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Real Submanifolds of (mathbf{C}^2) With Singularities 具有奇点的(mathbf{C}^2)的实子流形
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030020
V. K. Beloshapka
{"title":"Real Submanifolds of (mathbf{C}^2) With Singularities","authors":"V. K. Beloshapka","doi":"10.1134/S1061920823030020","DOIUrl":"10.1134/S1061920823030020","url":null,"abstract":"<p> We consider real submanifolds of <span>(mathbf{C}^2)</span> with singularities of three types: <span>(RC)</span>-singular 2 - dimensional surfaces, real quadratic cones, and hypersurfaces with degeneration of the Levi form. The holomorphic automorphisms of singular germs are evaluated. We also discuss resolution of singularities in the context of <span>(mathit{CR})</span> geometry. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"280 - 293"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235145","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
Localized Waves Propagating Along an Angular Junction of Two Thin Semi-Infinite Elastic Membranes Terminating an Acoustic Medium 沿两个半无限薄弹性膜的角交界处传播的局域波终止于声介质
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030068
M. A. Lyalinov
{"title":"Localized Waves Propagating Along an Angular Junction of Two Thin Semi-Infinite Elastic Membranes Terminating an Acoustic Medium","authors":"M. A. Lyalinov","doi":"10.1134/S1061920823030068","DOIUrl":"10.1134/S1061920823030068","url":null,"abstract":"<p> We study the existence of localized waves that can propagate in an acoustic medium bounded by two thin semi-infinite elastic membranes along their common edge. The membranes terminate an infinite wedge that is filled by the medium, and are rigidly connected at the points of their common edge. The acoustic pressure of the medium in the wedge satisfies the Helmholtz equation and the third-order boundary conditions on the bounding membranes as well as the other appropriate conditions like contact conditions at the edge. The existence of such localized waves is equivalent to existence of the discrete spectrum of a semi-bounded self-adjoint operator attributed to this problem. In order to compute the eigenvalues and eigenfunctions, we make use of an integral representation (of the Sommerfeld type) for the solutions and reduce the problem to functional equations. Their nontrivial solutions from a relevant class of functions exist only for some values of the spectral parameter. The asymptotics of the solutions (eigenfunctions) is also addressed. The far-zone asymptotics contains exponentially vanishing terms. The corresponding solutions exist only for some specific range of physical and geometrical parameters of the problem at hand. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"345 - 359"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235128","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
Whitney–Sullivan Constructions for Transitive Lie Algebroids–Smooth Case 传递李代数群的Whitney-Sullivan构造-光滑情况
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S106192082303007X
A. S. Mishchenko, J. R. Oliveira
{"title":"Whitney–Sullivan Constructions for Transitive Lie Algebroids–Smooth Case","authors":"A. S. Mishchenko,&nbsp;J. R. Oliveira","doi":"10.1134/S106192082303007X","DOIUrl":"10.1134/S106192082303007X","url":null,"abstract":"<p> Let <span>(M)</span> be a smooth manifold, smoothly triangulated by a simplicial complex <span>(K)</span>, and <span>( {cal A} )</span> a transitive Lie algebroid on <span>(M)</span>. A piecewise smooth form on <span>( {cal A} )</span> is a family <span>(omega=(omega_{Delta})_{Deltain K})</span> such that <span>(omega_{Delta})</span> is a smooth form on the Lie algebroid restriction of <span>( {cal A} )</span> to <span>(Delta)</span>, satisfying the compatibility condition concerning the restrictions of <span>(omega_{Delta})</span> to the faces of <span>(Delta)</span>, that is, if <span>(Delta')</span> is a face of <span>(Delta)</span>, the restriction of the form <span>(omega_{Delta})</span> to the simplex <span>(Delta')</span> coincides with the form <span>(omega_{Delta'})</span>. The set <span>(Omega^{ast}( {cal A} ;K))</span> of all piecewise smooth forms on <span>( {cal A} )</span> is a cochain algebra. There exists a natural morphism </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"360 - 374"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233944","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
Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition 具有奇异摄动Neumann边界条件的奇异摄动积分微分方程的边值问题
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030081
N. N. Nefedov, A. G. Nikitin, E. I. Nikulin
{"title":"Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition","authors":"N. N. Nefedov,&nbsp;A. G. Nikitin,&nbsp;E. I. Nikulin","doi":"10.1134/S1061920823030081","DOIUrl":"10.1134/S1061920823030081","url":null,"abstract":"<p> We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its asymptotic approximation, and establish its asymptotic Lyapunov stability. Illustrative examples are given. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"375 - 381"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233950","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
Miura Type Transform Between Non-Abelian Volterra and Toda Lattices and Inverse Spectral Problem for Band Operators 非阿贝尔Volterra格与Toda格之间的Miura型变换及带算子的逆谱问题
