Jean Ker's Books

Singularity Theory

By: Denis Cheniot,Jean-Paul Brasselet

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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.

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1083

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World Scientific

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ISBN 10

9812707492

ISBN 13

9789812707499

Representation Theory of Solvable Lie Groups and Related Topics

By: Ali Baklouti,Hidenori Fujiwara,Jean Ludwig

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Representation Theory of Solvable Lie Groups and Related Topics

By: Ali Baklouti,Hidenori Fujiwara,Jean Ludwig

The purpose of the book is to discuss the latest advances in the theory of unitary representations and harmonic analysis for solvable Lie groups. The orbit method created by Kirillov is the most powerful tool to build the ground frame of these theories. Many problems are studied in the nilpotent case, but several obstacles arise when encompassing exponentially solvable settings. The book offers the most recent solutions to a number of open questions that arose over the last decades, presents the newest related results, and offers an alluring platform for progressing in this research area. The book is unique in the literature for which the readership extends to graduate students, researchers, and beginners in the fields of harmonic analysis on solvable homogeneous spaces.

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620

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Springer Nature

Published Date

ISBN 10

3030820440

ISBN 13

9783030820442

Geometric Methods and Applications

For Computer Science and Engineering

By: Jean Gallier

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Geometric Methods and Applications

For Computer Science and Engineering

By: Jean Gallier

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

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584

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Springer Science & Business Media

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ISBN 10

1461301378

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9781461301370

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

By: Jean H Gallier,Jocelyn Quaintance

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Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

By: Jean H Gallier,Jocelyn Quaintance

For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.

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799

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World Scientific

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ISBN 10

9811245045

ISBN 13

9789811245046

Random Walks on Reductive Groups

By: Yves Benoist,Jean-François Quint

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Random Walks on Reductive Groups

By: Yves Benoist,Jean-François Quint

The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.

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319

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Springer

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ISBN 10

3319477218

ISBN 13

9783319477213

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

By: Jean H Gallier,Jocelyn Quaintance

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Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

By: Jean H Gallier,Jocelyn Quaintance

The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.

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760

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World Scientific

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ISBN 10

981129173X

ISBN 13

9789811291739

Markov Chains and Invariant Probabilities

By: Onésimo Hernández-Lerma,Jean B. Lasserre

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Markov Chains and Invariant Probabilities

By: Onésimo Hernández-Lerma,Jean B. Lasserre

This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).

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213

Publisher

Birkhäuser

Published Date

ISBN 10

3034880243

ISBN 13

9783034880244

Curves and Surfaces in Geometric Modeling

Theory and Algorithms

By: Jean H. Gallier

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Curves and Surfaces in Geometric Modeling

Theory and Algorithms

By: Jean H. Gallier

Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

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512

Publisher

Morgan Kaufmann

Published Date

ISBN 10

1558605991

ISBN 13

9781558605992

Integrable Systems

Actes Du Colloque International de Luminy

By: Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach

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Integrable Systems

Actes Du Colloque International de Luminy

By: Jean Louis Verdier,Pierre Cartier,Yvette Kosmann-Schwarzbach

This book contains fifteen articles by eminent specialists in the theory of completely integrable systems, bringing together the diverse approaches to classical and quantum integrable systems and covering the principal current research developments.

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392

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Springer Science & Business Media

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ISBN 10

0817636536

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9780817636531

Finite Elements II

Galerkin Approximation, Elliptic and Mixed PDEs

By: Alexandre Ern,Jean-Luc Guermond

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Finite Elements II

Galerkin Approximation, Elliptic and Mixed PDEs

By: Alexandre Ern,Jean-Luc Guermond

This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Céa's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix—Raviart, discontinuous Galerkin, hybrid high-order methods). These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows). Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.

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491

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Springer Nature

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ISBN 10

3030569233

ISBN 13

9783030569235

Unitary Representation Theory of Exponential Lie Groups

By: Horst Leptin,Jean Ludwig

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Unitary Representation Theory of Exponential Lie Groups

By: Horst Leptin,Jean Ludwig

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

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213

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110874237

ISBN 13

9783110874235

Harmonic Analysis on Exponential Solvable Lie Groups

By: Hidenori Fujiwara,Jean Ludwig

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Harmonic Analysis on Exponential Solvable Lie Groups

By: Hidenori Fujiwara,Jean Ludwig

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that G is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.

