Lectures on Geometric Methods in Mathematical Physics (CBMSNSF Regional Conference Series in Applied Mathematics)
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Author: Jerrold E. Marsden
Brand: Brand: Society for Industrial and Applied Mathematics

A monograph on some of the ways geometry and analysis can be used in mathematical problems of physical interest. The roles of symmetry, bifurcation and Hamiltonian systems in diverse applications are explored.
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Applied Integral Transforms (Crm Monograph Series)
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Author: M. Ya. Antimirov
Brand: Brand: Amer Mathematical Society

This book does what few books on integral transforms do: it constructs the kernels of the integral transforms by solving the generalized SturmLiouville problems associated with the partial differential equations at hand. In the first part of the book, the authors construct the kernels and then use them to solve elementary problems of mathematical physics. This section, which proceeds mainly by examples and includes exercises, requires little mathematical background and provides an introduction to the subject of integral transforms. In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy current testing. The choice of topics reflects the authors' research experience and involvement in industrial applications. The first part of the book is accessible to undergraduates, while the second part is aimed more at graduate students and researchers. Because of the applications it discusses, the book will interest engineers (especially petroleum engineers) and physicists.
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Deformation Theory and Quantum Groups With Applications to Mathematical Physics (Contemporary Mathematics)
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Author: Murray Gerstenhaber

Quantum groups are not groups at all, but special kinds of Hopf algebras of which the most important are closely related to Lie groups and play a central role in the statistical and wave mechanics of Baxter and Yang. Those occurring physically can be studied as essentially algebraic and closely related to the deformation theory of algebras (commutative, Lie, Hopf, and so on). One of the oldest forms of algebraic quantization amounts to the study of deformations of a commutative algebra A (of classical observables) to a noncommutative algebra A*h (of operators) with the infinitesimal deformation given by a Poisson bracket on the original algebra A. This volume grew out of an AMSIMSSIAM Joint Summer Research Conference, held in June 1990 at the University of Massachusetts at Amherst. The conference brought together leading researchers in the several areas mentioned and in areas such as q special functions, which have their origins in the last century but whose relevance to modern physics has only recently been understood. Among the advances taking place during the conference was Majid's reconstruction theorem for Drinfel$'$d's quasiHopf algebras. the mathematics of quantum groups and deformation theory.


The Complex Wkb Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics)
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Author: V. P. Maslov

When first published (in Russian), this book proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry. Indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. It uses topological methods to analyze isotropic invariant manifolds in order to obtain symptotic series of eigenvalues and eigenvectors for the multidimensional SchrĂ¶dinger equation also taking into account the socalled tunnel effects.


Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory
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Brand: Brand: Springer

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in twodimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physicallymotivated research on quantum integrable models, including elliptic deformations of groups, representation theory of noncompact quantum groups, and quantization of moduli spaces.
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The Theory of Finslerian Laplacians and Applications (Mathematics and Its Applications)
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Brand: Brand: Springer

Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local meanvalue approach to Finslerian Laplacians and a Hodgede Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, WeitzenbĂ¶ck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.
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A Course in Mathematical Physics: Volume 2: Classical Field Theory
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Author: Walter Thirring

Combining the corrected editions of both volumes on classical physics of Thirring's course in mathematical physics, this treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems. Problems discussed in detail include nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses differential geometry to examine both Maxwell's and Einstein's equations with new material added on guage theory.


Geometric and Quantum Aspects of Integrable Systems: Proceedings of the Eighth Scheveningen Conference Scheveningen, the Netherlands, August 1621, 1 (Lecture Notes in Physics, 424)
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Author: Scheveningen Conference 1992

This is a collection of outstanding review papers on integrable systems. It gives the algebraic geometric aspects of the subject, describes integrability techniques e.g. for the modified KdV equation, integrability of Hamiltonian systems, hierarchies of equations, probability distribution of eigenvalues, and modern aspects of quantum groups. It addresses researchers in mathematics and mathematical physics.


Mathematical Physics X: Proceedings of the Xth Congress on Mathematical Physics : Held at Leipzig, Germany, 30 July9 August, 1991
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Advances in the FreeLagrange Method: Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method : Proceedings of the (Lecture Notes in Physics, 395)
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Author: Wyo.) Next FreeLagrange Conference (1990 Moran
Brand: Brand: SpringerVerlag

The contributions in this volume focus on the use of general connectivity (unstructured) adaptive meshes for Lagrangian calculations but contain a substantial amount of material on Euler and arbitrary LagrangeEuler techniques as well. Contributions on the smooth particle hydrodynamics method and on deterministic vortex methods broaden the scope of the material and allow comparisons of different, though allied, techniques to be made. The format of the conference was designedto optimize the interaction among the attendees. An edited version of roundtable discussions is included in these proceedings.
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