David Kinderlehrer's Books

An Introduction to Variational Inequalities and Their Applications

By: David Kinderlehrer,Guido Stampacchia

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An Introduction to Variational Inequalities and Their Applications

By: David Kinderlehrer,Guido Stampacchia

Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.

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328

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SIAM

Published Date

ISBN 10

0898714664

ISBN 13

9780898714661

Duality Principles in Nonconvex Systems

Theory, Methods and Applications

By: David Yang Gao

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Duality Principles in Nonconvex Systems

Theory, Methods and Applications

By: David Yang Gao

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

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463

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475731760

ISBN 13

9781475731767

Liquid Crystals

Fundamentals

By: Shri Singh,David A. Dunmur

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Liquid Crystals

Fundamentals

By: Shri Singh,David A. Dunmur

Liquid crystals are partially ordered systems without a rigid, long-range structure. The study of these materials covers a wide area: chemical structure, physical properties and technical applications. Due to their dual nature -- anisotropic physical properties of solids and rheological behavior of liquids -- and easy response to externally applied electric, magnetic, optical and surface fields liquid crystals are of greatest potential for scientific and technological applications. The subject has come of age and has achieved the status of being a very exciting interdisciplinary field of scientific and industrial research. This book is an outgrowth of the enormous advances made during the last three decades in both our understanding of liquid crystals and our ability to use them in applications. It presents a systematic, self-contained and up-to-date overview of the structure and properties of liquid crystals. It will be of great value to graduates and research workers in condensed matter physics, chemical physics, biology, materials science, chemical and electrical engineering, and technology from a materials science and physics viewpoint of liquid crystals.

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556

Publisher

World Scientific

Published Date

ISBN 10

9810242506

ISBN 13

9789810242503

Network Economics: A Variational Inequality Approach

By: David Ben-Arieh

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Network Economics: A Variational Inequality Approach

By: David Ben-Arieh

Computational economics has been at the forefront in stimulating the de velopment of mathematical methodologies for the analysis and solution of complex, large-scale problems. The past decade, in particular, has witnessed a dramatic growth of interest in this area. Supported by the increasing avail ability of data and advances in computer architectures, the scale and scope of problems that can now be handled are unveiling new horizons in both theoretical modeling and policy analysis. Accompanying the activity in computational economics is a need for the unification, documentation, and presentation of fundamental methodologies for use by both researchers and practitioners. This volume aims to make a contribution in this direction. The focus of this book is on network economics. Physical networks are pervasive in today's society, be they in the form of transportation networks, telecommunication networks, energy pipelines, electric power networks, etc. Mathematical networks, on the other hand, may be used to represent not only physical networks but also interactions among economic agents. In many applications, the network representation of an economic equilibrium problem may be abstract in that the nodes of the network need not corre spond to locations in space and the links of the network to trade or travel routes.

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334

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401121788

ISBN 13

9789401121781

Modeling Dynamic Transportation Networks

An Intelligent Transportation System Oriented Approach

By: Bin Ran,David Boyce

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Modeling Dynamic Transportation Networks

An Intelligent Transportation System Oriented Approach

By: Bin Ran,David Boyce

This book seeks to summarize our recent progress in dynamic trans portation network modeling. It concentrates on ideal dynamic network models based on actual travel times and their corresponding solution algorithms. In contrast, our first book DynamIc Urban Transportation Network Models - The ory and Implications for Intelligent Vehicle-Hzghway Systems (Springer-Verlag, 1994) focused on instantaneous dynamic network models. Comparing the two books, the major differences can be summarized as follows: 1. This book uses the variational inequality problem as the basic formulation approach and considers the optimal control problem as a subproblem for solution purposes. The former book used optimal control theory as the basic formulation approach, which caused critical problems in some circumstances. 2. This book focuses on ideal dynamic network models based on actual travel times. The former book focused on instantaneous dynamic network models based on currently prevailing travel times. 3. This book formulates a stochastic dynamic route choice model which can utilize any possible route choice distribution function instead of only the logit function. 4. This book reformulates the bilevel problem of combined departure time/ route choice as a one-level variational inequality. 5. Finally, a set of problems is provided for classroom use. In addition, this book offers comprehensive insights into the complexity and challenge of applying these dynamic network models to Intelligent Trans portation Systems (ITS). Nevertheless, the models in this text are not yet fully evaluated and are subject to revision based on future research.

