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Global Regularity For The Yang Mills Equations On High Dimensional Minkowski Space
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Book Synopsis Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space by : Joachim Krieger
Download or read book Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space written by Joachim Krieger and published by American Mathematical Soc.. This book was released on 2013-04-22 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains a study of the global Cauchy problem for the Yang-Mills equations on $(6+1)$ and higher dimensional Minkowski space, when the initial data sets are small in the critical gauge covariant Sobolev space $\dot{H}_A^{(n-4)/{2}}$. Regularity is obtained through a certain ``microlocal geometric renormalization'' of the equations which is implemented via a family of approximate null Cronstrom gauge transformations. The argument is then reduced to controlling some degenerate elliptic equations in high index and non-isotropic $L^p$ spaces, and also proving some bilinear estimates in specially constructed square-function spaces.
Book Synopsis Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space by : Joachim Krieger
Download or read book Global Regularity for the Yang-Mills Equations on High Dimensional Minkowski Space written by Joachim Krieger and published by . This book was released on 2013 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces by : David Dos Santos Ferreira
Download or read book Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces written by David Dos Santos Ferreira and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.
Book Synopsis On the Regularity of the Composition of Diffeomorphisms by : H. Inci
Download or read book On the Regularity of the Composition of Diffeomorphisms written by H. Inci and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: For M a closed manifold or the Euclidean space Rn we present a detailed proof of regularity properties of the composition of Hs-regular diffeomorphisms of M for s > 12dimM+1.
Book Synopsis Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem by : Florin Diacu
Download or read book Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem written by Florin Diacu and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers the 3 -dimensional gravitational n -body problem, n32 , in spaces of constant Gaussian curvature k10 , i.e. on spheres S 3 ?1 , for ?>0 , and on hyperbolic manifolds H 3 ?1, for ?
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 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 Strange Attractors for Periodically Forced Parabolic Equations by : Kening Lu
Download or read book Strange Attractors for Periodically Forced Parabolic Equations written by Kening Lu and published by American Mathematical Soc.. This book was released on 2013-06-28 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.
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 Weighted Bergman Spaces Induced by Rapidly Increasing Weights by : Jose Angel Pelaez
Download or read book Weighted Bergman Spaces Induced by Rapidly Increasing Weights written by Jose Angel Pelaez and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.
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.
Book Synopsis Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms by : Andrew Knightly
Download or read book Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms written by Andrew Knightly and published by American Mathematical Soc.. This book was released on 2013-06-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.
Book Synopsis On Some Aspects of Oscillation Theory and Geometry by : Bruno Bianchini
Download or read book On Some Aspects of Oscillation Theory and Geometry written by Bruno Bianchini and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.
Book Synopsis On the Steady Motion of a Coupled System Solid-Liquid by : Josef Bemelmans
Download or read book On the Steady Motion of a Coupled System Solid-Liquid written by Josef Bemelmans and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B,L}, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.
Book Synopsis Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds by : Jose Luis Flores
Download or read book Gromov, Cauchy and Causal Boundaries for Riemannian, Finslerian and Lorentzian Manifolds written by Jose Luis Flores and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, the old notion of causal boundary for a spacetime V has been redefined consistently. The computation of this boundary ∂V on any standard conformally stationary spacetime V=R×M, suggests a natural compactification MB associated to any Riemannian metric on M or, more generally, to any Finslerian one. The corresponding boundary ∂BM is constructed in terms of Busemann-type functions. Roughly, ∂BM represents the set of all the directions in M including both, asymptotic and "finite" (or "incomplete") directions. This Busemann boundary ∂BM is related to two classical boundaries: the Cauchy boundary ∂CM and the Gromov boundary ∂GM. The authors' aims are: (1) to study the subtleties of both, the Cauchy boundary for any generalized (possibly non-symmetric) distance and the Gromov compactification for any (possibly incomplete) Finsler manifold, (2) to introduce the new Busemann compactification MB, relating it with the previous two completions, and (3) to give a full description of the causal boundary ∂V of any standard conformally stationary spacetime. J. L. Flores and J. Herrera, University of Malaga, Spain, and M. Sánchez, University of Granada, Spain. Publisher's note.
Book Synopsis Torsors, Reductive Group Schemes and Extended Affine Lie Algebras by : Philippe Gille
Download or read book Torsors, Reductive Group Schemes and Extended Affine Lie Algebras written by Philippe Gille and published by American Mathematical Soc.. This book was released on 2013-10-23 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.
Book Synopsis On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III by : Masaaki Furusawa
Download or read book On Central Critical Values of the Degree Four $L$-Functions for GSp(4): The Fundamental Lemma. III written by Masaaki Furusawa and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of Böcherer's conjecture on the central critical values of the degree four -functions for , and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.