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468

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Springer

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ISBN 10

443155288X

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9784431552888

Finite Elements III

First-Order and Time-Dependent PDEs

By: Alexandre Ern,Jean-Luc Guermond

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Finite Elements III

First-Order and Time-Dependent PDEs

By: Alexandre Ern,Jean-Luc Guermond

This book is the third volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume III is divided into 28 chapters. The first eight chapters focus on the symmetric positive systems of first-order PDEs called Friedrichs' systems. This part of the book presents a comprehensive and unified treatment of various stabilization techniques from the existing literature. It discusses applications to advection and advection-diffusion equations and various PDEs written in mixed form such as Darcy and Stokes flows and Maxwell's equations. The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems). It offers a fresh perspective on the analysis of well-known time-stepping methods. The last five chapters discuss the approximation of hyperbolic equations with finite elements. Here again a new perspective is proposed. These chapters should convince the reader that finite elements offer a good alternative to finite volumes to solve nonlinear conservation equations.

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417

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Springer Nature

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ISBN 10

3030573486

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9783030573485

Applied Functional Analysis

By: Jean-Pierre Aubin

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Applied Functional Analysis

By: Jean-Pierre Aubin

A novel, practical introduction to functional analysis In the twenty years since the first edition of Applied Functional Analysis was published, there has been an explosion in the number of books on functional analysis. Yet none of these offers the unique perspective of this new edition. Jean-Pierre Aubin updates his popular reference on functional analysis with new insights and recent discoveries-adding three new chapters on set-valued analysis and convex analysis, viability kernels and capture basins, and first-order partial differential equations. He presents, for the first time at an introductory level, the extension of differential calculus in the framework of both the theory of distributions and set-valued analysis, and discusses their application for studying boundary-value problems for elliptic and parabolic partial differential equations and for systems of first-order partial differential equations. To keep the presentation concise and accessible, Jean-Pierre Aubin introduces functional analysis through the simple Hilbertian structure. He seamlessly blends pure mathematics with applied areas that illustrate the theory, incorporating a broad range of examples from numerical analysis, systems theory, calculus of variations, control and optimization theory, convex and nonsmooth analysis, and more. Finally, a summary of the essential theorems as well as exercises reinforcing key concepts are provided. Applied Functional Analysis, Second Edition is an excellent and timely resource for both pure and applied mathematicians.

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520

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118030974

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9781118030974

Value Functions on Simple Algebras, and Associated Graded Rings

By: Jean-Pierre Tignol,Adrian R. Wadsworth

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Value Functions on Simple Algebras, and Associated Graded Rings

By: Jean-Pierre Tignol,Adrian R. Wadsworth

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of non crossed products and Platonov's solution of the Tannaka-Artin problem. This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased. The intended audience consists of graduate students and research mathematicians.

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652

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Springer

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ISBN 10

3319163604

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9783319163604

Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves

By: Jean-Benoît Bost

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Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves

By: Jean-Benoît Bost

This book presents the most up-to-date and sophisticated account of the theory of Euclidean lattices and sequences of Euclidean lattices, in the framework of Arakelov geometry, where Euclidean lattices are considered as vector bundles over arithmetic curves. It contains a complete description of the theta invariants which give rise to a closer parallel with the geometric case. The author then unfolds his theory of infinite Hermitian vector bundles over arithmetic curves and their theta invariants, which provides a conceptual framework to deal with the sequences of lattices occurring in many diophantine constructions. The book contains many interesting original insights and ties to other theories. It is written with extreme care, with a clear and pleasant style, and never sacrifices accessibility to sophistication.

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395

Publisher

Springer Nature

Published Date

ISBN 10

3030443299

ISBN 13

9783030443290

Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

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Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields.

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823

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World Scientific

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ISBN 10

9811206414

ISBN 13

9789811206412

Theory and Practice of Finite Elements

By: Alexandre Ern,Jean-Luc Guermond

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Theory and Practice of Finite Elements

By: Alexandre Ern,Jean-Luc Guermond

This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

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531

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Springer Science & Business Media

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ISBN 10

1475743556

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9781475743555

Rational Homotopy Theory Ii

By: Steve Halperin,Yves Felix,Jean-claude Thomas

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Rational Homotopy Theory Ii

By: Steve Halperin,Yves Felix,Jean-claude Thomas

This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.This monograph is a sequel to the book Rational Homotopy Theory [RHT], published by Springer in 2001, but is self-contained except only that some results from [RHT] are simply quoted without proof.

