Russian Journal of Mathematical Physics最新文献_第3页

Atiyah–Bott–Lefschetz Formula on Manifolds with Periodic Ends 具有周期末端流形的atiyah - bot - lefschetz公式

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/S1061920826020184

V.E. Nazaikinskii, A.Yu. Savin

引用次数: 0

Three Identical One-Dimensional Quantum Particles with Point Interaction as a Solvable Model: III. Positive Essential Spectrum 具有点相互作用的三个相同的一维量子粒子的可解模型正本质谱

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/S1061920826600236

M.A. Lyalinov

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Exploring Algebraic and Probabilistic Properties for Degenerate Bivariate Appell Polynomials 探讨退化二元阿佩尔多项式的代数和概率性质

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/S1061920824600867

M. Riyasat, S. Khan

{"title":"Exploring Algebraic and Probabilistic Properties for Degenerate Bivariate Appell Polynomials","authors":"M. Riyasat, S. Khan","doi":"10.1134/S1061920824600867","DOIUrl":"10.1134/S1061920824600867","url":null,"abstract":" The purpose of this paper is to carry out a comprehensive analysis of the properties of degenerate bivariate Appell polynomials by making extensive use of algebraic and probabilistic techniques. The determinant expressions for the degenerate cosine-Appell and sine-Appell polynomials and for their conjugate forms are established by employing several recursive formulas. Further, we focus on exploring probabilistic properties, in which there associated a family of degenerate bivariate Appell polynomials to every random variable (chi) with some exponential moments (e^{chi u}), which provides some powerful tools for a deeper understanding of the behavior and properties of degenerate bivariate Appell polynomials. Examples are framed which introduces a random variable whose mass function is given in terms of degenerate bivariate Bernoulli polynomials. Some expressions for the expectation (E[chi]) of the random variable associated with the degenerate bivariate Bernoulli polynomials are derived. It is demonstrated that the probabilistic approach offers interesting new results and developments for these polynomials. ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"417 - 430"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458755","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 the Homogenization of a Parabolic Equation with a Nonlocal Convolution Type Operator 一类具有非局部卷积型算子的抛物方程的齐化问题

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/S1061920826020147

A. Piatnitski, V. Sloushch, T. Suslina, E. Zhizhina

{"title":"On the Homogenization of a Parabolic Equation with a Nonlocal Convolution Type Operator","authors":"A. Piatnitski, V. Sloushch, T. Suslina, E. Zhizhina","doi":"10.1134/S1061920826020147","DOIUrl":"10.1134/S1061920826020147","url":null,"abstract":" In (L_2(mathbb{R}^d)), we consider a self-adjoint bounded operator ({mathbb A}_varepsilon(t)), (tge 0), (varepsilon >0), of the form It is assumed that (a(cdot)in L_1(mathbb R^d)) is a nonnegative function such that (int_{mathbb{R}^d} | mathbf{x} |^3 a(mathbf{x}),dmathbf{x}<infty) and (a(-mathbf{x}) = a(mathbf{x})); the function (mu(mathbf{x},mathbf{y},t)) is measurable and periodic in all variables, moreover, (mu(mathbf{x},mathbf{y},t) = mu(mathbf{y},mathbf{x},t)) and (0< mu_- leqslant mu(mathbf{x},mathbf{y},t) leqslant mu_+< infty). Let (u_varepsilon(mathbf{x},t)), (mathbf{x} in {mathbb R}^d), (t ge 0), be the solution of the Cauchy problem where (varphi in L_2({mathbb R}^d)). We show that, for a chosen (t>0), the solution (u_varepsilon(cdot,t)) converges in (L_2({mathbb R}^d)), as (varepsilon to 0), to the solution (u_0(cdot,t)) of the homogenized problem where ({mathbb A}^0= - operatorname{div} g^0 nabla) and (g^0) is a positive definite effective matrix. The following error estimate holds: ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 2","pages":"407 - 416"},"PeriodicalIF":1.9,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458752","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

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

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, A.Yu. Shubert","doi":"10.1134/S1061920826020123","DOIUrl":"10.1134/S1061920826020123","url":null,"abstract":" 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 ((J_1,J_2,J_3)) 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 ((J_1,J_2,J_3)) of principal moments of inertia and coordinates of the center of mass ((c_1,c_2,c_3)) 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. ","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":" 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 (int_{ mathcal{M} }frac{Fomega_ mathcal{M} }{Omega^2 + nu^2Gamma^2}) and (int_{ mathcal{M} }frac{Fcos(nu^{-1}Omega)omega_ mathcal{M} }{Omega^2 + nu^2Gamma^2}) plays a crucial role, where (nu>0) is a small parameter, ( mathcal{M} ) is a closed Riemannian manifold with volume form (omega_ mathcal{M} ), and the functions (Gamma > 0), (F), (Omega) are sufficiently smooth. We investigate the asymptotic behavior of the integrals in the limit as (nurightarrow 0). 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 ( mathcal{M} =mathbb{R}^d) and the function (Omega) 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. ","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, A.T. Karipova, A.M. Toleubay","doi":"10.1134/S1061920826600352","DOIUrl":"10.1134/S1061920826600352","url":null,"abstract":" In this paper, we investigate the Chafee–Infante equation in a locally periodic perforated domain with a small parameter (varepsilon>0) 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 (varepsilon^theta) in Fourier condition on the boundary of the cavities, leading to two distinct regimes. In contrast to the critical case ((theta=1)), 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. The subcritical case (( theta > 1)): 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. The supercritical case ((theta < 1)): 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. 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. ","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

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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

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