Annales Mathematiques du Quebec最新文献_第8页

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><p>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 <i>vibrations</i> and the research area can be referred as <i>vibrodynamics</i>. The governing equations represent a generic system of first-order ODEs containing a prescribed oscillating velocity <span>({varvec{u}})</span>, 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 <i>distinguished limits</i>, 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 <i>uniqueness or multiplicity of distinguished limits</i> and <i>universal structures of averaged equations</i>. 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 <span>({varvec{u}})</span> 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.</p></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

Conjugate and cut points in ideal fluid motion 理想流体运动中的共轭点和切点

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Annales Mathematiques du Quebec Pub Date : 2021-10-20 DOI: 10.1007/s40316-021-00176-4

Theodore D. Drivas, Gerard Misiołek, Bin Shi, Tsuyoshi Yoneda

{"title":"Conjugate and cut points in ideal fluid motion","authors":"Theodore D. Drivas, Gerard Misiołek, Bin Shi, Tsuyoshi Yoneda","doi":"10.1007/s40316-021-00176-4","DOIUrl":"10.1007/s40316-021-00176-4","url":null,"abstract":"<div><p>Two fluid configurations along a flow are conjugate if there is a one parameter family of geodesics (fluid flows) joining them to infinitesimal order. Geometrically, they can be seen as a consequence of the (infinite dimensional) group of volume preserving diffeomorphisms having sufficiently strong positive curvatures which ‘pull’ nearby flows together. Physically, they indicate a form of (transient) stability in the configuration space of particle positions: a family of flows starting with the same configuration deviate initially and subsequently re-converge (resonate) with each other at some later moment in time. Here, we first establish existence of conjugate points in an infinite family of Kolmogorov flows—a class of stationary solutions of the Euler equations—on the rectangular flat torus of any aspect ratio. The analysis is facilitated by a general criterion for identifying conjugate points in the group of volume preserving diffeomorphisms. Next, we show non-existence of conjugate points along Arnold stable steady states on the annulus, disk and channel. Finally, we discuss cut points, their relation to non-injectivity of the exponential map (impossibility of determining a flow from a particle configuration at a given instant) and show that the closest cut point to the identity is either a conjugate point or the midpoint of a time periodic Lagrangian fluid flow.</p></div>","PeriodicalId":42753,"journal":{"name":"Annales Mathematiques du Quebec","volume":"46 1","pages":"207 - 225"},"PeriodicalIF":0.5,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41528449","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: 9

On singularities in the quaternionic Burgers equation 关于四元数Burgers方程的奇异性

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Annales Mathematiques du Quebec Pub Date : 2021-10-20 DOI: 10.1007/s40316-021-00175-5

Vladimir Sverak

引用次数: 1

On singularities in the quaternionic Burgers equation 四元数Burgers方程的奇异性

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Annales Mathematiques du Quebec Pub Date : 2021-10-20 DOI: 10.1007/s40316-021-00175-5

V. Sverák

引用次数: 0

Interpolation of Beilinson–Kato elements and p-adic L-functions Beilinson-Kato元与p进l函数的插值

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Annales Mathematiques du Quebec Pub Date : 2021-10-08 DOI: 10.1007/s40316-021-00172-8

Denis Benois, Kâzım Büyükboduk

引用次数: 1

Kolmogorov’s theory of turbulence and its rigorous 1d model Kolmogorov湍流理论及其严格的一维模型

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Annales Mathematiques du Quebec Pub Date : 2021-10-05 DOI: 10.1007/s40316-021-00174-6

Sergei Kuksin

引用次数: 3

Asymptotic action and asymptotic winding number for area-preserving diffeomorphisms of the disk 盘的保面积微分同态的渐近作用和渐近圈数

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Annales Mathematiques du Quebec Pub Date : 2021-09-23 DOI: 10.1007/s40316-021-00173-7

David Bechara Senior

引用次数: 5