Russian Journal of Mathematical Physics最新文献_第6页

(mathbb{Z}_{2}-)Graded Lie Algebra of Quaternions and Superconformal Algebra in (D=4) Dimensions $$D=4$$ 维中的 $$mathbb{Z}_{2}-$$ 梯度四元数列代数和超共形代数

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S106192082402002X

B. C. S. Chauhan, P.K. Joshi, B.C. Chanyal

{"title":"(mathbb{Z}_{2}-)Graded Lie Algebra of Quaternions and Superconformal Algebra in (D=4) Dimensions","authors":"B. C. S. Chauhan, P.K. Joshi, B.C. Chanyal","doi":"10.1134/S106192082402002X","DOIUrl":"10.1134/S106192082402002X","url":null,"abstract":" In the present discussion, we have studied the (mathbb{Z}_{2}-)(grading) of the quaternion algebra ((mathbb{H})). We have made an attempt to extend the quaternion Lie algebra to the graded Lie algebra by using the matrix representations of quaternion units. The generalized Jacobi identities of (mathbb{Z}_{2}-graded) algebra then result in symmetric graded partners ((N_{1},N_{2},N_{3})). The graded partner algebra ((mathcal{F})) of quaternions ((mathbb{H})) thus has been constructed from this complete set of graded partner units ((N_{1},N_{2},N_{3})), and (N_{0}=C). Keeping in view the algebraic properties of the graded partner algebra ((mathcal{F})), the (mathbb{Z}_{2}-graded) superspace ((S^{l,m})) of quaternion algebra ((mathbb{H})) has been constructed. It has been shown that the antiunitary quaternionic supergroup (UU_{a}(l;m;mathbb{H})) describes the isometries of (mathbb{Z}_{2}-graded) superspace ((S^{l,m})). The Superconformal algebra in (D=4) dimensions is then established, where the bosonic sector of the Superconformal algebra has been constructed from the quaternion algebra ((mathbb{H})) and the fermionic sector from the graded partner algebra ((mathcal{F})): asymmetric space, convex set, (delta)-sun, (gamma)-sun. ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 2","pages":"162 - 176"},"PeriodicalIF":1.7,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504356","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}

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Asymptotics of the Solution of the Initial Boundary Value Problem for the One-Dimensional Klein–Gordon Equation with Variable Coefficients 具有可变系数的一维克莱因-戈登方程初始边界值问题解的渐近性

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020043

S.Yu. Dobrokhotov, E.S. Smirnova

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Natural Volume Forms on Pseudo-Finslerian Manifolds with (m)th Root Metrics 具有 $$m$$ th 根度量的伪芬斯勒方程上的自然体积形式

IF 1.7 3区物理与天体物理

Russian Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1134/S1061920824020146

A.V. Solov’yov

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Probabilistic Bernoulli and Euler Polynomials 概率伯努利和欧拉多项式

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/S106192084010072

T. Kim, D. S. Kim

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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}

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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}

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