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Russian Journal of Mathematical Physics最新文献

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On the Point Spectrum of a Non-Self-Adjoint Quasiperiodic Operator 论非自交准周期算子的点谱
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S106192082403004X
D.I. Borisov, A.A. Fedotov
{"title":"On the Point Spectrum of a Non-Self-Adjoint Quasiperiodic Operator","authors":"D.I. Borisov,&nbsp;A.A. Fedotov","doi":"10.1134/S106192082403004X","DOIUrl":"10.1134/S106192082403004X","url":null,"abstract":"<p> We consider a difference operator acting in <span>(l^2(mathbb Z))</span> by the formula <span>(( mathcal{A} psi)_n=psi_{n+1}+psi_{n-1}+lambda e^{-2pi mathrm{i} (theta+omega n)} psi_n)</span>, <span>(nin mathbb{Z})</span>, where <span>(omegain(0,1))</span>, <span>(lambda&gt;0)</span>, and <span>(thetain [0,1])</span> are parameters. This operator was introduced by P. Sarnak in 1982. For <span>(omeganotin mathbb Q)</span>, the operator <span>( mathcal{A} )</span> is quasiperiodic. Previously, within the framework of a renormalization approach (monodromization method), we described the location of the spectrum of this operator. In the present work, we first establish the existence of the point spectrum for different values of parameters, and then study the eigenfunctions. To do so, using ideas of the renormalization approach, we study the difference operator on the circle obtained from the original one by the Fourier transform. This allows us, first, to obtain a new type condition guaranteeing the existence of point spectrum and, second, to describe in detail a multi-scale self-similar structure of the Fourier transforms of the eigenfunctions. </p><p> <b> DOI</b> 10.1134/S106192082403004X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"389 - 406"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary 论沿边穿孔域中有漂移的泊松方程解的高积分性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030051
G.A. Chechkin, T.P. Chechkina
{"title":"On Higher Integrability of Solutions to the Poisson Equation with Drift in Domains Perforated Along the Boundary","authors":"G.A. Chechkin,&nbsp;T.P. Chechkina","doi":"10.1134/S1061920824030051","DOIUrl":"10.1134/S1061920824030051","url":null,"abstract":"<p> In the paper, we consider a linear second order elliptic problem with drift in a domain perforated along the boundary. Setting homogeneous Dirichlet condition on the boundary of the cavities and homogeneous Neumann condition on the outer boundary of the domain, we prove the higher integrability of the gradient of the solution to the problem (the Boyarsky–Meyers estimate). </p><p> <b> DOI</b> 10.1134/S1061920824030051 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"407 - 417"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maslov Rank Distributions for the Analysis of Two-Dimensional and Quasi-Two-Dimensional Turbulent Flows 用于分析二维和准二维湍流的马斯洛夫秩分布
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030075
M.A. Guzev, S.V. Fortova, A.N. Doludenko, A.O. Posudnevskaya, A.D. Ermakov
{"title":"Maslov Rank Distributions for the Analysis of Two-Dimensional and Quasi-Two-Dimensional Turbulent Flows","authors":"M.A. Guzev,&nbsp;S.V. Fortova,&nbsp;A.N. Doludenko,&nbsp;A.O. Posudnevskaya,&nbsp;A.D. Ermakov","doi":"10.1134/S1061920824030075","DOIUrl":"10.1134/S1061920824030075","url":null,"abstract":"<p> A new practice of applying V.P. Maslov’s theoretical results has been implemented for analyzing fluid flow regimes that arise during their numerical modelling. In this paper, using the example of a Kolmogorov-type flow for two-dimensional motion of a viscous fluid, a rank analysis of the vorticity field and its frequency of occurrence is proposed. A similar analysis has been performed for the problem of forming columnar structures in the spatial case. It has been shown that, for the turbulent, vortex, and laminar fluid motion regimes, the rank distributions exhibit characteristics that can be used to classify the flow types. </p><p> <b> DOI</b> 10.1134/S1061920824030075 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"438 - 449"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relations Between Various Types of Suns in Asymmetric Spaces 不对称空间中各类太阳之间的关系
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030166
I.G. Tsarkov
{"title":"Relations Between Various Types of Suns in Asymmetric Spaces","authors":"I.G. Tsarkov","doi":"10.1134/S1061920824030166","DOIUrl":"10.1134/S1061920824030166","url":null,"abstract":"<p> Left and right-inverse <span>(delta)</span>-suns and left and right <span>(gamma)</span>-suns are studied in asymmetric spaces. Sufficient conditions for the existence of best approximation and solarity of sets are obtained in the uniformly convex asymmetric spaces. </p><p> <b> DOI</b> 10.1134/S1061920824030166 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"562 - 567"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane 被薄弹性膜覆盖的声学介质容器边缘附近的渐近特征模定位
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030105
M.A. Lyalinov
