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Properties of an Operator Describing Acoustic Black Holes 描述声黑洞的算子的性质
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020081
N.V. Ivanov, A.I. Shafarevich
{"title":"Properties of an Operator Describing Acoustic Black Holes","authors":"N.V. Ivanov,&nbsp;A.I. Shafarevich","doi":"10.1134/S1061920826020081","DOIUrl":"10.1134/S1061920826020081","url":null,"abstract":"<p> The properties of the operator describing flexural waves are described. This operator is defined by a fourth-order differential expression with a singular point. A Hilbert space is constructed, and the domain of the operator and the Gelfand triple are found. For a model operator corresponding to a quadratic profile, the spectrum and corresponding (distributional) eigenfunctions are explicitly calculated. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"302 - 316"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458762","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
Canonical Form of the Inertia Tensor for Rigid Bodies on the Lobachevskii Plane and in a Pseudo-Euclidean Space Lobachevskii平面和伪欧几里德空间中刚体惯性张量的标准形式
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020123
E.A. Kudryavtseva, A.Yu. Shubert
{"title":"Canonical Form of the Inertia Tensor for Rigid Bodies on the Lobachevskii Plane and in a Pseudo-Euclidean Space","authors":"E.A. Kudryavtseva,&nbsp;A.Yu. Shubert","doi":"10.1134/S1061920826020123","DOIUrl":"10.1134/S1061920826020123","url":null,"abstract":"<p> This paper studies the properties of the inertia tensor for tops in 3-dimensional (pseudo-) Euclidean space and for plates on the Lobachevskii plane. A canonical form is described to which one can reduce the (pseudo-)Euclidean inner product and the inertia operator of any top by changing the basis. All tops whose inertia operators are nondiagonalizable (every top of this kind lies in a plane tangent to the isotropic cone) are described. All realizable triples <span>((J_1,J_2,J_3))</span> of principal moments of inertia are described in terms of triangle inequalities and their pseudo-Euclidean analogs. A criterion for the realizability of such a triple by a plate on the Lobachevskii plane is obtained. All realizable pairs of triples <span>((J_1,J_2,J_3))</span> of principal moments of inertia and coordinates of the center of mass <span>((c_1,c_2,c_3))</span> of a top in the principal axes of inertia are described in both the diagonalizable and nondiagonalizable cases. In all cases, it is shown that a body consisting of no more than six points can be taken as the realizing top. Eigenvalues of all degenerate inertia operators are described. As an application, realizable examples of integrable tops in 3-dimensional pseudo-Euclidean space (the Euler and Lagrange tops) are described. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"357 - 391"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458977","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
Asymptotics for a Class of Singular Integrals of Quotients with Highly Degenerate Denominators 一类高度退化分母商的奇异积分的渐近性
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920825601417
A.A. Elokhin
{"title":"Asymptotics for a Class of Singular Integrals of Quotients with Highly Degenerate Denominators","authors":"A.A. Elokhin","doi":"10.1134/S1061920825601417","DOIUrl":"10.1134/S1061920825601417","url":null,"abstract":"<p> In a rigorous study of stochastic models for the wave turbulence theory and Peierls’ kinetic theory for the thermal conductivity in solids, analysis of integrals of the form <span>(int_{ mathcal{M} }frac{Fomega_ mathcal{M} }{Omega^2 + nu^2Gamma^2})</span> and <span>(int_{ mathcal{M} }frac{Fcos(nu^{-1}Omega)omega_ mathcal{M} }{Omega^2 + nu^2Gamma^2})</span> plays a crucial role, where <span>(nu&gt;0)</span> is a small parameter, <span>( mathcal{M} )</span> is a closed Riemannian manifold with volume form <span>(omega_ mathcal{M} )</span>, and the functions <span>(Gamma &gt; 0)</span>, <span>(F)</span>, <span>(Omega)</span> are sufficiently smooth. We investigate the asymptotic behavior of the integrals in the limit as <span>(nurightarrow 0)</span>. This paper continues the studies S. B. Kuksin, J. Math. Phys. Anal. Geom., 2018, vol. 14, no. 4, pp. 510тАУ518 and A. V. Dymov, Theoret. and Math. Phys., 2023, vol. 214, no. 2, pp. 153тАУ169, in which the authors considered similar integrals for the case in which <span>( mathcal{M} =mathbb{R}^d)</span> and the function <span>(Omega)</span> is Morse. We significantly weaken the latter assumption, which played an important role in the aforementioned papers. This makes the results thus obtained applicable to the problem of rigorous justification of Peierls’ kinetic theory. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"288 - 301"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458759","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
Homogenization of Attractors to the Chafee–Infante Equations in a Perforated Domain with Locally Periodic Obstacles: Subcritical and Supercritical Cases 具有局部周期障碍的穿孔区域上Chafee-Infante方程吸引子的均匀化：亚临界和超临界情况
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600352
G.A. Chechkin, A.T. Karipova, A.M. Toleubay
{"title":"Homogenization of Attractors to the Chafee–Infante Equations in a Perforated Domain with Locally Periodic Obstacles: Subcritical and Supercritical Cases","authors":"G.A. Chechkin,&nbsp;A.T. Karipova,&nbsp;A.M. Toleubay","doi":"10.1134/S1061920826600352","DOIUrl":"10.1134/S1061920826600352","url":null,"abstract":"<p> In this paper, we investigate the Chafee–Infante equation in a locally periodic perforated domain with a small parameter <span>(varepsilon&gt;0)</span> characterizing the diameter of the cavities and the distance between them. The asymptotic behavior of the problem depends on the scaling of the boundary effects, characterized by the parameter <span>(varepsilon^theta)</span> in Fourier condition on the boundary of the cavities, leading to two distinct regimes. In contrast to the critical case (<span>(theta=1)</span>), in which the condition at the boundary of the cavities gives a potential term and new coefficients of the elliptic operator to the homogenized equation, in the subcritical and supercritical cases the situation changes radically. </p><p> The subcritical case (<span>( theta &gt; 1)</span>): The influence of boundary conditions on perforations does not contribute to the potential term but still changes the coefficients of the homogenized equation. We prove that both trajectory and global attractors of the original problem converge to those of the homogenized problem. </p><p> The supercritical case (<span>(theta &lt; 1)</span>): In this case, the solutions degenerate as the small parameter tends to zero. It has been proven that the attractors also tend to zero in the corresponding topology. </p><p> In the subcritical case, the homogenized limit is rigorously derived via auxiliary cell problems and asymptotic expansions. Appropriate functional spaces with weak topology are introduced, and the existence of trajectory attractors is established. In the supercritical case, we use integral estimates to prove the degeneration of solutions and attractors. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"276 - 287"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458979","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