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Page Count

365

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642802303

ISBN 13

9783642802300

Function Spaces and Potential Theory

By: David R. Adams,Lars I. Hedberg

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Function Spaces and Potential Theory

By: David R. Adams,Lars I. Hedberg

..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

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372

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662032821

ISBN 13

9783662032824

Inverse Scattering Theory and Transmission Eigenvalues

Second Edition

By: Fioralba Cakoni,David Colton,Houssem Haddar

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Inverse Scattering Theory and Transmission Eigenvalues

Second Edition

By: Fioralba Cakoni,David Colton,Houssem Haddar

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

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Page Count

259

Publisher

SIAM

Published Date

ISBN 10

1611977428

ISBN 13

9781611977424

Time Series

Data Analysis and Theory

By: David R. Brillinger

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Time Series

Data Analysis and Theory

By: David R. Brillinger

This text employs basic techniques of univariate and multivariate statistics for the analysis of time series and signals.

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556

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SIAM

Published Date

ISBN 10

0898715016

ISBN 13

9780898715019

Dynamic Urban Transportation Network Models

Theory and Implications for Intelligent Vehicle-Highway Systems

By: Bin Ran,David Boyce

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Dynamic Urban Transportation Network Models

Theory and Implications for Intelligent Vehicle-Highway Systems

By: Bin Ran,David Boyce

Intelligent Vehicle-Highway Systems are providing a welcome stimulus to research on dynamic urban transportation network models. This book presents a new generation of models for solving dynamic travel choice problems including traveler's destination choice, mode choice, departure/arrival time choice and route choice. These models are expected to function as off-line travel forecasting and evaluation tools, and eventually as on-line prediction and control models in advanced traveler information and traffic management systems. In addition to a rich set of new formulations and solution algorithms, the book provides a summary of the necessary mathematical background and concludes with a discussion of the requirements for model implementation.

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395

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662007738

ISBN 13

9783662007730

Integral Equation Methods in Scattering Theory

By: David Colton,Rainer Kress

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Integral Equation Methods in Scattering Theory

By: David Colton,Rainer Kress

This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

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286

Publisher

SIAM

Published Date

ISBN 10

1611973163

ISBN 13

9781611973167

Elliptic Partial Differential Equations of Second Order

By: David Gilbarg,Neil S. Trudinger

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Elliptic Partial Differential Equations of Second Order

By: David Gilbarg,Neil S. Trudinger

From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student." --New Zealand Mathematical Society, 1985

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531

Publisher

Springer

Published Date

ISBN 10

3642617980

ISBN 13

9783642617980

Nutrients Quiet the Unquiet Brain

A Four-Generation Bipolar Odyssey

By: David Moyer LCSW

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Nutrients Quiet the Unquiet Brain

A Four-Generation Bipolar Odyssey

By: David Moyer LCSW

Can nutrients successfully reduce and even stop symptoms of bipolar disorder and other mental disorders? Can Lyme disease treatment stop psychosis? Can antibodies to a milk protein contribute to mania? These are some of the questions answered in this revised edition of Nutrients Quiet the Unquiet Brain. Licensed Clinical Social Worker Moyer updates his readers on his familys journey by presenting research findings from the 12 intervening years since the book was first published. Part medical memoir, part medical detective story, the book describes the authors four-generation bipolar family odyssey that led him to paths less traveled. Moyer describes his efforts to help his father and son, whose lives were severely disrupted by mood swings and psychotic episodes. While trying to cope with the consequences of the illness, he explores the role of genes, foods, vaccines, microbes and nutrients. He discusses multiple biological triggers and leading edge interventions for those suffering from bipolar and other mental disorders. He explores new ways to assess and treat what he now calls biobehavioral syndromes. The book gives readers a view into bipolar disorder through the writings of his father and his son. He critically examines assumptions and practices in the justice and mental health care system that adversely impact those called the mentally ill. He describes new ways for patients, family members, education, criminal justice and mental health care professionals to understand and respond to mental illness. The book was the first of what ultimately became The Transformation Trilogy, three books that collectively argue for a fundamental transformation in the response of society, and, most importantly, the mental health care industry, to victims of mental illness.