{"title":"Asymptotic Eigenmodes Localized Near the Edge of a Vessel, with Acoustic Medium, Which Is Covered by a Thin Elastic Membrane","authors":"M.A. Lyalinov","doi":"10.1134/S1061920824030105","DOIUrl":"10.1134/S1061920824030105","url":null,"abstract":"<p> The paper deals with the formal short-wavelength asymptotic solutions describing the acoustic eigenoscillations in a vessel having a hard bottom, filled in by an acoustic medium, and covered by a thin elastic membrane. The solutions are localized in the medium near the line of the rigid contact of the membrane covering the vessel with the edge of the vessel. The coefficients in the asymptotic expansion of the solutions satisfy a recurrent sequence of solvable problems, whereas the frequencies, for which such nontrivial formal solutions exist, obey an asymptotic ‘quantization-type condition. </p><p> <b> DOI</b> 10.1134/S1061920824030105 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"477 - 494"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Erratum to: “Natural Volume Forms on Pseudo-Finslerian Manifolds with (m)th Root Metrics” [RJMP 31 (2), 317–324 (2024)] 勘误："Natural Volume Forms on Pseudo-Finslerian Manifolds with (m)th Root Metrics" [RJMP 31 (2), 317-324 (2024)] 的勘误。
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030191
A.V. Solov’yov
{"title":"Erratum to: “Natural Volume Forms on Pseudo-Finslerian Manifolds with (m)th Root Metrics” [RJMP 31 (2), 317–324 (2024)]","authors":"A.V. Solov’yov","doi":"10.1134/S1061920824030191","DOIUrl":"10.1134/S1061920824030191","url":null,"abstract":"","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"574 - 574"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Product Hausdorff Operator on Two-Weighted Morrey–Herz Spaces 双权重莫里-赫兹空间上的广义积豪斯多夫算子
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030063
D.V. Duong, N.T. Hong
{"title":"Generalized Product Hausdorff Operator on Two-Weighted Morrey–Herz Spaces","authors":"D.V. Duong,&nbsp;N.T. Hong","doi":"10.1134/S1061920824030063","DOIUrl":"10.1134/S1061920824030063","url":null,"abstract":"<p> In this paper, we introduce the generalized product Hausdorff operator and study the boundedness of this operator on product two-weighted Morrey, Morrey–Herz spaces. As consequences, we obtain some results about the bounds of product Hausdorff operator associated with the Opdam–Cherednik transform and the sharp bounds for the product weighted Hardy–Littlewood average operator and the product Hardy–Cesàro operator on such spaces. </p><p> <b> DOI</b> 10.1134/S1061920824030063 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"418 - 437"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stokes Phenomenon and Spectral Locus in a Problem of Singular Perturbation Theory 奇异扰动理论问题中的斯托克斯现象和频谱焦点
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030026
A.A. Arzhanov, S.A. Stepin, V.A. Titov, V.V. Fufaev
{"title":"Stokes Phenomenon and Spectral Locus in a Problem of Singular Perturbation Theory","authors":"A.A. Arzhanov,&nbsp;S.A. Stepin,&nbsp;V.A. Titov,&nbsp;V.V. Fufaev","doi":"10.1134/S1061920824030026","DOIUrl":"10.1134/S1061920824030026","url":null,"abstract":"<p> The paper deals with the spectral localization in a model problem of singular perturbation theory and the role of the Stokes phenomenon in this context. We study some typical properties of the asymptotic distribution of eigenvalues and, in particular, topologically different types of the spectral configurations in the semiclassical approximation. In this setting the question naturally arises about the corresponding spectral dynamics and the deformation of the actual limit spectral configurations. </p><p> <b> DOI</b> 10.1134/S1061920824030026 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"351 - 378"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inner Transition Layer in Solutions of the Discrete Painlevé II Equation 离散潘列维方程 II 解中的内过渡层
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030130
V.Yu. Novokshenov
{"title":"Inner Transition Layer in Solutions of the Discrete Painlevé II Equation","authors":"V.Yu. Novokshenov","doi":"10.1134/S1061920824030130","DOIUrl":"10.1134/S1061920824030130","url":null,"abstract":"<p> We study real-valued asymptotic solutions of the discrete Painlevé equation of second type (dPII) </p><p> In the case of <span>(n/nu = O(1))</span>, and as <span>(ntoinfty)</span>, the asymptotics is nonuniform. Near the point <span>(n= 2nu)</span>, an <i> inner transition layer</i> occurs, which matches regular asymptotics to the left and to the right of this point. The matching procedure involves classical Painlevé II transcendents. The asymptotics are applied to discrete gap probabilities and random matrix theory. </p><p> <b> DOI</b> 10.1134/S1061920824030130 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"517 - 525"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quasi-Classical Asymptotics Describing the Electron-Hole Interaction and the Klein Effect for the (2+1)-Dirac Equation in Abruptly Varying Fields 描述突变场中 (2+1)- 迪拉克方程的电子-空穴相互作用和克莱因效应的准经典渐近线
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2024-10-03 DOI: 10.1134/S1061920824030014
A.I. Allilueva, A.I. Shafarevich
{"title":"Quasi-Classical Asymptotics Describing the Electron-Hole Interaction and the Klein Effect for the (2+1)-Dirac Equation in Abruptly Varying Fields","authors":"A.I. Allilueva,&nbsp;A.I. Shafarevich","doi":"10.1134/S1061920824030014","DOIUrl":"10.1134/S1061920824030014","url":null,"abstract":"<p> Using Maslov’s canonical operator in the Cauchy problem for a Dirac equation, we consider the asymptotics of the solution of the Cauchy problem in which the potential depends irregularly on a small parameter. </p><p> <b> DOI</b> 10.1134/S1061920824030014 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"339 - 350"},"PeriodicalIF":1.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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