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Russian Journal of Mathematical Physics最新文献

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Brinkman’s Filtration Law and the Stability of the Water-Over-Vapor Systems in Geothermal Reservoirs 布林克曼过滤定律与地热储层水汽系统的稳定性
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/S1061920826010085
A.T. Il’ichev, G.G. Tsypkin
{"title":"Brinkman’s Filtration Law and the Stability of the Water-Over-Vapor Systems in Geothermal Reservoirs","authors":"A.T. Il’ichev,&nbsp;G.G. Tsypkin","doi":"10.1134/S1061920826010085","DOIUrl":"10.1134/S1061920826010085","url":null,"abstract":"<p> The problem of the stability of a layer of water above a layer of vapor separated by a phase transition surface in high-temperature rocks is considered. A mathematical model of the flow with a generalized Brinkman filtration equation is proposed. Dynamic conditions on the interface are derived. The stability of the flow was studied by the method of normal modes. A dispersion equation was obtained, which was investigated analytically and numerically. A criterion for the stability of the flow is found and the characteristic linear size of the most unstable disturbance is determined. The comparison of the obtained results is carried out with the results of the study of stability in the Darcy approximation. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"79 - 88"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561782","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 a Measure-Theoretic Description of Logarithmic Hamiltonians for Volterra-Type Lattices volterra型格的对数哈密顿量的测度理论描述
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/S1061920826010140
A.S. Osipov
{"title":"On a Measure-Theoretic Description of Logarithmic Hamiltonians for Volterra-Type Lattices","authors":"A.S. Osipov","doi":"10.1134/S1061920826010140","DOIUrl":"10.1134/S1061920826010140","url":null,"abstract":"<p> We establish a correspondence between the semi-infinite and infinite Volterra lattices with a finite logarithmic Hamiltonian and certain classes of even probability measures. In doing so, we apply the inverse spectral theory of Jacobi operators and the theory of orthogonal polynomials. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"138 - 154"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561789","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 Operator Fields in an Upper Triangular Toeplitz Form 上三角Toeplitz形式中的算子域
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/S1061920825601697
M.M. Chernin, A.Yu. Konyaev
{"title":"On Operator Fields in an Upper Triangular Toeplitz Form","authors":"M.M. Chernin,&nbsp;A.Yu. Konyaev","doi":"10.1134/S1061920825601697","DOIUrl":"10.1134/S1061920825601697","url":null,"abstract":"<p> In this paper, we solve the problem of describing the coordinate transformations that preserve an upper triangular Toeplitz form of a given operator field. This problem is of fundamental importance in geometry, and its solution yields auxiliary transformations for the corresponding nondiagonalizable quasilinear systems. Surprisingly, this problem is closely related to the description of all Nijenhuis operators in the same form. This description, as well as the formulas for the aforementioned coordinate transformations, are given by the implicit formulas involving matrix-valued functions. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"42 - 55"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561962","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
Remarks on the Determination of the Lorentzian Metric by the Lengths of Geodesics or Null-Geodesics 关于用测地线长度或零测地线长度确定洛伦兹度规的注释
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/S1061920826010061
G. Eskin
{"title":"Remarks on the Determination of the Lorentzian Metric by the Lengths of Geodesics or Null-Geodesics","authors":"G. Eskin","doi":"10.1134/S1061920826010061","DOIUrl":"10.1134/S1061920826010061","url":null,"abstract":"<p> We consider a Lorentzian metric in <span>( mathbb{R} times mathbb{R} ^n)</span>. We show that, if we know the lengths of the space-time geodesics starting at <span>((0,y,eta))</span> when <span>(t=0)</span>, then we can recover the metric at <span>(y)</span>. We prove the rigidity of Lorentzian metrics. We also prove a variant of the rigidity property for the case of null-geodesics: if two metrics are close and if the corresponding null-geodesics have equal Euclidian lengths, then the metrics are equal. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"56 - 64"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561788","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
Semiclassical Asymptotics of the Solution to the Cauchy Problem for the Three-Dimensional Schrödinger Equation with a Point Potential 具有点势的三维Schrödinger方程Cauchy问题解的半经典渐近性
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/S1061920826600066
O.A. Shchegortsova
{"title":"Semiclassical Asymptotics of the Solution to the Cauchy Problem for the Three-Dimensional Schrödinger Equation with a Point Potential","authors":"O.A. Shchegortsova","doi":"10.1134/S1061920826600066","DOIUrl":"10.1134/S1061920826600066","url":null,"abstract":"<p> The semiclassical asymptotics of the solution to the Cauchy problem for the nonstationary Schrödinger equation </p><p> with a point <span>(delta)</span>-potential in <span>(mathbb{R}^3)</span> is described. The initial condition is taken in the form of a rapidly oscillating wave packet with compact support contained in a ball of sufficiently small radius <span>(R &lt; |x_0|)</span>. Explicit asymptotic formulas describing the evolution of the wave packet and its scattering by the <span>(delta)</span>-potential are obtained. It is proved that, for the considered class of initial conditions, the scattered wave is purely outgoing. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"163 - 179"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561958","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
Integrable Perturbations of Polynomial Hamiltonian Systems 多项式哈密顿系统的可积扰动
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/S1061920825601892
D. Treschev