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030093
A. Osipov
{"title":"Miura Type Transform Between Non-Abelian Volterra and Toda Lattices and Inverse Spectral Problem for Band Operators","authors":"A. Osipov","doi":"10.1134/S1061920823030093","DOIUrl":"10.1134/S1061920823030093","url":null,"abstract":"<p> We study a discrete Miura-type transformation between the hierarcies of non-Abelian semi-infinite Volterra (Kac–van Moerbeke) and Toda lattices with operator coefficients in terms of the inverse spectral problem for three-diagonal band operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments of its Weyl operator-valued function, can be used in solving initial-boundary value problem for the systems of both these hierarchies. It is shown that the Miura transformation can be easily described in terms of these moments. Using this description we establish a bijection between the Volterra hierarchy and the Toda sub-hierarchy which can be characterized via Lax operators corresponding to its lattices. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"382 - 396"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233951","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
Darwin’s Algorithms 达尔文的算法
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030123
Yu. N. Zhuravlev, M. A. Guzev
{"title":"Darwin’s Algorithms","authors":"Yu. N. Zhuravlev,&nbsp;M. A. Guzev","doi":"10.1134/S1061920823030123","DOIUrl":"10.1134/S1061920823030123","url":null,"abstract":"<p> An algorithmic concept of the physical world is proposed in which the main ideas of the Darwinian evolution act as algorithms of becoming. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"418 - 424"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233953","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 Resonance Problem for Jacobi Operators on a Half-Lattice 半格上Jacobi算子的反共振问题
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030056
E. Korotyaev, E. Leonova
{"title":"Inverse Resonance Problem for Jacobi Operators on a Half-Lattice","authors":"E. Korotyaev,&nbsp;E. Leonova","doi":"10.1134/S1061920823030056","DOIUrl":"10.1134/S1061920823030056","url":null,"abstract":"<p> We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real and complex resonances. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"320 - 344"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4230931","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
Reflexivity for Spaces With Extended Norm 扩展范数空间的自反性
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030111
I. G. Tsar’kov
{"title":"Reflexivity for Spaces With Extended Norm","authors":"I. G. Tsar’kov","doi":"10.1134/S1061920823030111","DOIUrl":"10.1134/S1061920823030111","url":null,"abstract":"<p> An analogue of reflexivity in asymmetric cone spaces is introduced and studied. Some classical results known for ordinary normalized spaces are carried over to the case of essentially asymmetric spaces. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"399 - 417"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4233952","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
Normal Ordering Associated with (lambda)-Whitney Numbers of the First Kind in (lambda)-Shift Algebra 与(lambda) -移位代数中第一类(lambda) -Whitney数相关的正常排序
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S1061920823030044
D. S. Kim, T. K. Kim
{"title":"Normal Ordering Associated with (lambda)-Whitney Numbers of the First Kind in (lambda)-Shift Algebra","authors":"D. S. Kim,&nbsp;T. K. Kim","doi":"10.1134/S1061920823030044","DOIUrl":"10.1134/S1061920823030044","url":null,"abstract":"<p> It is known that the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra. The aim of this paper is to consider the <span>(lambda)</span>-shift algebra, which is a <span>(lambda)</span>-analogue of the shift algebra, and to study <span>(lambda)</span>-analogues of Whitney numbers of the first kind (called <span>(lambda)</span>-Whitney numbers of the first kind) and those of <span>(r)</span>-Whitney numbers of the first kind arising from normal orderings in the <span>(lambda)</span>-shift algebra. From the normal orderings in the <span>(lambda)</span>-shift algebra, we derive some explicit expressions and recurrence relations on both of those numbers. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"310 - 319"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4235147","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 Discontinuity Group of a Locally Bounded Homomorphism of a Connected Lie Group into a Connected Lie Group Is Commutative 连通李群局部有界同态成连通李群的不连续群是可交换的
IF 1.4 3区 物理与天体物理
Russian Journal of Mathematical Physics Pub Date : 2023-09-05 DOI: 10.1134/S106192082303010X
A. I. Shtern
{"title":"The Discontinuity Group of a Locally Bounded Homomorphism of a Connected Lie Group into a Connected Lie Group Is Commutative","authors":"A. I. Shtern","doi":"10.1134/S106192082303010X","DOIUrl":"10.1134/S106192082303010X","url":null,"abstract":"<p> We prove that the discontinuity group of every locally bounded homomorphism of a Lie group into a Lie group is not only compact and connected, which is known, but also commutative. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 3","pages":"397 - 398"},"PeriodicalIF":1.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4232891","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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