Diffraction of Singularities for the Wave Equation on Manifolds with Corners

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ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Diffraction of Singularities for the Wave Equation on Manifolds with Corners by : Richard B. Melrose

Download or read book Diffraction of Singularities for the Wave Equation on Manifolds with Corners written by Richard B. Melrose and published by . This book was released on 2013 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the fundamental solution to the wave equation on a manifold with corners of arbitrary codimension. If the initial pole of the solution is appropriately situated, the authors show that the singularities which are diffracted by the corners (i.e., loosely speaking, are not propagated along limits of transversely reflected rays) are smoother than the main singularities of the solution. More generally, the authors show that subject to a hypothesis of nonfocusing, diffracted wavefronts of any solution to the wave equation are smoother than the incident singularities. These results extend the authors' previous work on edge manifolds to a situation where the fibers of the boundary fibration, obtained here by blowup of the corner in question, are themselves manifolds with corners.

Evolution Equations

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Publisher : American Mathematical Soc.
ISBN 13 : 0821868616
Total Pages : 587 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Evolution Equations by : David Ellwood

Download or read book Evolution Equations written by David Ellwood and published by American Mathematical Soc.. This book was released on 2013-06-26 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Inverse Problems and Applications

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Publisher : Cambridge University Press
ISBN 13 : 1107032016
Total Pages : 593 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Inverse Problems and Applications by : Gunther Uhlmann

Download or read book Inverse Problems and Applications written by Gunther Uhlmann and published by Cambridge University Press. This book was released on 2013 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.

Partial Differential Equations II

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Publisher : Springer Nature
ISBN 13 : 303133700X
Total Pages : 706 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Partial Differential Equations II by : Michael E. Taylor

Download or read book Partial Differential Equations II written by Michael E. Taylor and published by Springer Nature. This book was released on 2023-12-06 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)

Abstracts of Papers Presented to the American Mathematical Society

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ISBN 13 :
Total Pages : 754 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Abstracts of Papers Presented to the American Mathematical Society by : American Mathematical Society

Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2007 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Advances in Differential Equations and Mathematical Physics

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Publisher : American Mathematical Soc.
ISBN 13 : 0821838407
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Differential Equations and Mathematical Physics by : Nikolai Chernov

Download or read book Recent Advances in Differential Equations and Mathematical Physics written by Nikolai Chernov and published by American Mathematical Soc.. This book was released on 2006 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Surveys topics in differential equations that are associated with mathematical physics. This book includes such topics as asymptotic formulas for the ground-state energy of fermionic gas, $J$-self adjoint Dirac operators, and spectral theory of Schrodinger operators. It is suitable for mathematicians and physicists.

A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs

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ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs by : Huanchen Bao

Download or read book A New Approach to Kazhdan-Lusztig Theory of Type B Via Quantum Symmetric Pairs written by Huanchen Bao and published by . This book was released on 2018 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satsify a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a quantum symmetric pair. A new theory of canonical bases arising from quantum symmetric pairs is initiated. It is then applied to formulate and establish for the first time a Kazhdan-Lusztig theory for the BGG category [O] of the orthosymplectic Lie superalgebras osp(2m + 1[vertical bar]2n). In particular, our approach provides a new formulation of the Kazhdan-Lusztig theory for Lie algebras of type B/C.

A Torsion Jacquet-Langlands Correspondence

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ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis A Torsion Jacquet-Langlands Correspondence by : Frank Calegari

Download or read book A Torsion Jacquet-Langlands Correspondence written by Frank Calegari and published by . This book was released on 2019 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We prove a numerical form of a Jacquet-Langlands correspondence for torsion classes on arithmetic hyperbolic 3-manifolds." -- Prové de l'editor.

Semi-linear Diffraction of Conormal Waves

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Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Semi-linear Diffraction of Conormal Waves by : Richard B. Melrose

Download or read book Semi-linear Diffraction of Conormal Waves written by Richard B. Melrose and published by . This book was released on 1996 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

National Research Symposium on Geometric Analysis and Applications (ANU, June 26-30, 2000)

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ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis National Research Symposium on Geometric Analysis and Applications (ANU, June 26-30, 2000) by : Alexander Isaev

Download or read book National Research Symposium on Geometric Analysis and Applications (ANU, June 26-30, 2000) written by Alexander Isaev and published by . This book was released on 2001 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceeding of the National Research Symposium on Geometric Analysis and Applications held at the Centre for Mathematics and its Applications, Australian National University, Canberra, from June 26-30, 2000. The Symposium celebrated the many significant contributions of Professor Derek W.

