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On Suspensions over Cartesian Products of Rough Transformations of the Circle 圆的粗糙变换的笛卡尔积上的悬架
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601794
E. Nozdrinova, O. Pochinka, V. Shmukler, S. Zinina
{"title":"On Suspensions over Cartesian Products of Rough Transformations of the Circle","authors":"E. Nozdrinova,&nbsp;O. Pochinka,&nbsp;V. Shmukler,&nbsp;S. Zinina","doi":"10.1134/S1061920824601794","DOIUrl":"10.1134/S1061920824601794","url":null,"abstract":"<p> One of the constructions for obtaining flows on a manifold is the construction of a suspension over a diffeomorphism. S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. The converse is not true in the general case. A classic illustration of this fact are examples of nonconjugate diffeomorphisms of a circle whose suspensions are equivalent. In this paper, we establish relations between the invariants of topological conjugacy of Cartesian products of rough transformations of a circle and the invariants of topological equivalence of suspensions over them. </p><p> <b> DOI</b> 10.1134/S1061920824601794 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"129 - 140"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908687","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
Index of Inönü–Wigner Contractions of Semisimple Lie Algebras 半单李代数的Inönü-Wigner缩约指标
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600199
D.A. Timashev
{"title":"Index of Inönü–Wigner Contractions of Semisimple Lie Algebras","authors":"D.A. Timashev","doi":"10.1134/S1061920825600199","DOIUrl":"10.1134/S1061920825600199","url":null,"abstract":"<p> We give an explicit formula for the index of a Lie algebra of the shape <span>( {mathfrak{g}} _0= {mathfrak{h}} oplus( {mathfrak{g}} / {mathfrak{h}} )^{ text{ab} })</span>, where <span>( {mathfrak{g}} )</span> is a semisimple Lie algebra, <span>( {mathfrak{h}} )</span> is a subalgebra in <span>( {mathfrak{g}} )</span> regarded as a subalgebra in <span>( {mathfrak{g}} _0)</span>, and <span>(( {mathfrak{g}} / {mathfrak{h}} )^{ text{ab} })</span> is an <span>( {mathfrak{h}} )</span>-module <span>( {mathfrak{g}} / {mathfrak{h}} )</span> regarded as an Abelian ideal of <span>( {mathfrak{g}} _0)</span>. This formula has applications to Poisson commutative subalgebras in the symmetric algebra <span>( operatorname{S} ( {mathfrak{g}} ))</span> and to completely integrable systems. </p><p> <b> DOI</b> 10.1134/S1061920825600199 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"189 - 195"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908689","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
Efficient Semiclassical Asymptotics with Simple Caustics in a Boundary Value Problem 边值问题中具有简单焦散的有效半经典渐近性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600072
S.Yu. Dobrokhotov, V.E. Nazaikinskiih, A.V. Tsvetkova, A.V. Turin
{"title":"Efficient Semiclassical Asymptotics with Simple Caustics in a Boundary Value Problem","authors":"S.Yu. Dobrokhotov,&nbsp;V.E. Nazaikinskiih,&nbsp;A.V. Tsvetkova,&nbsp;A.V. Turin","doi":"10.1134/S1061920825600072","DOIUrl":"10.1134/S1061920825600072","url":null,"abstract":"<p> In this paper we continue to develop the approach to constructing global uniform asymptotics of solutions of (pseudo)differential problems in terms of special functions based on the theory of the Maslov canonical operator. In particular, we show that if the corresponding Lagrangian manifold has a fold-type singularity, then the canonical operator on it is represented via the Airy function Ai and its derivative of complex arguments. This approach is illustrated by a known problem about construction of asymptotic eigenfunctions of the Laplace operator in an elliptic domain with Dirichlet boundary conditions. </p><p> <b> DOI</b> 10.1134/S1061920825600072 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"28 - 43"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908684","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
Icosahedron in Birational Geometry 几何中的二十面体
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601800
Yu. Prokhorov
{"title":"Icosahedron in Birational Geometry","authors":"Yu. Prokhorov","doi":"10.1134/S1061920824601800","DOIUrl":"10.1134/S1061920824601800","url":null,"abstract":"<p> We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions. </p><p> <b> DOI</b> 10.1134/S1061920824601800 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"160 - 184"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908691","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
