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A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side


A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side
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A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side


A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side
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Author : Chen Wan
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-12-02

A Local Relative Trace Formula For The Ginzburg Rallis Model The Geometric Side written by Chen Wan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Education categories.


Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.



Geometric Optics For Surface Waves In Nonlinear Elasticity


Geometric Optics For Surface Waves In Nonlinear Elasticity
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Author : Jean-François Coulombel
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03

Geometric Optics For Surface Waves In Nonlinear Elasticity written by Jean-François Coulombel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.


This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.



The Mother Body Phase Transition In The Normal Matrix Model


The Mother Body Phase Transition In The Normal Matrix Model
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Author : Pavel M. Bleher
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

The Mother Body Phase Transition In The Normal Matrix Model written by Pavel M. Bleher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.


In this present paper, the authors consider the normal matrix model with cubic plus linear potential.



Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces


Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces
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Author : Luigi Ambrosio
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-02-13

Nonlinear Diffusion Equations And Curvature Conditions In Metric Measure Spaces written by Luigi Ambrosio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-13 with Education categories.


The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.



Global Smooth Solutions For The Inviscid Sqg Equation


Global Smooth Solutions For The Inviscid Sqg Equation
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Author : Angel Castro
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Global Smooth Solutions For The Inviscid Sqg Equation written by Angel Castro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.


In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.



Degree Theory Of Immersed Hypersurfaces


Degree Theory Of Immersed Hypersurfaces
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Author : Harold Rosenberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Degree Theory Of Immersed Hypersurfaces written by Harold Rosenberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.


The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.



Rigid Character Groups Lubin Tate Theory And Modules


Rigid Character Groups Lubin Tate Theory And Modules
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Author : Laurent Berger
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-03

Rigid Character Groups Lubin Tate Theory And Modules written by Laurent Berger and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Education categories.


The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-modules in a different fashion. Instead of the p-adic open unit disk, the authors work over a character variety that parameterizes the locally L-analytic characters on oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.



Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R


Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R
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Author : Peter Poláčik
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13

Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R written by Peter Poláčik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.


The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near γ for x≈−∞ and near 0 for x≈∞. If the steady states 0 and γ are both stable, the main theorem shows that at large times, the graph of u(⋅,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(⋅,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their ω-limit sets with respect to the locally uniform convergence consist of steady states. In the author's proofs he employs phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories {(u(x,t),ux(x,t)):x∈R}, t>0, of the solutions in question.



Minimal Weak Truth Table Degrees And Computably Enumerable Turing Degrees


Minimal Weak Truth Table Degrees And Computably Enumerable Turing Degrees
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Author : Rodney G. Downey
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Minimal Weak Truth Table Degrees And Computably Enumerable Turing Degrees written by Rodney G. Downey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.


First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.



Affine Flag Varieties And Quantum Symmetric Pairs


Affine Flag Varieties And Quantum Symmetric Pairs
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Author : Zhaobing Fan
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28

Affine Flag Varieties And Quantum Symmetric Pairs written by Zhaobing Fan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.


The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.