Annales Mathematiques du Quebec最新文献_第6页

Aut-invariant quasimorphisms on free products 自由积上的非不变拟同态

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Annales Mathematiques du Quebec Pub Date : 2021-12-03 DOI: 10.1007/s40316-021-00184-4

Bastien Karlhofer

引用次数: 4

Trace singularities in obstacle scattering and the Poisson relation for the relative trace 障碍散射中的迹奇异性及相对迹的Poisson关系

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Annales Mathematiques du Quebec Pub Date : 2021-11-25 DOI: 10.1007/s40316-021-00188-0

Yan-Long Fang, Alexander Strohmaier

{"title":"Trace singularities in obstacle scattering and the Poisson relation for the relative trace","authors":"Yan-Long Fang, Alexander Strohmaier","doi":"10.1007/s40316-021-00188-0","DOIUrl":"10.1007/s40316-021-00188-0","url":null,"abstract":"<div>We consider the case of scattering by several obstacles in ({mathbb {R}}^d), (d ge 2) for the Laplace operator (Delta ) with Dirichlet boundary conditions imposed on the obstacles. In the case of two obstacles, we have the Laplace operators (Delta _1) and (Delta _2) obtained by imposing Dirichlet boundary conditions only on one of the objects. The relative operator (g(Delta ) - g(Delta _1) - g(Delta _2) + g(Delta _0)) was introduced in Hanisch, Waters and one of the authors in (A relative trace formula for obstacle scattering. arXiv:2002.07291, 2020) and shown to be trace-class for a large class of functions g, including certain functions of polynomial growth. When g is sufficiently regular at zero and fast decaying at infinity then, by the Birman–Krein formula, this trace can be computed from the relative spectral shift function (xi _mathrm {rel}(lambda ) = -frac{1}{pi } {text {Im}}(Xi (lambda ))), where (Xi (lambda )) is holomorphic in the upper half-plane and fast decaying. In this paper we study the wave-trace contributions to the singularities of the Fourier transform of (xi _mathrm {rel}). In particular we prove that ({hat{xi }}_mathrm {rel}) is real-analytic near zero and we relate the decay of (Xi (lambda )) along the imaginary axis to the first wave-trace invariant of the shortest bouncing ball orbit between the obstacles. The function (Xi (lambda )) is important in the physics of quantum fields as it determines the Casimir interactions between the objects.</div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"55 - 75"},"PeriodicalIF":0.5,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40316-021-00188-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50514308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Isometries of CAT(0) cube complexes are semi-simple CAT（0）立方体配合物的异构体是半简单的

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Annales Mathematiques du Quebec Pub Date : 2021-11-24 DOI: 10.1007/s40316-021-00186-2

Frédéric Haglund

引用次数: 60

On abelian (ell )-towers of multigraphs II 关于多图的abelian $$ell $$ -塔II

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Annales Mathematiques du Quebec Pub Date : 2021-11-20 DOI: 10.1007/s40316-021-00183-5

Kevin McGown, Daniel Vallières

引用次数: 4

Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon Steklov本征函数在翘曲积流形上的指数局部化：象上跳蚤现象

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Annales Mathematiques du Quebec Pub Date : 2021-11-20 DOI: 10.1007/s40316-021-00185-3