Conjugation Equation for Quaternionic Conjugation Spaces 四元数共轭空间的共轭方程
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920825600096
A. Kryazhev, D. Kuznetsov, Th. Popelensky
{"title":"Conjugation Equation for Quaternionic Conjugation Spaces","authors":"A. Kryazhev,&nbsp;D. Kuznetsov,&nbsp;Th. Popelensky","doi":"10.1134/S1061920825600096","DOIUrl":"10.1134/S1061920825600096","url":null,"abstract":"<p> There is a considerable collection of examples of spaces <span>(X)</span> equipped with an involution <span>(tau)</span> such that the mod 2-cohomology rings <span>(H^{2*}(X))</span> and <span>(H^*(X^tau))</span> are isomorphic. In [4], it was shown that such an isomorphism is a part of a certain structure on the equivariant cohomology of <span>(X)</span> and <span>(X^tau)</span>, which is called an <span>(H)</span><i>-frame</i>. An important part of the <span>(H)</span>-frame structure in [4] was the so-called <i> conjugation equation</i>. In [3], the coefficients of the conjugation equation were calculated in terms of the Steenrod squares. Later, another proofs were obtained, [9, 10]. In this paper, we develop a similar notion of a <span>(Q)</span>-framing, which occurs in the situation when a space <span>(X)</span> is equipped with two commuting involutions <span>(tau_1,tau_2)</span> and the mod 2-cohomology rings <span>(H^{4*}(X))</span> and <span>(H^*(X^{tau_1,tau_2}))</span> are isomorphic. Basic examples are the quaternionic Grassmannians and the quaternionic flag manifolds equipped with two complex involutions. Our main result is the establishment of the quaternionic conjugation equations and identifying their coefficients in terms of Steenrod operations. </p><p> <b> DOI</b> 10.1134/S1061920825600096 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"105 - 122"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908688","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
Spatial Decay/Asymptotics in the Navier–Stokes Equation Navier-Stokes方程的空间衰减/渐近性
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1134/S1061920824601812
P. Topalov
{"title":"Spatial Decay/Asymptotics in the Navier–Stokes Equation","authors":"P. Topalov","doi":"10.1134/S1061920824601812","DOIUrl":"10.1134/S1061920824601812","url":null,"abstract":"<p> We discuss the occurrence of spatial asymptotic expansions of solutions to the Navier–Stokes equation on <span>( {mathbb{R}} ^d)</span>. In particular, we prove that the Navier–Stokes equation is locally well-posed in a class of weighted Sobolev and asymptotic spaces. The solutions depend analytically on the initial data and time and (generically) develop nontrivial asymptotic terms as <span>(|x|toinfty)</span>. In addition, the solutions have a spatial smoothing property that depends on the order of the asymptotic expansion. </p><p> <b> DOI</b> 10.1134/S1061920824601812 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"196 - 209"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908692","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 Laguerre Polynomials with Random Variables 随机变量的概率退化拉盖尔多项式
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040095
L. Luo, Y. Ma, T. Kim, W. Liu
{"title":"Probabilistic Degenerate Laguerre Polynomials with Random Variables","authors":"L. Luo,&nbsp;Y. Ma,&nbsp;T. Kim,&nbsp;W. Liu","doi":"10.1134/S1061920824040095","DOIUrl":"10.1134/S1061920824040095","url":null,"abstract":"<p> In this paper, we define the probabilistic degenerate Laguerre polynomials associated with random variables and the probabilistic degenerate generalized Laguerre polynomials associated with random variables. We investigate some expressions, recurrence relations, and properties associated with the probabilistic degenerate Laguerre polynomials, the probabilistic degenerate generalized Laguerre polynomials, the probabilistic Lah numbers, and the partial Bell polynomials. </p><p> <b> DOI</b> 10.1134/S1061920824040095 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"706 - 712"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1134/S1061920824040095.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Systems of Differential Equations for Determining the Fundamental Vector of Special Wave Catastrophes 确定特殊波浪灾害基本矢量的微分方程组
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040083
A.S. Kryukovsky, D.S. Lukin, D.V. Rastyagaev