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449

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World Scientific

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ISBN 10

9814651451

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9789814651455

Introduction to Pseudodifferential and Fourier Integral Operators

Pseudodifferential Operators

By: Jean-François Treves

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Introduction to Pseudodifferential and Fourier Integral Operators

Pseudodifferential Operators

By: Jean-François Treves

I have tried in this book to describe those aspects of pseudodifferential and Fourier integral operator theory whose usefulness seems proven and which, from the viewpoint of organization and "presentability," appear to have stabilized. Since, in my opinion, the main justification for studying these operators is pragmatic, much attention has been paid to explaining their handling and to giving examples of their use. Thus the theoretical chapters usually begin with a section in which the construction of special solutions of linear partial differential equations is carried out, constructions from which the subsequent theory has emerged and which continue to motivate it: parametrices of elliptic equations in Chapter I (introducing pseudodifferen tial operators of type 1, 0, which here are called standard), of hypoelliptic equations in Chapter IV (devoted to pseudodifferential operators of type p, 8), fundamental solutions of strongly hyperbolic Cauchy problems in Chap ter VI (which introduces, from a "naive" standpoint, Fourier integral operators), and of certain nonhyperbolic forward Cauchy problems in Chapter X (Fourier integral operators with complex phase). Several chapters-II, III, IX, XI, and XII-are devoted entirely to applications. Chapter II provides all the facts about pseudodifferential operators needed in the proof of the Atiyah-Singer index theorem, then goes on to present part of the results of A. Calderon on uniqueness in the Cauchy problem, and ends with a new proof (due to J. J. Kohn) of the celebrated sum-of-squares theorem of L. Hormander, a proof that beautifully demon strates the advantages of using pseudodifferential operators.

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335

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Springer Science & Business Media

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ISBN 10

1468487809

ISBN 13

9781468487800

Critical Point Theory and Hamiltonian Systems

By: Jean Mawhin

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Critical Point Theory and Hamiltonian Systems

By: Jean Mawhin

FACHGEB The last decade has seen a tremendous development in critical point theory in infinite dimensional spaces and its application to nonlinear boundary value problems. In particular, striking results were obtained in the classical problem of periodic solutions of Hamiltonian systems. This book provides a systematic presentation of the most basic tools of critical point theory: minimization, convex functions and Fenchel transform, dual least action principle, Ekeland variational principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1 symmetries, Morse theory for possibly degenerate critical points and non-degenerate critical manifolds. Each technique is illustrated by applications to the discussion of the existence, multiplicity, and bifurcation of the periodic solutions of Hamiltonian systems. Among the treated questions are the periodic solutions with fixed period or fixed energy of autonomous systems, the existence of subharmonics in the non-autonomous case, the asymptotically linear Hamiltonian systems, free and forced superlinear problems. Application of those results to the equations of mechanical pendulum, to Josephson systems of solid state physics and to questions from celestial mechanics are given. The aim of the book is to introduce a reader familiar to more classical techniques of ordinary differential equations to the powerful approach of modern critical point theory. The style of the exposition has been adapted to this goal. The new topological tools are introduced in a progressive but detailed way and immediately applied to differential equation problems. The abstract tools can also be applied to partial differential equations and the reader will also find the basic references in this direction in the bibliography of more than 500 items which concludes the book. ERSCHEIN

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292

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Springer Science & Business Media