Phase-Field System as a Regularization of the Free-Boundary Problem for an Incompressible Immiscible Two-Component Flow 不可压缩非混相双组分流自由边界问题的正则化相场系统
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600297
N.A. Burov, R.K. Gaydukov
{"title":"Phase-Field System as a Regularization of the Free-Boundary Problem for an Incompressible Immiscible Two-Component Flow","authors":"N.A. Burov,&nbsp;R.K. Gaydukov","doi":"10.1134/S1061920826600297","DOIUrl":"10.1134/S1061920826600297","url":null,"abstract":"<p> The spreading of a droplet of incompressible fluid over a substrate under the action of capillary forces and gravity is studied within a phase-field framework. An asymptotic analysis shows that the solution of the phase-field system (the regularized problem) converges to the solution of the corresponding limit problem when a regularization parameter tends to zero. The theoretical results are illustrated by numerical simulations for hydrophobic and hydrophilic substrates. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"263 - 275"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458981","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
Norm Continuous Representations of Locally Compact Groups in a Hilbert Space Hilbert空间中局部紧群的范数连续表示
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020160
A.I. Shtern
{"title":"Norm Continuous Representations of Locally Compact Groups in a Hilbert Space","authors":"A.I. Shtern","doi":"10.1134/S1061920826020160","DOIUrl":"10.1134/S1061920826020160","url":null,"abstract":"<p> The structure of norm continuous representations of some locally compact groups in a Hilbert spaces is refined. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"431 - 433"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148459037","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
Nonself-adjoint Three-Dimensional Operators with Point Interactions Supported by Curves 曲线支持点相互作用的非自伴三维算子
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826020044
D.I. Borisov
{"title":"Nonself-adjoint Three-Dimensional Operators with Point Interactions Supported by Curves","authors":"D.I. Borisov","doi":"10.1134/S1061920826020044","DOIUrl":"10.1134/S1061920826020044","url":null,"abstract":"<p> In a general three-dimensional domain we consider a second order differential operator with variable coefficients subject to an arbitrary boundary condition; the operator is supposed to be <span>(m)</span>-sectorial. We show how to add a point interaction supported by a given curve <span>( Gamma )</span> with a complex-valued coupling function to this operator. We provide a rigorous way for defining such an operator with point interaction and study its basic properties. Our approach is based on the main idea used to define the Laplacian in the three-dimensional space on a given curve, but we modify this idea quite essentially avoiding at the same time any implicit Green functions. Our definition provides an effective tool for studying general operators in three-dimensional domains with point interactions on given curves. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"241 - 262"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458757","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
Scattering for Anisotropic Potentials 各向异性势的散射
IF 1.9 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-07-15 DOI: 10.1134/S1061920826600443
E. Korotyaev
{"title":"Scattering for Anisotropic Potentials","authors":"E. Korotyaev","doi":"10.1134/S1061920826600443","DOIUrl":"10.1134/S1061920826600443","url":null,"abstract":"<p> We consider the scattering for the operator <span>(H=H_0+V)</span>, where the unperturbed operator <span>(H_0)</span> is not assumed to be elliptic and the potential <span>(V)</span> is anisotropic. Under some conditions on <span>(H_0)</span> and <span>(V)</span>, we show that the wave operators for <span>(H_0)</span> and <span>(H)</span> exist and are complete, <span>(H)</span> has no singular continuous spectrum, and the eigenvalues of <span>(H)</span> can accumulate only to zero. Under stronger conditions on <span>(V)</span>, the operator <span>(H)</span> has finitely many eigenvalues only. These results are applied to the invariance principle and for time-dependent potentials. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"340 - 356"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458978","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
Inverse Semigroup of Metrics on a Double is Fundamental 双上度量的逆半群是基本的
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920825601958
V. Manuilov
{"title":"Inverse Semigroup of Metrics on a Double is Fundamental","authors":"V. Manuilov","doi":"10.1134/S1061920825601958","DOIUrl":"10.1134/S1061920825601958","url":null,"abstract":"<p> We show that the inverse semigroup of equivalence classes of metrics on two copies of a metric space is fundamental. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"126 - 128"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561966","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
New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart” 多环“心之泪”展开的新数值不变量
IF 1.5 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1134/S1061920826600170
Yu.S. Ilyashenko, S. Minkov, I. Shilin
{"title":"New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart”","authors":"Yu.S. Ilyashenko,&nbsp;S. Minkov,&nbsp;I. Shilin","doi":"10.1134/S1061920826600170","DOIUrl":"10.1134/S1061920826600170","url":null,"abstract":"<p> In this paper, new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological invariant of two arithmetic progressions, both perturbed and unperturbed, on the real line. For the pairs of the unperturbed arithmetic progressions, we give a complete topological classification. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"89 - 106"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561964","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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