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Scattering Resonances For Several Small Convex Bodies And The Lax Phillips Conjecture
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Book Synopsis Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture by : Luchezar N. Stoyanov
Download or read book Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture written by Luchezar N. Stoyanov and published by American Mathematical Soc.. This book was released on 2009 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type which is considered are contained in a given (large) ball and have some additional properties.
Book Synopsis Modeling, Dynamics, Optimization and Bioeconomics I by : Alberto Adrego Pinto
Download or read book Modeling, Dynamics, Optimization and Bioeconomics I written by Alberto Adrego Pinto and published by Springer. This book was released on 2014-06-20 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the emerging and current, cutting-edge theories and methods of modeling, optimization, dynamics and bio economy. It provides an overview of the main issues, results and open questions in these fields as well as covers applications to biology, economy, energy, industry, physics, psychology and finance. The majority of the contributed papers for this volume come from the participants of the International Conference on Modeling, Optimization and Dynamics (ICMOD 2010), a satellite conference of EURO XXIV Lisbon 2010, which took place at Faculty of Sciences of University of Porto, Portugal and from the Berkeley Bio economy Conference 2012, at the University of California, Berkeley, USA.
Book Synopsis On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields by : Michael Thoreau Lacey
Download or read book On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields written by Michael Thoreau Lacey and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 965 (fourth of 5 numbers)."
Book Synopsis The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions by : Mihai Ciucu
Download or read book The Scaling Limit of the Correlation of Holes on the Triangular Lattice with Periodic Boundary Conditions written by Mihai Ciucu and published by American Mathematical Soc.. This book was released on 2009-04-10 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author defines the correlation of holes on the triangular lattice under periodic boundary conditions and studies its asymptotics as the distances between the holes grow to infinity. He proves that the joint correlation of an arbitrary collection of triangular holes of even side-lengths (in lattice spacing units) satisfies, for large separations between the holes, a Coulomb law and a superposition principle that perfectly parallel the laws of two dimensional electrostatics, with physical charges corresponding to holes, and their magnitude to the difference between the number of right-pointing and left-pointing unit triangles in each hole. The author details this parallel by indicating that, as a consequence of the results, the relative probabilities of finding a fixed collection of holes at given mutual distances (when sampling uniformly at random over all unit rhombus tilings of the complement of the holes) approach, for large separations between the holes, the relative probabilities of finding the corresponding two dimensional physical system of charges at given mutual distances. Physical temperature corresponds to a parameter refining the background triangular lattice. He also gives an equivalent phrasing of the results in terms of covering surfaces of given holonomy. From this perspective, two dimensional electrostatic potential energy arises by averaging over all possible discrete geometries of the covering surfaces.
Book Synopsis The Dynamics of Modulated Wave Trains by : A. Doelman
Download or read book The Dynamics of Modulated Wave Trains written by A. Doelman and published by American Mathematical Soc.. This book was released on 2009 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.
Book Synopsis Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces by : Volkmar Liebscher
Download or read book Random Sets and Invariants for (Type II) Continuous Tensor Product Systems of Hilbert Spaces written by Volkmar Liebscher and published by American Mathematical Soc.. This book was released on 2009-04-10 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
Book Synopsis Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three by : Robert C. Dalang
Download or read book Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three written by Robert C. Dalang and published by American Mathematical Soc.. This book was released on 2009-04-10 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension $d=3$. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed $x\in\mathbb{R}^3$, the sample paths in time are Holder continuous functions. Further, the authors obtain joint Holder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one- and two-dimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Holder exponents that they obtain are optimal.
Book Synopsis Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems by : Vesselin M. Petkov
Download or read book Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems written by Vesselin M. Petkov and published by John Wiley & Sons. This book was released on 2017-01-30 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents these in a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory. The content of the first edition is still relevant, however the new edition will include several new results established after 1992; new text will comprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques which will be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.
Book Synopsis Gazette - Australian Mathematical Society by : Australian Mathematical Society
Download or read book Gazette - Australian Mathematical Society written by Australian Mathematical Society and published by . This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete and Continuous Dynamical Systems by :
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2004 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Méthodes Semi-classiques written by and published by . This book was released on 1992 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Theory of Scattering Resonances by : Semyon Dyatlov
Download or read book Mathematical Theory of Scattering Resonances written by Semyon Dyatlov and published by American Mathematical Soc.. This book was released on 2019-09-10 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Download or read book Mathematical Reviews written by and published by . This book was released on 1996 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Distribution of Resonances in Scattering by Thin Barriers by : Jeffrey Galkowski
Download or read book Distribution of Resonances in Scattering by Thin Barriers written by Jeffrey Galkowski and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies high energy resonances for the operators where is strictly convex with smooth boundary, may depend on frequency, and is the surface measure on .
Book Synopsis Chaotic Billiards by : Nikolai Chernov
Download or read book Chaotic Billiards written by Nikolai Chernov and published by American Mathematical Society. This book was released on 2023-09-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.
Book Synopsis Spectral Geometry by : Pierre H. Berard
Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Mechanics in Mathematics, Chemistry, and Physics by : Karl Gustafson
Download or read book Quantum Mechanics in Mathematics, Chemistry, and Physics written by Karl Gustafson and published by Springer. This book was released on 2011-11-01 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew from a Special Session in }~thematical Physics organized as a part of the 774th Heeting of the American }~thematical Society in Boulder, Colorado, ,27-29 l~rch, 1980. The organizers attempted to include a mix of mathematicians, physi cists and chemists. As interest in the session increased and as it became clear that a significant number of leading contributors would be here, we were offered the opportunity to have these pro ceedings published by Plenum Press. We would like first to express our thanks to Plenum Press, to the American Hathematical Society, and to the University of Colorado Graduate School, and in particular, respectively, to James Busis, Dr. William LeVeque, and Vice Chancellor Hilton Lipetz, for their help in this undertaking. We would also like to thank Burt Rashbaum and }~rtha Troetschel of the Department of l~thematics and Karen Dirks, Donna Falkenhein, Lorraine Volsky, Gwendy Romey, and Leslie Haas of the Joint Institute for labora tory Astrophysics for their excellent help in the preparation of these proceedings. The session took on an international character, representing the countries Federal Republic of Germany, India, Belgium, Peoples Republic of China, Switzerland, Iran, Hexico, GerPlan Democratic Republic, England, and the United States. In all there were fi nally 37 speakers and all have contributed to this volume. The success of the meeting is above all due to them.
