Doklady Mathematics最新文献_第7页

On Kernels of Invariant Schrödinger Operators with Point Interactions. Grinevich–Novikov Conjecture 论具有点相互作用的薛定谔不变算子的核。格里涅维奇-诺维科夫猜想

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-05-02 DOI: 10.1134/S1064562424701904

M. M. Malamud, V. V. Marchenko

{"title":"On Kernels of Invariant Schrödinger Operators with Point Interactions. Grinevich–Novikov Conjecture","authors":"M. M. Malamud, V. V. Marchenko","doi":"10.1134/S1064562424701904","DOIUrl":"10.1134/S1064562424701904","url":null,"abstract":"According to Berezin and Faddeev, a Schrödinger operator with point interactions –Δ + (sumlimits_{j = 1}^m {{alpha }_{j}}delta (x - {{x}_{j}}),X = { {{x}_{j}}} _{1}^{m} subset {{mathbb{R}}^{3}},{ {{alpha }_{j}}} _{1}^{m} subset mathbb{R},) is any self-adjoint extension of the restriction ({{Delta }_{X}}) of the Laplace operator ( - Delta ) to the subset ({ f in {{H}^{2}}({{mathbb{R}}^{3}}):f({{x}_{j}}) = 0,;1 leqslant j leqslant m} ) of the Sobolev space ({{H}^{2}}({{mathbb{R}}^{3}})). The present paper studies the extensions (realizations) invariant under the symmetry group of the vertex set (X = { {{x}_{j}}} _{1}^{m}) of a regular m-gon. Such realizations HB are parametrized by special circulant matrices (B in {{mathbb{C}}^{{m times m}}}). We describe all such realizations with non-trivial kernels. А Grinevich–Novikov conjecture on simplicity of the zero eigenvalue of the realization HB with a scalar matrix (B = alpha I) and an even m is proved. It is shown that for an odd m non-trivial kernels of all realizations HB with scalar (B = alpha I) are two-dimensional. Besides, for arbitrary realizations ((B ne alpha I)) the estimate (dim (ker {{{mathbf{H}}}_{B}}) leqslant m - 1) is proved, and all invariant realizations of the maximal dimension (dim (ker {{{mathbf{H}}}_{B}}) = m - 1) are described. One of them is the Krein realization, which is the minimal positive extension of the operator ({{Delta }_{X}}).","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 2","pages":"125 - 129"},"PeriodicalIF":0.5,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Induced Forests and Trees in Erdős–Rényi Random Graph 厄尔多斯-雷尼随机图中的诱导森林和树

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-05-02 DOI: 10.1134/S1064562424701886

M. B. Akhmejanova, V. S. Kozhevnikov

引用次数: 0

A Joint Logic of Problems and Propositions 问题与命题的联合逻辑

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-05-02 DOI: 10.1134/S1064562424701916

S. A. Melikhov

引用次数: 0

Exact Estimates of Functions in Sobolev Spaces with Uniform Norm 具有统一规范的索波列夫空间中函数的精确估算

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424701862

D. D. Kazimirov, I. A. Sheipak

引用次数: 0

TOMMANO—Virtualised Network Functions Management in Cloud Environment based on the TOSCA Standard TOMMANO--基于 TOSCA 标准的云环境中的虚拟化网络功能管理

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424701850

R. K. Stolyarov, V. V. Shvetcova, O. D. Borisenko

{"title":"TOMMANO—Virtualised Network Functions Management in Cloud Environment based on the TOSCA Standard","authors":"R. K. Stolyarov, V. V. Shvetcova, O. D. Borisenko","doi":"10.1134/S1064562424701850","DOIUrl":"10.1134/S1064562424701850","url":null,"abstract":"Since 2012 NFV (Network Functions Virtualisation) technology has evolved significantly and became widespread. Before the advent of this technology, proprietary network devices had to be used to process traffic. NFV technology allows you to simplify the configuration of network functions and reduce the cost of traffic processing by using software modules running on completely standard datacenter servers (in virtual machines). However, deploying and maintaining virtualised network functions (such as firewall, NAT, spam filter, access speed restriction) in the form of software components, changing the configurations of these components, and manually configuring traffic routing are still complicated operations. The problems described exist due to the huge number of network infrastructure components and differences in the functionality of chosen software, network operating systems and cloud platforms. In particular, the problem is relevant for the biomedical data analysis platform of the world-class Scientific Center of Sechenov University. In this article, we propose a solution to this problem by creating a framework TOMMANO that allows you to automate the deployment of virtualised network functions on virtual machines in cloud environments. It converts OASIS TOSCA [5, 6] declarative templates in notation corresponding to the ETSI MANO [2] for NFV standard into normative TOSCA templates and sets of Ansible scripts. Using these outputs an application containing virtualised network functions can be deployed by the TOSCA orchestrator in any cloud environment it supports. The developed TOMMANO framework received a certificate of state registration of the computer program no. 2023682112 dated October 23, 2023. In addition, this article provides an example of using this framework for the automatic deployment of network functions. In this solution Cumulus VX is used as the provider operating system of network functions. Clouni is used as an orchestrator. Openstack is used as a cloud provider.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 1","pages":"84 - 92"},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140625746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Topological Product of Modal Logics with the McKinsey Axiom 模态逻辑的拓扑积与麦肯锡公理