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ISBN 10

1475720610

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9781475720617

The Ever-Present Origin

By: Jean Gebser

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The Ever-Present Origin

By: Jean Gebser

This English translation of Gebser’s major work, Ursprung und Gegenwart (Stuttgart, Deutsche Verlag, 1966), offers certain fundamental insights which should be beneficial to any sensitive scientist and makes it available to the English-speaking world for the recognition it deserves. “The path which led Gebser to his new and universal perception of the world is, briefly, as follows. In the wake of materialism and social change, man had been described in the early years of our century as the “dead end” of nature. Freud had redefined culture as illness—a result of drive sublimation; Klages had called the spirit (and he was surely speaking of the hypertrophied intellect) the “adversary of the soul,” propounding a return to a life like that of the Pelasgi, the aboriginal inhabitants of Greece; and Spengler had declared the “Demise of the West” during the years following World War I. The consequences of such pessimism continued to proliferate long after its foundations had been superseded. It was with these foundations—the natural sciences—that Gebser began. As early as Planck it was known that matter was not at all what materialists had believed it to be, and since 1943 Gebser has repeatedly emphasized that the so-called crisis of Western culture was in fact an essential restructuration.… Gebser has noted two results that are of particular significance: first, the abandonment of materialistic determinism, of a one-sided mechanistic-causal mode of thought; and second, a manifest “urgency of attempts to discover a universal way of observing things, and to overcome the inner division of contemporary man who, as a result of his one-sided rational orientation, thinks only in dualisms.” Against this background of recent discoveries and conclusions in the natural sciences Gebser discerned the outlines of a potential human universality. He also sensed the necessity to go beyond the confines of this first treatise so as to include the humanities (such as political economics and sociology) as well as the arts in a discussion along similar lines. This was the point of departure of The Ever-Present Origin. From In memoriam Jean Gebser by Jean Keckeis

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771

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Ohio University Press

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ISBN 10

082144719X

ISBN 13

9780821447192

C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics

An Introduction

By: Jean-Bernard Bru,Walter Alberto de Siqueira Pedra

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C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics

An Introduction

By: Jean-Bernard Bru,Walter Alberto de Siqueira Pedra

This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.

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497

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Springer Nature

Published Date

ISBN 10

3031289498

ISBN 13

9783031289491

Caustics for Dissipative Semilinear Oscillations

By: Jean-Luc Joly,Guy Métivier,Jeffrey Rauch

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Caustics for Dissipative Semilinear Oscillations

By: Jean-Luc Joly,Guy Métivier,Jeffrey Rauch

This book is intended for graduate students and research mathematicians interested in partial differential equations.

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American Mathematical Soc.

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ISBN 10

0821820419

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9780821820414

Almgren's Big Regularity Paper

Q-valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-minimizing Rectifiable Currents Up to Codimension 2

By: Frederick J. Almgren,Vladimir Scheffer,Jean E. Taylor

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Almgren's Big Regularity Paper

Q-valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-minimizing Rectifiable Currents Up to Codimension 2

By: Frederick J. Almgren,Vladimir Scheffer,Jean E. Taylor

Fred Almgren created the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Holder continuity except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious exposition of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here. This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.

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976

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World Scientific

Published Date

ISBN 10

9810241089

ISBN 13

9789810241087

The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167)

By: Jean-Michel Bismut,Gilles Lebeau

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The Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167)

By: Jean-Michel Bismut,Gilles Lebeau

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.

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377

Publisher

Princeton University Press

Published Date

ISBN 10

0691137323

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9780691137322

Automorphic Forms and Even Unimodular Lattices

Kneser Neighbors of Niemeier Lattices

By: Gaëtan Chenevier,Jean Lannes

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Automorphic Forms and Even Unimodular Lattices

Kneser Neighbors of Niemeier Lattices

By: Gaëtan Chenevier,Jean Lannes

This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.

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Page Count

428

Publisher

Springer

Published Date

ISBN 10

3319958917

ISBN 13

9783319958910

Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit

By: Vladimir Scheffer,Jean E Taylor

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Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit

By: Vladimir Scheffer,Jean E Taylor

Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hölder continuous differentiability except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious development of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.

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973

Publisher

World Scientific

Published Date

ISBN 10

9814494119

ISBN 13

9789814494113

Exercises in Computational Mathematics with MATLAB

By: Tom Lyche,Jean-Louis Merrien

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Exercises in Computational Mathematics with MATLAB

By: Tom Lyche,Jean-Louis Merrien

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.

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377

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Springer

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ISBN 10

366243511X

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9783662435113

Differential Geometry and Lie Groups

A Computational Perspective

By: Jean Gallier,Jocelyn Quaintance

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Differential Geometry and Lie Groups

A Computational Perspective

By: Jean Gallier,Jocelyn Quaintance

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.