Thierry Daudé, Bernard Helffer, François Nicoleau

{"title":"Exponential localization of Steklov eigenfunctions on warped product manifolds: the flea on the elephant phenomenon","authors":"Thierry Daudé, Bernard Helffer, François Nicoleau","doi":"10.1007/s40316-021-00185-3","DOIUrl":"10.1007/s40316-021-00185-3","url":null,"abstract":"<div>This paper is devoted to the analysis of Steklov eigenvalues and Steklov eigenfunctions on a class of warped product Riemannian manifolds (M, g) whose boundary (partial M) consists in two distinct connected components (Gamma _0) and (Gamma _1). First, we show that the Steklov eigenvalues can be divided into two families ((lambda _m^pm )_{m ge 0}) which satisfy accurate asymptotics as (m rightarrow infty ). Second, we consider the associated Steklov eigenfunctions which are the harmonic extensions of the boundary Dirichlet to Neumann eigenfunctions. In the case of symmetric warped product, we prove that the Steklov eigenfunctions are exponentially localized on the whole boundary (partial M) as (m rightarrow infty ). When we add an asymmetric perturbation of the metric to a symmetric warped product, we observe in almost all cases a flea on the elephant effect. Roughly speaking, we prove that “half” the Steklov eigenfunctions are exponentially localized on one connected component of the boundary, say (Gamma _0), and the other half on the other connected component (Gamma _1) as (m rightarrow infty ).</div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"47 2","pages":"295 - 330"},"PeriodicalIF":0.5,"publicationDate":"2021-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49026701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

On quantum jumps and attractors of the Maxwell–Schrödinger equations 关于Maxwell–Schrödinger方程的量子跳跃和吸引子

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Annales Mathematiques du Quebec Pub Date : 2021-11-01 DOI: 10.1007/s40316-021-00179-1

Alexander I. Komech

引用次数: 2

p-adic families of (mathfrak d)th Shintani liftings $$mathfrak d$$th Shintani电梯的p-adic家族

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Annales Mathematiques du Quebec Pub Date : 2021-10-30 DOI: 10.1007/s40316-021-00182-6

Daniele Casazza, Carlos de Vera-Piquero

引用次数: 1

Limiting absorption principle and virtual levels of operators in Banach spaces Banach空间中算子的极限吸收原理和虚能级

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Annales Mathematiques du Quebec Pub Date : 2021-10-28 DOI: 10.1007/s40316-021-00181-7

Nabile Boussaid, Andrew Comech

引用次数: 1

Distinguished limits and drifts: between nonuniqueness and universality 可分辨的极限和漂移：在非唯一性和普遍性之间

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Annales Mathematiques du Quebec Pub Date : 2021-10-21 DOI: 10.1007/s40316-021-00177-3

V. A. Vladimirov

{"title":"Distinguished limits and drifts: between nonuniqueness and universality","authors":"V. A. Vladimirov","doi":"10.1007/s40316-021-00177-3","DOIUrl":"10.1007/s40316-021-00177-3","url":null,"abstract":"<div>This paper deals with a version of the two-timing method which describes various ‘slow’ effects caused by externally imposed ‘fast’ oscillations. Such small oscillations are often called vibrations and the research area can be referred as vibrodynamics. The governing equations represent a generic system of first-order ODEs containing a prescribed oscillating velocity ({varvec{u}}), given in a general form. Two basic small parameters stand in for the inverse frequency and the ratio of two time-scales; they appear in equations as regular perturbations. The proper connections between these parameters yield the distinguished limits, leading to the existence of closed systems of asymptotic equations. The aim of this paper is twofold: (i) to clarify (or to demystify) the choices of a slow variable, and (ii) to give a coherent exposition which is accessible for practical users in applied mathematics, sciences and engineering. We focus our study on the usually hidden aspects of the two-timing method such as the uniqueness or multiplicity of distinguished limits and universal structures of averaged equations. The main result is the demonstration that there are two (and only two) different distinguished limits. The explicit instruction for practically solving ODEs for different classes of ({varvec{u}}) is presented. The key roles of drift velocity and the qualitatively new appearance of the linearized equations are discussed. To illustrate the broadness of our approach, two examples from mathematical biology are shown.</div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"77 - 91"},"PeriodicalIF":0.5,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50503018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Distinguished limits and drifts: between nonuniqueness and universality 区分界限与漂移:在非唯一性与普遍性之间

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Annales Mathematiques du Quebec Pub Date : 2021-10-21 DOI: 10.1007/s40316-021-00177-3

V. Vladimirov

引用次数: 0