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The Sine Gordon Equation In The Semiclassical Limit Dynamics Of Fluxon Condensates
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Book Synopsis The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates by : Robert J. Buckingham
Download or read book The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates written by Robert J. Buckingham and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
Book Synopsis The Sine-Gordon Equation in the Semiclassical Limit by : Robert J. Buckingham
Download or read book The Sine-Gordon Equation in the Semiclassical Limit written by Robert J. Buckingham and published by . This book was released on 2014-09-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: September 2013, volume 225, number 1059 (fourth of 4 numbers).
Book Synopsis Large Deviations for Additive Functionals of Markov Chains by : Alejandro D. de Acosta
Download or read book Large Deviations for Additive Functionals of Markov Chains written by Alejandro D. de Acosta and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions by : Ioan Bejenaru
Download or read book Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions written by Ioan Bejenaru and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the Schrödinger Map equation in 2+1 dimensions, with values into \mathbb{S}^2. This admits a lowest energy steady state Q, namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space \dot H^1. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology X \subset \dot H^1.
Book Synopsis Spectra of Symmetrized Shuffling Operators by : Victor Reiner
Download or read book Spectra of Symmetrized Shuffling Operators written by Victor Reiner and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of O -noninversions of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.
Book Synopsis Automorphisms of Manifolds and Algebraic $K$-Theory: Part III by : Michael S. Weiss
Download or read book Automorphisms of Manifolds and Algebraic $K$-Theory: Part III written by Michael S. Weiss and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.
Book Synopsis Index Theory for Locally Compact Noncommutative Geometries by : A. L. Carey
Download or read book Index Theory for Locally Compact Noncommutative Geometries written by A. L. Carey and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
Book Synopsis Algebraic and Geometric Aspects of Integrable Systems and Random Matrices by : Anton Dzhamay
Download or read book Algebraic and Geometric Aspects of Integrable Systems and Random Matrices written by Anton Dzhamay and published by American Mathematical Soc.. This book was released on 2013-06-26 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Book Synopsis Combinatorial Floer Homology by : Vin de Silva
Download or read book Combinatorial Floer Homology written by Vin de Silva and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
Book Synopsis Stochastic Flows in the Brownian Web and Net by : Emmanuel Schertzer
Download or read book Stochastic Flows in the Brownian Web and Net written by Emmanuel Schertzer and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.
Book Synopsis Special Values of Automorphic Cohomology Classes by : Mark Green
Download or read book Special Values of Automorphic Cohomology Classes written by Mark Green and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.
Book Synopsis Effective Hamiltonians for Constrained Quantum Systems by : Jakob Wachsmuth
Download or read book Effective Hamiltonians for Constrained Quantum Systems written by Jakob Wachsmuth and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.
Book Synopsis Operator-Valued Measures, Dilations, and the Theory of Frames by : Deguang Han
Download or read book Operator-Valued Measures, Dilations, and the Theory of Frames written by Deguang Han and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation results for bounded linear maps that are not necessarily completely bounded, and from domain algebras that are not necessarily abelian. In the non-cb case the dilation space often needs to be a Banach space. They give applications to both the discrete and the continuous frame theory. There are natural associations between the theory of frames (including continuous frames and framings), the theory of operator-valued measures on sigma-algebras of sets, and the theory of continuous linear maps between -algebras. In this connection frame theory itself is identified with the special case in which the domain algebra for the maps is an abelian von Neumann algebra and the map is normal (i.e. ultraweakly, or weakly, or w*) continuous.
Book Synopsis Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem by : A. L. Carey
Download or read book Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem written by A. L. Carey and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.
Book Synopsis Cohomology for Quantum Groups via the Geometry of the Nullcone by : Christopher P. Bendel
Download or read book Cohomology for Quantum Groups via the Geometry of the Nullcone written by Christopher P. Bendel and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.
Book Synopsis To an Effective Local Langlands Correspondence by : Colin J. Bushnell
Download or read book To an Effective Local Langlands Correspondence written by Colin J. Bushnell and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let F be a non-Archimedean local field. Let \mathcal{W}_{F} be the Weil group of F and \mathcal{P}_{F} the wild inertia subgroup of \mathcal{W}_{F}. Let \widehat {\mathcal{W}}_{F} be the set of equivalence classes of irreducible smooth representations of \mathcal{W}_{F}. Let \mathcal{A}^{0}_{n}(F) denote the set of equivalence classes of irreducible cuspidal representations of \mathrm{GL}_{n}(F) and set \widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F). If \sigma \in \widehat {\mathcal{W}}_{F}, let ^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F} be the cuspidal representation matched with \sigma by the Langlands Correspondence. If \sigma is totally wildly ramified, in that its restriction to \mathcal{P}_{F} is irreducible, the authors treat ^{L}{\sigma} as known. From that starting point, the authors construct an explicit bijection \mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}, sending \sigma to ^{N}{\sigma}. The authors compare this "naïve correspondence" with the Langlands correspondence and so achieve an effective description of the latter, modulo the totally wildly ramified case. A key tool is a novel operation of "internal twisting" of a suitable representation \pi (of \mathcal{W}_{F} or \mathrm{GL}_{n}(F)) by tame characters of a tamely ramified field extension of F, canonically associated to \pi. The authors show this operation is preserved by the Langlands correspondence.
Book Synopsis A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials by : Florica C. Cîrstea
Download or read book A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials written by Florica C. Cîrstea and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.