{"title":"Integrable Perturbations of Polynomial Hamiltonian Systems","authors":"D. Treschev","doi":"10.1134/S1061920825601892","DOIUrl":"10.1134/S1061920825601892","url":null,"abstract":"<p> We consider a Hamiltonian system on the symplectic space <span>(( mathbb{R} ^{2n}, dywedge dx))</span> with a real-analytic Hamiltonian <span>(H : mathbb{R} ^{2n}to mathbb{R} )</span>. We assume that the system has a nondegenerate equilibrium position at the origin. Under some nonresonance assumptions, we prove the following. </p><p> For any positive integer <span>(M)</span>, there exists a real-analytic function <span>(F: mathbb{R} ^{2n}to mathbb{R} )</span> such that </p><p> (1) <span>(F = Obig( (|x|+|y|)^{M+1} big))</span> at the origin, </p><p> (2) the system with Hamiltonian <span>(H+F)</span> is completely integrable in <span>( mathbb{R} ^{2n})</span>. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"183 - 188"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561960","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
Approximative Properties of Multivariate Exponential Sums 多元指数和的近似性质
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/S1061920825602046
A.R. Alimov, I.G. Tsar’kov
{"title":"Approximative Properties of Multivariate Exponential Sums","authors":"A.R. Alimov,&nbsp;I.G. Tsar’kov","doi":"10.1134/S1061920825602046","DOIUrl":"10.1134/S1061920825602046","url":null,"abstract":"<p> Approximative properties of multivariate exponential sums are studied in <span>(C(D))</span>, <span>(D)</span> is a nonempty convex compact body in <span>(mathbb{R}^d)</span>. Properties of existence, uniqueness, solarity, and monotone path-connectedness are considered. Several classes of multivariate exponential sums are shown to be proximinal in <span>(C(D))</span>. The set <span>(mathbf{E}_n^+)</span> of multivariate exponential sums with nonnegative coefficients is shown to be a monotone path-connected strict sun in <span>(C(Q))</span>, but not a uniqueness set. We also obtain some negative results on the lack of solarity and monotone path-connectedness for <span>(E_n)</span> (the set of extended univariate exponential sums) in <span>(C[a,b])</span>. In particular, we show that <span>(E_n)</span>, <span>(nge 2)</span>, is not monotone path-connected and is not Menger-connected in <span>(C[a,b])</span>. It is also proved that <span>(E_n)</span>, <span>(n&gt; 2)</span>, is not a sun in <span>(C[a,b])</span>. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"12 - 23"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561961","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
Convexity and Concavity of (boldsymbol f)-Potentials (Kolmogorov Means) (boldsymbol f) -势（Kolmogorov均值）的凸性和凹性
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/S1061920825601351
V.I. Bakhtin, N.A. Tsarev
{"title":"Convexity and Concavity of (boldsymbol f)-Potentials (Kolmogorov Means)","authors":"V.I. Bakhtin,&nbsp;N.A. Tsarev","doi":"10.1134/S1061920825601351","DOIUrl":"10.1134/S1061920825601351","url":null,"abstract":"<p> In the paper, we prove criteria for convexity and concavity of <span>(f)</span>-potentials (Kolmogorov means, weighted quasi-arithmetic means), whose particular cases are the arithmetic, geometric, harmonic means, thermodynamic potential (exponential mean), cumulant generating function, and the <span>(displaystyle L^{p})</span>-norm. Then we compute in quadratures all functions <span>(f)</span> satisfying these criteria. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"24 - 33"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561963","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
A Formula of Atiyah–Bott–Lefschetz Type and Its Application to Operators with a Finite Group of Shifts atiyah - bot - lefschetz型的一个公式及其在有限平移群算子上的应用
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/S1061920826010139
N.R. Orlova, A.Yu. Savin
{"title":"A Formula of Atiyah–Bott–Lefschetz Type and Its Application to Operators with a Finite Group of Shifts","authors":"N.R. Orlova,&nbsp;A.Yu. Savin","doi":"10.1134/S1061920826010139","DOIUrl":"10.1134/S1061920826010139","url":null,"abstract":"<p> The Lefschetz number of an endomorphism of an elliptic complex is expressed in terms of regularized traces of the operators defining the endomorphism. This result is obtained under certain conditions on the wavefront sets of the operators in question. In the particular case of geometric endomorphisms of the complex, we obtain the classical Atiyah–Bott formula. As an application, we compute the Lefschetz numbers of nonlocal elliptic operators associated with an action of a finite group on a closed smooth manifold. For the de Rham complex, this gives a formula for the Lefschetz number in the cohomology of the orbit space in terms of fixed points. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"129 - 137"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561965","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
Is Born-Jordan Really the Universal Path Integral Quantization Rule? Born-Jordan真的是通用路径积分量子化规则吗？
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/S1061920825601922
J.E. Gough
{"title":"Is Born-Jordan Really the Universal Path Integral Quantization Rule?","authors":"J.E. Gough","doi":"10.1134/S1061920825601922","DOIUrl":"10.1134/S1061920825601922","url":null,"abstract":"<p> It has been argued that the Feynman path integral formalism leads to a quantization rule, and that this is the Born–Jordan rule which gives the unique quantization rule consistent with the correct short-time propagator behavior of the propagator for nonrelativistic systems. We examine this short-time approximation and conclude, contrary to prevailing views, that the asymptotic expansion applies only to Hamiltonian functions that are at most quadratic in the momentum and with constant mass. While the Born–Jordan rule suggests the appropriate quantization of functions in this class, there are other rules which give the same answer, most notably the Weyl quantization scheme. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"33 1","pages":"65 - 78"},"PeriodicalIF":1.5,"publicationDate":"2026-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561508","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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