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774

Publisher

Springer Nature

Published Date

ISBN 10

3030460401

ISBN 13

9783030460402

Navier-stokes Equations In Planar Domains

By: Matania Ben-artzi,Jean Pierre Croisille,Dalia Fishelov

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Navier-stokes Equations In Planar Domains

By: Matania Ben-artzi,Jean Pierre Croisille,Dalia Fishelov

This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics./a

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315

Publisher

World Scientific

Published Date

ISBN 10

1783263016

ISBN 13

9781783263011

Introduction to Symplectic Geometry

By: Jean-Louis Koszul,Yi Ming Zou

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Introduction to Symplectic Geometry

By: Jean-Louis Koszul,Yi Ming Zou

This introductory book offers a unique and unified overview of symplectic geometry, highlighting the differential properties of symplectic manifolds. It consists of six chapters: Some Algebra Basics, Symplectic Manifolds, Cotangent Bundles, Symplectic G-spaces, Poisson Manifolds, and A Graded Case, concluding with a discussion of the differential properties of graded symplectic manifolds of dimensions (0,n). It is a useful reference resource for students and researchers interested in geometry, group theory, analysis and differential equations.This book is also inspiring in the emerging field of Geometric Science of Information, in particular the chapter on Symplectic G-spaces, where Jean-Louis Koszul develops Jean-Marie Souriau's tools related to the non-equivariant case of co-adjoint action on Souriau’s moment map through Souriau’s Cocycle, opening the door to Lie Group Machine Learning with Souriau-Fisher metric.

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166

Publisher

Springer

Published Date

ISBN 10

9811339872

ISBN 13

9789811339875

Visual Mathematics, Illustrated by the TI-92 and the TI-89

By: George C. Dorner,Jean M. Ferrard,Henri Lemberg

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Visual Mathematics, Illustrated by the TI-92 and the TI-89

By: George C. Dorner,Jean M. Ferrard,Henri Lemberg

The aim of this book is to present basic and advanced mathematical concepts using the graphical and traditional calculator, the TI 92 and the TI 89. These mathematical concepts are commonly taught at some stage of the first three years of college curricula; Analysis (approximations, convergence, differential equations, etc.) Linear Algebra (orthogonality, reduction, etc.). The idea behind this book is totally original and will teach the reader not only all the necessary theorems and examples, but illustrations of the calculator screens and the programs (short versions) will allow the reader to visualize these new concepts directly from the book, or on the calculator, leading to a better understanding through "seeing" and "touching" the mathematical lesson being taught.

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Page Count

454

Publisher

Springer Science & Business Media

Published Date

ISBN 10

2817802012

ISBN 13

9782817802015

Trends in Khmer Art

By: Jean Boisselier

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Trends in Khmer Art

By: Jean Boisselier

A translation of Professor Boisselier's original work. This monograph discusses twenty-four sculptures representative of Khmer art. Includes brief chapters on the history and religions of Cambodia as background for understanding the discussion of the statuary itself, as well as beautiful black-and-white reproductions and a glossary.

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132

Publisher

SEAP Publications

Published Date

ISBN 10

0877277052

ISBN 13

9780877277057

Arithmetic Algebraic Geometry

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Trento, Italy, June 24-July 2, 1991

By: Jean-Louis Colliot-Thelene,Kazuya Kato,Paul Vojta

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Arithmetic Algebraic Geometry

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Trento, Italy, June 24-July 2, 1991

By: Jean-Louis Colliot-Thelene,Kazuya Kato,Paul Vojta

This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.

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Page Count

218

Publisher

Springer

Published Date

ISBN 10

3540479090

ISBN 13

9783540479093

Transport Survey Methods

Keeping Up with a Changing World

By: Jean-Loup Madre,Patrick Bonnel,Johanna Zmud,Martin Lee-Gosselin

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Transport Survey Methods

Keeping Up with a Changing World

By: Jean-Loup Madre,Patrick Bonnel,Johanna Zmud,Martin Lee-Gosselin

Identifies various challenges to the world community of transport survey specialists as well as the larger constituency of practitioners, planners, and decision-makers that it serves and provides potential solutions and recommendations for addressing them.

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Page Count

662

Publisher

Emerald Group Publishing

Published Date

ISBN 10

1848558449

ISBN 13

9781848558441

Rational Homotopy Theory

By: Yves Felix,Stephen Halperin,Jean-Claude Thomas

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Rational Homotopy Theory

By: Yves Felix,Stephen Halperin,Jean-Claude Thomas

This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.

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Page Count

589

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387950680

ISBN 13

9780387950686

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