems and robots.
Download or read book A Mathematical Approach to Research Problems of Science and Technology written by Ryuei Nishii and published by Springer. This book was released on 2014-07-14 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.
Download or read book Caustics Catastrophes and Wave Fields written by Yu.A. Kravtsov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" by analysing caustics and their fields on the basis of modern catastrophe theory. The present volume covers local and uniform caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of canonical operators , Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.
Download or read book Differential Geometry written by A. M. Naveira and published by Springer. This book was released on 2006-11-14 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catastrophe Theory written by A. Okninski and published by Elsevier. This book was released on 1992-06-12 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide a straightforward introduction to chemical applications of the catastrophe theory. It is primarily intended for chemists interested in placing chemical reactions in the broader context of non-linear science, but it has a practical relevance for scientists in general. Catastrophe theory deals with those non-linear phenomena in which a continuous change in the control parameters results in a discontinuous alteration of a characteristic quantity of the system. The author discusses the origins of catastrophe theory, giving examples of occurrences in the areas of physics, chemistry and biology. Elementary theory and non-chemical applications are also described. The chemical kinetics and methods of analysis of chemical kinetic equations arising from elementary and generalized catastrophe theories are reviewed. Finally, the theory is applied to analyse and classify phenomena associated with the stability loss that may occur in chemical reactions. The book contains over 100 figures and an extensive subject index.
Download or read book Optimization of Complex Systems Theory Models Algorithms and Applications written by Hoai An Le Thi and published by Springer. This book was released on 2019-06-15 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.
Download or read book Singular Trajectories and their Role in Control Theory written by Bernard Bonnard and published by Springer Science & Business Media. This book was released on 2003-05-12 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The role of singular trajectories in control theory is analysed in this volume that contains about 60 exercieses and problems. A section is devoted to the applications of singular trajectories to the optimisation of batch reactors. The theoretical paart based on the Martinet case concerns the singulatrity analysis of singular trajectories in sub-Riemannian geometry. An algorithm is gibven to evaluate conjugate points and a final chapter discusses open problems. The volume will interest mathematicians and engineers.
Download or read book Singularity Theory Dedicated To Jean paul Brasselet On His 60th Birthday Proceedings Of The 2005 Marseille Singularity School And Conference written by Jean-paul Brasselet and published by World Scientific. This book was released on 2007-02-08 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Download or read book Singularity Theory written by Denis Cheniot and published by World Scientific. This book was released on 2007 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.
Download or read book Lie Groups Lie Algebras and Their Representations written by V.S. Varadarajan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.
Download or read book Lectures On Dynamical Systems Structural Stability And Their Applications written by Kotik K Lee and published by World Scientific. This book was released on 1992-05-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Download or read book Progress and Challenges in Dynamical Systems written by Santiago Ibáñez and published by Springer Science & Business Media. This book was released on 2013-09-20 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers based on talks given at the International Conference Dynamical Systems: 100 years after Poincaré held at the University of Oviedo, Gijón in Spain, September 2012. It provides an overview of the state of the art in the study of dynamical systems. This book covers a broad range of topics, focusing on discrete and continuous dynamical systems, bifurcation theory, celestial mechanics, delay difference and differential equations, Hamiltonian systems and also the classic challenges in planar vector fields. It also details recent advances and new trends in the field, including applications to a wide range of disciplines such as biology, chemistry, physics and economics. The memory of Henri Poincaré, who laid the foundations of the subject, inspired this exploration of dynamical systems. In honor of this remarkable mathematician, theoretical physicist, engineer and philosopher, the authors have made a special effort to place the reader at the frontiers of current knowledge in the discipline.