{"title":"Systems of Differential Equations for Determining the Fundamental Vector of Special Wave Catastrophes","authors":"A.S. Kryukovsky,&nbsp;D.S. Lukin,&nbsp;D.V. Rastyagaev","doi":"10.1134/S1061920824040083","DOIUrl":"10.1134/S1061920824040083","url":null,"abstract":"<p> Uniform asymptotic solutions of the field structures in the vicinity of focusing based on the use of the Maslov canonical operator leads to investigation of special functions of wave catastrophe (SWC) and their first derivatives. The method for constructing a system of differential equations to determine the fundamental vector of special functions of wave catastrophes (SWC) is created. This approach allows us to reduce the solution of the problem of determining the SWCs and their derivatives to the solution of the Cauchy problem for a system of ordinary differential equations. The paper provides examples of the construction of such systems for special functions of edge catastrophes corresponding to Lagrange manifolds with boundary and special functions of main catastrophes corresponding to Lagrange manifolds without restrictions. </p><p> <b> DOI</b> 10.1134/S1061920824040083 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"691 - 705"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373285","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
Influence of Boundary Conditions on the Dynamic Properties of the Logistic Equation with Delay and Diffusion 边界条件对时滞扩散Logistic方程动力学性质的影响
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S106192082404006X
S.A. Kashchenko, D.O. Loginov
{"title":"Influence of Boundary Conditions on the Dynamic Properties of the Logistic Equation with Delay and Diffusion","authors":"S.A. Kashchenko,&nbsp;D.O. Loginov","doi":"10.1134/S106192082404006X","DOIUrl":"10.1134/S106192082404006X","url":null,"abstract":"<p> The logistic equation with delay and diffusion, which is important in mathematical ecology, is considered. It is assumed that the boundary conditions at either end of the interval [0,1] contain parameters. The problem of local dynamics, in a neighborhood of the equilibrium state, of the corresponding boundary value problem is investigated for all values of the boundary condition parameters. Critical cases are identified in the problem of stability of the equilibrium state and normal forms are constructed, which are scalar complex ordinary differential equations of the first order. Their nonlocal dynamics determines the behavior of solutions of the original problem in a small neighborhood of the equilibrium state. The problem of the role of asymptotically small values of the diffusion coefficient in the dynamics of the boundary value problems under consideration is studied separately. In particular, it is shown that boundary layer functions may arise when constructing asymptotic solutions in a neighborhood of the boundary points 0 and 1. </p><p> <b> DOI</b> 10.1134/S106192082404006X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"666 - 681"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373287","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
Real Semiclassical Approximation for the Asymptotics of Jacobi Polynomials Given by a Difference Equation 差分方程给出的雅可比多项式渐近的实半经典逼近
IF 1.7 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2025-02-09 DOI: 10.1134/S1061920824040162
A.V. Tsvetkova
{"title":"Real Semiclassical Approximation for the Asymptotics of Jacobi Polynomials Given by a Difference Equation","authors":"A.V. Tsvetkova","doi":"10.1134/S1061920824040162","DOIUrl":"10.1134/S1061920824040162","url":null,"abstract":"<p> The paper is devoted to constructing the global asymptotics of Jacobi polynomials by the method of “real semiclassics for problems with complex phases,тАЩтАЩ which is based on the study of recurrence relations. The method is based on the semiclassical approximation and the study of the geometry and types of singularities of the arising Lagrangian manifolds. While manifolds with a turning point in whose neighborhood the asymptotics is determined by the Airy function are well studied, the methods for the case in which the asymptotics is determined by the Bessel functions are not so well developed. In this paper, we demonstrate the application of the above-mentioned method in both situations, in particular, we describe the Lagrangian manifold that arises in the second case. </p><p> <b> DOI</b> 10.1134/S1061920824040162 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"774 - 784"},"PeriodicalIF":1.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373381","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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