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920

Publisher

Xlibris Corporation

Published Date

ISBN 10

1499045360

ISBN 13

9781499045369

An Introduction to Nonlinear Functional Analysis and Elliptic Problems

By: Antonio Ambrosetti,David Arcoya Álvarez

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An Introduction to Nonlinear Functional Analysis and Elliptic Problems

By: Antonio Ambrosetti,David Arcoya Álvarez

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems and displays how various approaches can easily be applied to a range of model cases. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.

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Page Count

203

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817681140

ISBN 13

9780817681142

Hans Lewy Selecta

By: Hans Lewy

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Hans Lewy Selecta

By: Hans Lewy

The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge--Ampère Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, François Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorary degree from the University of Bonn.

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Page Count

452

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817635238

ISBN 13

9780817635237

Hans Lewy Selecta

By: David Kinderlehrer

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Hans Lewy Selecta

By: David Kinderlehrer

The work of Hans Lewy (1904--1988) has had a profound influence in the direction of applied mathematics and partial differential equations, in particular, from the late 1920s. Two of the particulars are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL condition, was devised to obtain existence and approximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. Lewy's example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regularity theory of elliptic equations and systems, the Monge-- AmpSre Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and several complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help one understand the essential concepts embedded in an issue, although at a cost in generality. This approach was extremely successful. In this two-volume work, most all of Lewy's papers are presented, in chronological order. They are preceded by several short essays about Lewy himself, prepared by Helen Lewy, Constance Reid, and David Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax, Jean Leray, Richard MacCamy, Fran?ois Treves, and Louis Nirenberg. Additionally, there are Lewy's own remarks on the occasion of his honorary degree from the University of Bonn.

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Page Count

472

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817635246

ISBN 13

9780817635244

Hans Lewy Selecta

By: Hans Lewy

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Hans Lewy Selecta

By: Hans Lewy

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452

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Springer Science & Business Media

Published Date

ISBN 10

0817635238

ISBN 13

9780817635237

Amorphous Polymers and Non-Newtonian Fluids

By: Constantine Dafermos,J.L. Ericksen,David Kinderlehrer

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Amorphous Polymers and Non-Newtonian Fluids

By: Constantine Dafermos,J.L. Ericksen,David Kinderlehrer

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise.

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Page Count

202

Publisher

Springer

Published Date

ISBN 10

0387965564

ISBN 13

9780387965567

The Antioxidant Save-Your-Life Cookbook

150 Nutritious High-Fiber, Low-Fat Recipes to Protect You Against the Damaging Effects of Free Radicals

By: Jane Kinderlehrer

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The Antioxidant Save-Your-Life Cookbook

150 Nutritious High-Fiber, Low-Fat Recipes to Protect You Against the Damaging Effects of Free Radicals

By: Jane Kinderlehrer

Here are 150 family- and kitchen-tested recipes, each packed with antioxidants to nutritionally protect you against cancer and disease-causing free radicals--without sacrificing variety or flavor. Emphasizing the benefits of antioxidant-rich foods high in vi-tamins C, E, and A, as well as selenium and beta-carotene, these delicious recipes will: enhance your immune system strengthen your bones build up your resistance to viral attacks, infections, even allergic reactions reinvigorate your love life help you overcome fatigue keep your blood sugar on an even level and much more. The introduction by Dr. Daniel Kinderlehrer explains in clear, plain language the often-confusing terms free radicals and oxidation, then goes on to detail the many medical benefits of antioxidants and the ingredients found here. These include providing protection against a variety of cancers, Alzheimer's disease, immune disorders, arthritis, diabetic conditions, and the complications of aging. Separate chapters include recipes for jump-start breakfasts; tasty appetizers, side dishes, and snacks; sumptuous soups and stews; satisfying vegetarian meals; hearty main courses featuring chicken, fish, or meat; flavorful dressings, dips, spreads, and vinaigrettes; and tempting desserts. This useful cookbook also features a valuable section on stocking your pantry--"What to Stash and What to Trash"--loaded with healthy advice to guide you at the supermarket and when choosing foods. Also included is a glossary of some of the major antioxidants found in food. With recipes low in fat and calories, high in fiber and nutrients--with no white flour, hydrogenated fats, or chemical additives--this collection is a must-have for every cook concerned with eating healthfully, preventing disease, and living a longer life.

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Page Count

224

Published Date

ISBN 10

1557045011

ISBN 13

9781557045010

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