Scattering Theory Some Old And New Problems

Author : Dmitri R. Yafaev
Publisher : Springer
Page : 185 pages
File Size : 51,5 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540451709

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Scattering Theory: Some Old and New Problems by Dmitri R. Yafaev Pdf

Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject.

Author : Anonim
Publisher : Unknown
Page : 168 pages
File Size : 53,7 Mb
Release : 2000
Category : Electronic
ISBN : OCLC:897811838

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Scattering Theory by Anonim Pdf

Author : Trygve Johnsen,Andreas L. Knutsen
Publisher : Springer Science & Business Media
Page : 180 pages
File Size : 42,5 Mb
Release : 2004
Category : Projective modules (Algebra)
ISBN : 3540215050

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K3 Projective Models in Scrolls by Trygve Johnsen,Andreas L. Knutsen Pdf

Author : Georgina M Dopico Black,Ricardo Weder,Pavel Exner,Benoit Grébert
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 42,5 Mb
Release : 2002
Category : Science
ISBN : 9780821829004

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Mathematical Results in Quantum Mechanics by Georgina M Dopico Black,Ricardo Weder,Pavel Exner,Benoit Grébert Pdf

This work contains contributions presented at the conference, QMath-8: Mathematical Results in Quantum Mechanics'', held at Universidad Nacional Autonoma de Mexico in December 2001. The articles cover a wide range of mathematical problems and focus on various aspects of quantum mechanics, quantum field theory and nuclear physics. Topics vary from spectral properties of the Schrodinger equation of various quantum systems to the analysis of quantum computation algorithms. The book should be suitable for graduate students and research mathematicians interested in the mathematical aspects of quantum mechanics.

Author : Damir Filipovic
Publisher : Springer
Page : 138 pages
File Size : 55,8 Mb
Release : 2004-11-02
Category : Mathematics
ISBN : 9783540445487

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Consistency Problems for Heath-Jarrow-Morton Interest Rate Models by Damir Filipovic Pdf

Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.

Author : Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 528 pages
File Size : 42,7 Mb
Release : 2007
Category : Mathematical physics
ISBN : 9780821842485

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Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday by Fritz Gesztesy Pdf

This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.

Author : Michael Wilson
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 55,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9783540745822

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Weighted Littlewood-Paley Theory and Exponential-Square Integrability by Michael Wilson Pdf

Littlewood-Paley theory is an essential tool of Fourier analysis, with applications and connections to PDEs, signal processing, and probability. It extends some of the benefits of orthogonality to situations where orthogonality doesn’t really make sense. It does so by letting us control certain oscillatory infinite series of functions in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper than was previously suspected. The present book tries to give a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications.

Author : Francis Nier,Bernard Helffer
Publisher : Springer
Page : 209 pages
File Size : 49,5 Mb
Release : 2005-01-17
Category : Mathematics
ISBN : 9783540315537

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Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians by Francis Nier,Bernard Helffer Pdf

There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction, this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart, the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes, and the Morse inequalities.

Author : Olivier Catoni
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 55,8 Mb
Release : 2004
Category : Electronic
ISBN : 3540225722

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Statistical learning theory and stochastic optimization by Olivier Catoni Pdf

Author : Amir Dembo,Tadahisa Funaki
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 41,8 Mb
Release : 2005-11-03
Category : Mathematics
ISBN : 3540260692

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Lectures on Probability Theory and Statistics by Amir Dembo,Tadahisa Funaki Pdf

This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.

Author : Luis Barreira,Claudia Valls
Publisher : Springer
Page : 291 pages
File Size : 54,8 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540747758

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Stability of Nonautonomous Differential Equations by Luis Barreira,Claudia Valls Pdf

This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

Author : Avner Friedman
Publisher : Springer
Page : 210 pages
File Size : 54,9 Mb
Release : 2008-04-26
Category : Mathematics
ISBN : 9783540743316

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Tutorials in Mathematical Biosciences IV by Avner Friedman Pdf

This book offers an introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. It reviews the concept and methodologies of phylogenetic trees, introduces ecological models, examines a broad range of ongoing research in population dynamics, and deals with gene frequencies under the action of migration and selection. The book features computational schemes, illustrations, and mathematical theorems.

Author : Jaya P. N. Bishwal
Publisher : Springer
Page : 268 pages
File Size : 42,8 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540744481

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Parameter Estimation in Stochastic Differential Equations by Jaya P. N. Bishwal Pdf

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Author : Jörn Steuding
Publisher : Springer
Page : 322 pages
File Size : 43,8 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540448228

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Value-Distribution of L-Functions by Jörn Steuding Pdf

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.

Author : Alexander Isaev
Publisher : Springer
Page : 144 pages
File Size : 43,6 Mb
Release : 2007-03-11
Category : Mathematics
ISBN : 9783540691532

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Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds by Alexander Isaev Pdf

In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.