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424701825

A. V. Kudinov

引用次数: 0

Two-Dimensional Self-Trapping Structures in Three-Dimensional Space 三维空间中的二维自陷结构

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424701837

V. O. Manturov, A. Ya. Kanel-Belov, S. Kim, F. K. Nilov

{"title":"Two-Dimensional Self-Trapping Structures in Three-Dimensional Space","authors":"V. O. Manturov, A. Ya. Kanel-Belov, S. Kim, F. K. Nilov","doi":"10.1134/S1064562424701837","DOIUrl":"10.1134/S1064562424701837","url":null,"abstract":"It is known that a finite set of convex figures on the plane with disjoint interiors has at least one outermost figure, i.e., one that can be continuously moved “to infinity” (outside a large circle containing the other figures), while the other figures are left stationary and their interiors are not crossed during the movement. It has been discovered that, in three-dimensional space, there exists a phenomenon of self-trapping structures. A self-trapping structure is a finite (or infinite) set of convex bodies with non-intersecting interiors, such that if all but one body are fixed, that body cannot be “carried to infinity.” Since ancient times, existing structures have been based on the consideration of layers made of cubes, tetrahedra, and octahedra, as well as their variations. In this work, we consider a fundamentally new phenomenon of two-dimensional self-trapping structures: a set of two-dimensional polygons in three-dimensional space, where each polygonal tile cannot be carried to infinity. Thin tiles are used to assemble self-trapping decahedra, from which second-order structures are then formed. In particular, a construction of a column composed of decahedra is presented, which is stable when we fix two outermost decahedra, rather than the entire boundary of the layer, as in previously investigated structures.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 1","pages":"73 - 79"},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140625748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Finding the Area and Perimeter Distributions for Flat Poisson Processes of a Straight Line and Voronoi Diagrams 求直线和沃罗诺图平面泊松过程的面积和周长分布

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424701801

A. Ya. Kanel-Belov, M. Golafshan, S. G. Malev, R. P. Yavich

{"title":"Finding the Area and Perimeter Distributions for Flat Poisson Processes of a Straight Line and Voronoi Diagrams","authors":"A. Ya. Kanel-Belov, M. Golafshan, S. G. Malev, R. P. Yavich","doi":"10.1134/S1064562424701801","DOIUrl":"10.1134/S1064562424701801","url":null,"abstract":"The study of distribution functions (with respect to areas, perimeters) for partitioning a plane (space) by a random field of straight lines (hyperplanes) and for obtaining Voronoi diagrams is a classical problem in statistical geometry. Moments for such distributions have been investigated since 1972 [1]. We give a complete solution of these problems for the plane, as well as for Voronoi diagrams. The following problems are solved: 1. A random set of straight lines is given on the plane, all shifts are equiprobable, and the distribution law has the form (F(varphi ).) What is the area (perimeter) distribution of the parts of the partition? 2. A random set of points is marked on the plane. Each point A is associated with a “region of attraction,” which is a set of points on the plane to which A is the closest of the marked set. The idea is to interpret a random polygon as the evolution of a segment on a moving one and construct kinetic equations. It is sufficient to take into account a limited number of parameters: the covered area (perimeter), the length of the segment, and the angles at its ends. We show how to reduce these equations to the Riccati equation using the Laplace transform.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 1","pages":"56 - 61"},"PeriodicalIF":0.5,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140625626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Orbital Stability of Pendulum Motions of a Rigid Body in the Hess Case 论海斯情况下刚体摆动运动的轨道稳定性

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424701795

B. S. Bardin, A. A. Savin

引用次数: 0

On Reconstruction of Kolmogorov Operators with Discontinuous Coefficients 论具有不连续系数的柯尔莫哥洛夫算子的重构

IF 0.5 4区数学

Doklady Mathematics Pub Date : 2024-04-18 DOI: 10.1134/S1064562424600052

V. I. Bogachev, S. V. Shaposhnikov

引用次数: 0