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Trends in Nonlinear Analysis
  • Language: en
  • Pages: 427

Trends in Nonlinear Analysis

Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.

Mathematical Methods in Liquid Crystal Optics and Lens Design
  • Language: en
  • Pages: 284

Mathematical Methods in Liquid Crystal Optics and Lens Design

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The Golden Anniversary Celebration of the National Association of Mathematicians
  • Language: en
  • Pages: 184

The Golden Anniversary Celebration of the National Association of Mathematicians

This volume is put together by the National Association of Mathematicians to commemorate its 50th anniversary. The articles in the book are based on lectures presented at several events at the Joint Mathematics Meeting held from January 16–19, 2019, in Baltimore, Maryland, including the Claytor-Woodard Lecture as well as the NAM David Harold Blackwell Lecture, which was held on August 2, 2019, in Cincinnati, Ohio.

partial differential equations and applications
  • Language: en
  • Pages: 392

partial differential equations and applications

  • Type: Book
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  • Published: 2017-10-02
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  • Publisher: Routledge

Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
  • Language: en
  • Pages: 458

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

A Cold War Exodus
  • Language: en
  • Pages: 456

A Cold War Exodus

  • Type: Book
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  • Published: 2024-04-23
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  • Publisher: NYU Press

Reveals the mass mobilization tactics that helped free Soviet Jews and reshaped the Jewish American experience from the Johnson era through the Reagan–Bush years What do these things have in common? Ingrid Bergman, Passover matzoh, Banana Republic®, the fitness craze, the Philadelphia Flyers, B-grade spy movies, and ten thousand Bar and Bat Mitzvah sermons? Nothing, except that social movement activists enlisted them all into the most effective human rights campaign of the Cold War. The plight of Jews in the USSR was marked by systemic antisemitism, a problem largely ignored by Western policymakers trying to improve relations with the Soviets. In the face of governmental apathy, activists...

Operator Methods in Wavelets, Tilings, and Frames
  • Language: en
  • Pages: 192

Operator Methods in Wavelets, Tilings, and Frames

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13-14, 2013, in Boulder, Colorado. Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more. The papers in this volume touch on a wide variety...

Oscillation and Dynamics in Delay Equations
  • Language: en
  • Pages: 274

Oscillation and Dynamics in Delay Equations

Oscillation theory and dynamical systems have long been rich and active areas of research. Containing frontier contributions by some of the leaders in the field, this book brings together papers based on presentations at the AMS meeting in San Francisco in January 1991. With special emphasis on delay equations, the papers cover a broad range of topics in ordinary, partial, and difference equations and include applications to problems in commodity prices, biological modelling, and number theory. The book would be of interest to graduate students and researchers in mathematics or those in other fields who have an interest in delay equations and their applications.

Affine Bernstein Problems and Monge-Ampere Equations
  • Language: en
  • Pages: 193

Affine Bernstein Problems and Monge-Ampere Equations

In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Amp re equations. From the methodical point of view, it introduces the solution of certain Monge-Amp re equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.

Chaotic Numerics
  • Language: en
  • Pages: 290

Chaotic Numerics

Much of what is known about specific dynamical systems is obtained from numerical experiments. Although the discretization process usually has no significant effect on the results for simple, well-behaved dynamics, acute sensitivity to changes in initial conditions is a hallmark of chaotic behavior. How confident can one be that the numerical dynamics reflects that of the original system? Do numerically calculated trajectories always shadow a true one? What role does numerical analysis play in the study of dynamical systems? And conversely, can advances in dynamical systems provide new insights into numerical algorithms? These and related issues were the focus of the workshop on Chaotic Numerics, held at Deakin University in Geelong, Australia, in July 1993. The contributions to this book are based on lectures presented during the workshop and provide a broad overview of this area of research.