Electromagnetic Wave Diffraction by Conducting Screens pseudodifferential operators in diffraction problems

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Publisher : CRC Press
ISBN 13 : 0429610564
Total Pages : 127 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Electromagnetic Wave Diffraction by Conducting Screens pseudodifferential operators in diffraction problems by : Yu. G. Smirnov

Download or read book Electromagnetic Wave Diffraction by Conducting Screens pseudodifferential operators in diffraction problems written by Yu. G. Smirnov and published by CRC Press. This book was released on 2022-03-23 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the latest problems of modern mathematical methods for three-dimensional problems of diffraction by arbitrary conducting screens. This comprehensive study provides an introduction to methods of constructing generalized solutions, elements of potential theory, and other underlying mathematical tools. The problem settings, which turn out to be extremely effective, differ significantly from the known approaches and are based on the original concept of vector spaces 'produced' by Maxwell equations. The formalism of pseudodifferential operators enables to prove uniqueness theorems and the Fredholm property for all problems studied. Readers will gain essential insight into the state-of-the-art technique of investigating three-dimensional problems for closed and unclosed screens based on systems of pseudodifferential equations. A detailed treatment of the properties of their kernels, in particular degenerated, is included. Special attention is given to the study of smoothness of generalized solutions and properties of traces.

Analytical and Numerical Approaches to Asymptotic Problems in Analysis

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Publisher : Elsevier
ISBN 13 : 0080871585
Total Pages : 399 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Analytical and Numerical Approaches to Asymptotic Problems in Analysis by : O. Axelsson

Download or read book Analytical and Numerical Approaches to Asymptotic Problems in Analysis written by O. Axelsson and published by Elsevier. This book was released on 2010-07-03 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytical and Numerical Approaches to Asymptotic Problems in Analysis

Wave Factorization of Elliptic Symbols: Theory and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9401594481
Total Pages : 184 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Wave Factorization of Elliptic Symbols: Theory and Applications by : V. Vasil'ev

Download or read book Wave Factorization of Elliptic Symbols: Theory and Applications written by V. Vasil'ev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: To summarize briefly, this book is devoted to an exposition of the foundations of pseudo differential equations theory in non-smooth domains. The elements of such a theory already exist in the literature and can be found in such papers and monographs as [90,95,96,109,115,131,132,134,135,136,146, 163,165,169,170,182,184,214-218]. In this book, we will employ a theory that is based on quite different principles than those used previously. However, precisely one of the standard principles is left without change, the "freezing of coefficients" principle. The first main difference in our exposition begins at the point when the "model problem" appears. Such a model problem for differential equations and differential boundary conditions was first studied in a fundamental paper of V. A. Kondrat'ev [134]. Here also the second main difference appears, in that we consider an already given boundary value problem. In some transformations this boundary value problem was reduced to a boundary value problem with a parameter . -\ in a domain with smooth boundary, followed by application of the earlier results of M. S. Agranovich and M. I. Vishik. In this context some operator-function R('-\) appears, and its poles prevent invertibility; iffor differential operators the function is a polynomial on A, then for pseudo differential operators this dependence on . -\ cannot be defined. Ongoing investigations of different model problems are being carried out with approximately this plan, both for differential and pseudodifferential boundary value problems.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 964 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2002 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Séminaire Bourbaki

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ISBN 13 :
Total Pages : 604 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Séminaire Bourbaki by : Société mathématique de France

Download or read book Séminaire Bourbaki written by Société mathématique de France and published by . This book was released on 2019 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This 69th volume of the Bourbaki Seminar contains the texts of the fifteen survey lectures done during the year 2016/2017. Topics addressed covered Langlands correspondence, NIP property in model theory, Navier-Stokes equation, algebraic and complex analytic geometry, algorithmic and geometric questions in knot theory, analytic number theory formal moduli problems, general relativity, sofic entropy, sphere packings, subriemannian geometry." -- Prové de l'editor.

Rendiconti

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ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.:/5 (4 download)

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Book Synopsis Rendiconti by : Università di Padova. Seminario matematico

Download or read book Rendiconti written by Università di Padova. Seminario matematico and published by . This book was released on 1987 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rendiconti del Seminario matematico della Università di Padova

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ISBN 13 :
Total Pages : 672 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Rendiconti del Seminario matematico della Università di Padova by : Università di Padova. Seminario matematico

Download or read book Rendiconti del Seminario matematico della Università di Padova written by Università di Padova. Seminario matematico and published by . This book was released on 1987 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: