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Russian Journal of Mathematical Physics最新文献

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Nonlinear Long Standing Waves with Support Bounded by Caustics or Localized in the Vicinity of a Two-Link Trajectory 非线性长驻波，其支撑点受凹陷约束或在双链轨迹附近局部化
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040106
A.I. Klevin, A.V. Tsvetkova
{"title":"Nonlinear Long Standing Waves with Support Bounded by Caustics or Localized in the Vicinity of a Two-Link Trajectory","authors":"A.I. Klevin,&nbsp;A.V. Tsvetkova","doi":"10.1134/S1061920823040106","DOIUrl":"10.1134/S1061920823040106","url":null,"abstract":"<p> The paper is devoted to describing the dynamics and uprush of time-periodic long waves in basins with gentle shores. We consider waves that are defined by solutions localized between caustics in the domain bounded by the shores of the basin. We also consider solutions localized in the vicinity of a periodic trajectory which, during the period, has exactly two intersections with the boundary of such a domain. </p><p> <b> DOI</b> 10.1134/S1061920823040106 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"543 - 551"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056557","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
Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums 用傅里叶和估计连续周期函数的近似值
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040179
T.Yu. Semenova
{"title":"Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums","authors":"T.Yu. Semenova","doi":"10.1134/S1061920823040179","DOIUrl":"10.1134/S1061920823040179","url":null,"abstract":"<p> An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered. </p><p> <b> DOI</b> 10.1134/S1061920823040179 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"691 - 700"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056858","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
High-Energy Homogenization of a Multidimensional Nonstationary Schrödinger Equation 多维非稳态薛定谔方程的高能量均质化
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040064
M. Dorodnyi
{"title":"High-Energy Homogenization of a Multidimensional Nonstationary Schrödinger Equation","authors":"M. Dorodnyi","doi":"10.1134/S1061920823040064","DOIUrl":"10.1134/S1061920823040064","url":null,"abstract":"<p> In <span>(L_2(mathbb{R}^d))</span>, we consider an elliptic differential operator <span>(mathcal{A}_varepsilon ! = ! - operatorname{div} g(mathbf{x}/varepsilon) nabla + varepsilon^{-2} V(mathbf{x}/varepsilon))</span>, <span>( varepsilon &gt; 0)</span>, with periodic coefficients. For the nonstationary Schrödinger equation with the Hamiltonian <span>(mathcal{A}_varepsilon)</span>, analogs of homogenization problems related to an arbitrary point of the dispersion relation of the operator <span>(mathcal{A}_1)</span> are studied (the so called high-energy homogenization). For the solutions of the Cauchy problems for these equations with special initial data, approximations in <span>(L_2(mathbb{R}^d))</span>-norm for small <span>(varepsilon)</span> are obtained. </p><p> <b> DOI</b> 10.1134/S1061920823040064 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"480 - 500"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056384","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 of Long Nonlinear Propagating Waves in a One-Dimensional Basin with Gentle Shores 具有平缓海岸的一维盆地中长非线性传播波的渐近学
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040143
D.S. Minenkov, M.M. Votiakova
{"title":"Asymptotics of Long Nonlinear Propagating Waves in a One-Dimensional Basin with Gentle Shores","authors":"D.S. Minenkov,&nbsp;M.M. Votiakova","doi":"10.1134/S1061920823040143","DOIUrl":"10.1134/S1061920823040143","url":null,"abstract":"<p> The Cauchy problem for a one-dimensional (nonlinear) shallow water equations over a variable bottom <span>(D(x))</span> is considered in an extended basin bounded from two sides by shores (where the bottom degenerates, <span>(D(a)=0)</span>), or by a shore and a wall. The short-wave asymptotics of the linearized system in the form of a propagating localized wave is constructed. After applying to the constructed functions a simple parametric or explicit change of variables proposed in recent papers (Dobrokhotov, Minenkov, Nazaikinsky, 2022 and Dobrokhotov, Kalinichenko, Minenkov, Nazaikinsky, 2023), we obtain the asymptotics of the original nonlinear problem. On the constructed families of functions, the ratio of the amplitude and the wavelength is studied for which hte wave does not collapse when running up to the shore. </p><p> <b> DOI</b> 10.1134/S1061920823040143 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"621 - 642"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056586","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
Elementary Differential Singularities of Three-Dimensional Nijenhuis Operators 三维尼延胡斯算子的初等微分奇异性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040015
D. Akpan, A. Oshemkov
{"title":"Elementary Differential Singularities of Three-Dimensional Nijenhuis Operators","authors":"D. Akpan,&nbsp;A. Oshemkov","doi":"10.1134/S1061920823040015","DOIUrl":"10.1134/S1061920823040015","url":null,"abstract":"<p> In the paper, three-dimensional Nijenhuis operators are studied that have differential singularities, i.e., such points at which the coefficients of the characteristic polynomials are dependent. The case is studied in which the differentials of all invariants of the Nijenhuis operator are proportional, as well as the case when two invariants are functionally independent and the third defines a fold-type singularity. In particular, new examples of three-dimensional Nijenhuis operators with singularities of the specified type are constructed. </p><p> <b> DOI</b> 10.1134/S1061920823040015 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"425 - 431"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056778","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
Lie’s Theorem for Solvable Connected Lie Groups Without the Continuity Assumption 无连续性假设的可解连通李群的李氏定理
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040180
A. I. Shtern
{"title":"Lie’s Theorem for Solvable Connected Lie Groups Without the Continuity Assumption","authors":"A. I. Shtern","doi":"10.1134/S1061920823040180","DOIUrl":"10.1134/S1061920823040180","url":null,"abstract":"<p> It is proved that if <span>(G)</span> is a connected solvable group and <span>(pi)</span> is a (not necessarily continuous) representation of <span>(G)</span> in a finite-dimensional vector space <span>(E)</span>, then there is a basis in <span>(E)</span> in which the matrices of the representation operators of <span>(pi)</span> have upper triangular form. The assertion is extended to connected solvable locally compact groups <span>(G)</span> having a connected normal subgroup for which the quotient group is a Lie group. </p><p> <b> DOI</b> 10.1134/S1061920823040180 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"701 - 703"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056387","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
Probabilistic Degenerate Bell Polynomials Associated with Random Variables 与随机变量相关的概率退化贝尔多项式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S106192082304009X
T. Kim, D. S. Kim
{"title":"Probabilistic Degenerate Bell Polynomials Associated with Random Variables","authors":"T. Kim,&nbsp;D. S. Kim","doi":"10.1134/S106192082304009X","DOIUrl":"10.1134/S106192082304009X","url":null,"abstract":"<p> The aim of this paper is to study probabilistic versions of the degenerate Stirling numbers of the second kind and the degenerate Bell polynomials, namely the probabilisitc degenerate Stirling numbers of the second kind associated with <span>(Y)</span> and the probabilistic degenerate Bell polynomials associated with <span>(Y)</span>, which are also degenerate versions of the probabilisitc Stirling numbers of the second and the probabilistic Bell polynomials considered earlier. Here <span>(Y)</span> is a random variable whose moment generating function exists in some neighborhood of the origin. We derive some properties, explicit expressions, certain identities and recurrence relations for those numbers and polynomials. In addition, we treat the special cases that <span>(Y)</span> is the Poisson random variable with parameter <span>(alpha (&gt;0))</span> and the Bernoulli random variable with probability of success <span>(p)</span>. </p><p> <b> DOI</b> 10.1134/S106192082304009X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"528 - 542"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056429","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
Flow Around a Curved Plate with Small Periodic Irregularities: a Double-Deck Boundary Layer 小周期不规则曲面板周围的流动：双层边界层
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040040
V. G. Danilov, A. M. Glazunova
{"title":"Flow Around a Curved Plate with Small Periodic Irregularities: a Double-Deck Boundary Layer","authors":"V. G. Danilov,&nbsp;A. M. Glazunova","doi":"10.1134/S1061920823040040","DOIUrl":"10.1134/S1061920823040040","url":null,"abstract":"<p> In this paper, equations describing a double-dimensional flow along a curved smooth plate with small periodic irregularities are derived. The parameters of the irregularities are chosen so that the flow has a double-deck structure. The equations describing the terms of the asymptotic solution are written in the original coordinate system, which required changes in the form of the usual ansatz. </p><p> <b> DOI</b> 10.1134/S1061920823040040 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"453 - 465"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056511","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
The Mean Square of the Pauli–Jordan–Dirac Anticommutator With Respect to Spatial Variables 相对于空间变量的保利-乔丹-狄拉克反调和器均方差
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S1061920823040088
E.A. Karatsuba
{"title":"The Mean Square of the Pauli–Jordan–Dirac Anticommutator With Respect to Spatial Variables","authors":"E.A. Karatsuba","doi":"10.1134/S1061920823040088","DOIUrl":"10.1134/S1061920823040088","url":null,"abstract":"<p> The Pauli–Jordan–Dirac anticommutator mean-square formula is presented. </p><p> <b> DOI</b> 10.1134/S1061920823040088 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"522 - 527"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056561","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
Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems 周期性双曲系统同质化的特洛特-卡托定理主题变奏曲
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-12-25 DOI: 10.1134/S106192082304012X
Yu.M. Meshkova
{"title":"Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems","authors":"Yu.M. Meshkova","doi":"10.1134/S106192082304012X","DOIUrl":"10.1134/S106192082304012X","url":null,"abstract":"<p> In <span>(L_2(mathbb{R}^d;mathbb{C}^n))</span>, we consider a matrix elliptic second order differential operator <span>(B_varepsilon &gt;0)</span>. Coefficients of the operator <span>(B_varepsilon)</span> are periodic with respect to some lattice in <span>(mathbb{R}^d)</span> and depend on <span>(mathbf{x}/varepsilon)</span>. We study the quantitative homogenization for the solutions of the hyperbolic system <span>(partial _t^2mathbf{u}_varepsilon =-B_varepsilonmathbf{u}_varepsilon)</span>. In operator terms, we are interested in approximations of the operators <span>(cos (tB_varepsilon ^{1/2}))</span> and <span>(B_varepsilon ^{-1/2}sin (tB_varepsilon ^{1/2}))</span> in suitable operator norms. Approximations for the resolvent <span>(B_varepsilon ^{-1})</span> have been already obtained by T.A. Suslina. So, we rewrite hyperbolic equation as a system for the vector with components <span>(mathbf{u}_varepsilon )</span> and <span>(partial _tmathbf{u}_varepsilon)</span>, and consider the corresponding unitary group. For this group, we adapt the proof of the Trotter-Kato theorem by introduction of some correction term and derive hyperbolic results from elliptic ones. </p><p> <b> DOI</b> 10.1134/S106192082304012X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"561 - 598"},"PeriodicalIF":1.7,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139056390","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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