Russian Journal of Mathematical Physics最新文献_第8页

Another Billiard Problem 另一个台球问题

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010047

S. Bolotin, D. Treschev

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On the Homogenization of Nonlocal Convolution Type Operators 论非局部卷积型算子的均质化

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010114

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

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On Perturbation of Thresholds in Essential Spectrum under Coexistence of Virtual Level and Spectral Singularity 论虚拟水平与频谱奇异性共存下本质频谱中的阈值扰动

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010059

D.I. Borisov, D.A. Zezyulin

{"title":"On Perturbation of Thresholds in Essential Spectrum under Coexistence of Virtual Level and Spectral Singularity","authors":"D.I. Borisov, D.A. Zezyulin","doi":"10.1134/S106192084010059","DOIUrl":"10.1134/S106192084010059","url":null,"abstract":" We study the perturbation of the Schrödinger operator on the plane with a bounded potential of the form (V_1(x)+V_2(y),) where (V_1) is a real function and (V_2) is a compactly supported function. It is assumed that the one-dimensional Schrödinger operator ( mathcal{H} _1) with the potential (V_1) has two real isolated eigenvalues ( Lambda _0,) ( Lambda _1) in the lower part of its spectrum, and the one-dimensional Schrödinger operator ( mathcal{H} _2) with the potential (V_2) has a virtual level at the boundary of its essential spectrum, i.e., at (lambda=0), and a spectral singularity at the inner point of the essential spectrum (lambda=mu>0). In addition, the eigenvalues and the spectral singularity overlap in the sense of the equality ( lambda _0:= Lambda _0+mu= Lambda _1.) We show that a perturbation by an abstract localized operator leads to a bifurcation of the internal threshold ( lambda _0) into four spectral objects which are resonances and/or eigenvalues. These objects correspond to the poles of the local meromorphic continuations of the resolvent. The spectral singularity of the operator ( mathcal{H} _2) qualitatively changes the structure of these poles as compared to the previously studied case where no spectral singularity was present. This effect is examined in detail, and the asymptotic behavior of the emerging poles and corresponding spectral objects of the perturbed Schrödinger operator is described. DOI 10.1134/S106192084010059 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"60 - 78"},"PeriodicalIF":1.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171672","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 (q)-Analog of the Quantum Theory of Angular Momentum: a Review from Special Functions 角动量量子理论的 $$q$$ 对应：特殊函数回顾

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010023

R. Álvarez-Nodarse, A. Arenas-Gómez

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On the Linearization of Certain Singularities of Nijenhuis Operators 论尼延胡斯算子某些奇点的线性化

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010084

A.Yu. Konyaev

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Analytical Complexity and Signal Coding 分析复杂性与信号编码

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010035

V.K. Beloshapka

{"title":"Analytical Complexity and Signal Coding","authors":"V.K. Beloshapka","doi":"10.1134/S106192084010035","DOIUrl":"10.1134/S106192084010035","url":null,"abstract":" There are two ways to describe a geometric object (L): the object as an image of a mapping and the object as a preimage. Every method has its own advantages and shortcomings; together, they give a complete picture. In order to compare these descriptions by complexity, one can use Kolmogorov’s approach: i.e., after the clarification of the system of basic operations, the complexity of a description is the minimum length of the defining text. Accordingly, we obtain two Kolmogorov complexities: in the first case, (K^{+}(L)), and in the other, (K^{-}(L)). Let (Cl^n) be the class of functions of two variables that can be represented by analytic functions of one variable and by the addition of the depth not exceeding (n), and let (K^{+}(Cl^n)) and (K^{-}(Cl^n)) be their corresponding Kolmogorov complexities. There are arguments in favor of the fact that, for (n geq 2), the value of (K^{-}(Cl^n)) is very large, and the task of constructing a description of (Cl^n) in the form of a preimage (by defining relations) even for (n=2) is computationally unrealizable. Based on this observation, a signal encoding-decoding scheme is proposed, and arguments are given in favor of the fact that the decoding of a signal encoded using such a scheme is inaccessible to a quantum computer. DOI 10.1134/S106192084010035 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"44 - 49"},"PeriodicalIF":1.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171664","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

Mapping Graph Homology to (K)-Theory of Roe Algebras 将图同调映射到 $$K$$ - Roe 算法理论

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010102

V. Manuilov

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Extension of Characters from the Radical of a Connected Lie Group to a One-Dimensional Pure Pseudorepresentation of the Group Revisited 从连通李群的辐射到该群的一维纯伪表示的字符扩展再探讨

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010126

A.I. Shtern

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Asymptotics of Long Nonlinear Coastal Waves in Basins with Gentle Shores 平缓海岸盆地中长非线性海岸波的渐近线

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010060

S.Yu. Dobrokhotov, D.S. Minenkov, M.M. Votiakova

{"title":"Asymptotics of Long Nonlinear Coastal Waves in Basins with Gentle Shores","authors":"S.Yu. Dobrokhotov, D.S. Minenkov, M.M. Votiakova","doi":"10.1134/S106192084010060","DOIUrl":"10.1134/S106192084010060","url":null,"abstract":" We construct asymptotic solutions of a special type for the nonlinear system of shallow water equations in two-dimensional basins with gentle shores and depth function (D(x)), where (x=(x_1,x_2)). These solutions represent waves localized near the shorelines (coastal waves) and generalize the (linear) Stokes and Ursell waves. The waves we consider are periodic or close to periodic in time. The corresponding asymptotic solutions are represented in a parametric form based on the modification of the Carrier–Greenspan transformation and are generated by asymptotic eigenfunctions (quasimodes) of the operator (hat{H} = -nablacdot(gD(x)nabla)), where (g) is the gravity acceleration. These eigenfunctions are, in general, related to the trajectories of a Hamiltonian system with the Hamiltonian (H = gD(x)(p_1^2+p_2^2)), which forms billiards with “semi-rigid walls.” In the general case, the existence of such billiards assumes the integrability condition that is practically impossible to be satisfied in real situations. However, we consider a “degenerate” situation where the trajectories are localized in a very narrow vicinity of the boundary (Gamma_0={D(x)=0}), and the asymptotic eigenfunctions resemble the well-known “whispering gallery” wave functions in acoustics. In this case, the requirement of integrability is eliminated (the corresponding billiard is “almost integrable” for the considered set of trajectories). One important difference between the problem we study and the classical whispering gallery situation is that, due to the degeneracy of the depth function (D(x)) on the boundary (Gamma_0), the trajectories are always normal to the boundary, and the requirement of convexity of the domain of the considered problem is absent. DOI 10.1134/S106192084010060 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"79 - 93"},"PeriodicalIF":1.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140171704","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

Bogoyavlensky Lattices and Generalized Catalan Numbers 博格雅夫林斯基网格和广义加泰罗尼亚数

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-03-19 DOI: 10.1134/S106192084010011

V.E. Adler

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