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On an Invariant of Pure Braids 论纯辫的不变量
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S1064562424701977
V. O. Manturov, I. M. Nikonov
{"title":"On an Invariant of Pure Braids","authors":"V. O. Manturov,&nbsp;I. M. Nikonov","doi":"10.1134/S1064562424701977","DOIUrl":"10.1134/S1064562424701977","url":null,"abstract":"<p>Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941156","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
Maximum Induced Trees in Sparse Random Graphs 稀疏随机图中的最大诱导树
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S1064562424701989
J. C. Buitrago Oropeza
{"title":"Maximum Induced Trees in Sparse Random Graphs","authors":"J. C. Buitrago Oropeza","doi":"10.1134/S1064562424701989","DOIUrl":"10.1134/S1064562424701989","url":null,"abstract":"<p>We prove that for any <span>(varepsilon &gt; 0)</span> and <span>({{n}^{{ - frac{{e - 2}}{{3e - 2}} + varepsilon }}} leqslant p = o(1))</span> the maximum size of an induced subtree of the binomial random graph <span>(G(n,p))</span> is concentrated asymptotically almost surely at two consecutive points.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941154","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
Continued Fractions in Hyperelliptic Fields with an Arbitrarily Long Period 具有任意长周期的超椭圆场中的连续分数
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S1064562424701928
V. P. Platonov, G. V. Fedorov
{"title":"Continued Fractions in Hyperelliptic Fields with an Arbitrarily Long Period","authors":"V. P. Platonov,&nbsp;G. V. Fedorov","doi":"10.1134/S1064562424701928","DOIUrl":"10.1134/S1064562424701928","url":null,"abstract":"<p>The article proves the following statement: in any hyperelliptic field <i>L</i> defined over the field of algebraic numbers <i>K</i> which having non-trivial units of the ring of integer elements of the field <i>L</i>, there is an element for which the period length of the continued fraction is greater any pre-given number.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941159","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
Invariants of Seventh-Order Homogeneous Dynamical Systems with Dissipation 带耗散的七阶均相动力系统的不变式
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S1064562424701941
M. V. Shamolin
{"title":"Invariants of Seventh-Order Homogeneous Dynamical Systems with Dissipation","authors":"M. V. Shamolin","doi":"10.1134/S1064562424701941","DOIUrl":"10.1134/S1064562424701941","url":null,"abstract":"<p>New cases of integrable seventh-order dynamical systems that are homogeneous with respect to some of the variables are presented, in which a system on the tangent bundle of a three-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external component, which has dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941211","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
Machine Learning to Control Network Powered by Computing Infrastructure 机器学习控制由计算基础设施驱动的网络
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S106456242470193X
R. L. Smeliansky, E. P. Stepanov
{"title":"Machine Learning to Control Network Powered by Computing Infrastructure","authors":"R. L. Smeliansky,&nbsp;E. P. Stepanov","doi":"10.1134/S106456242470193X","DOIUrl":"10.1134/S106456242470193X","url":null,"abstract":"<p>Machine learning (ML) methods are applied to optimal resource control for Network Powered by Computing Infrastructure (NPC)—a new generation computing infrastructure. The relation between the proposed computing infrastructure and the GRID concept is considered. It is shown how ML methods applied to computing infrastructure control make it possible to solve the problems of computing infrastructure control that did not allow the GRID concept to be implemented in full force. As an example, the application of multi-agent optimization methods with reinforcement learning for network resource management is considered. It is shown that multi-agent ML methods increase the speed of distribution of transport flows and ensure optimal NPC network channel load based on uniform load balancing; moreover, such control of network resources is more effective than a centralized approach.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941210","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 an Extremal Problem for Compactly Supported Positive Definite Functions 论紧凑支持正定函数的极值问题
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S1064562424701965
A. D. Manov
{"title":"On an Extremal Problem for Compactly Supported Positive Definite Functions","authors":"A. D. Manov","doi":"10.1134/S1064562424701965","DOIUrl":"10.1134/S1064562424701965","url":null,"abstract":"<p>An extremal problem for positive definite functions on <span>({{mathbb{R}}^{n}})</span> with a fixed support and a fixed value at the origin (the class <span>({{mathfrak{F}}_{r}}({{mathbb{R}}^{n}}))</span>) is considered. It is required to find the least upper bound for a special form functional over <span>({{mathfrak{F}}_{r}}({{mathbb{R}}^{n}}))</span>. This problem is a generalization of the Turán problem for functions with support in a ball. A general solution to this problem for <span>(n ne 2)</span> is obtained. As a consequence, new sharp inequalities are obtained for derivatives of entire functions of exponential spherical type.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941818","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
Generalized Solution of a Mixed Problem for the Wave Equation with a Nonsmooth Right-Hand Side 非光滑右边波方程混合问题的广义解法
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-02 DOI: 10.1134/S1064562424701898
I. S. Lomov
{"title":"Generalized Solution of a Mixed Problem for the Wave Equation with a Nonsmooth Right-Hand Side","authors":"I. S. Lomov","doi":"10.1134/S1064562424701898","DOIUrl":"10.1134/S1064562424701898","url":null,"abstract":"<p>A generalized solution of a mixed problem for the wave equation is constructed under minimal conditions on the right side of the equation. The solution is represented as a series from the Fourier method, and its sum is found. The form of a generalized solution of a mixed problem for an inhomogeneous telegraph equation is given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884543","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 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,&nbsp;V. V. Marchenko","doi":"10.1134/S1064562424701904","DOIUrl":"10.1134/S1064562424701904","url":null,"abstract":"<p>According to Berezin and Faddeev, a Schrödinger operator with point interactions –Δ + <span>(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},)</span> is any self-adjoint extension of the restriction <span>({{Delta }_{X}})</span> of the Laplace operator <span>( - Delta )</span> to the subset <span>({ f in {{H}^{2}}({{mathbb{R}}^{3}}):f({{x}_{j}}) = 0,;1 leqslant j leqslant m} )</span> of the Sobolev space <span>({{H}^{2}}({{mathbb{R}}^{3}}))</span>. The present paper studies the extensions (realizations) invariant under the symmetry group of the vertex set <span>(X = { {{x}_{j}}} _{1}^{m})</span> of a regular <i>m</i>-gon. Such realizations <b>H</b><sub><i>B</i></sub> are parametrized by special circulant matrices <span>(B in {{mathbb{C}}^{{m times m}}})</span>. We describe all such realizations with non-trivial kernels. А Grinevich–Novikov conjecture on simplicity of the zero eigenvalue of the realization <b>H</b><sub><i>B</i></sub> with a scalar matrix <span>(B = alpha I)</span> and an even <i>m</i> is proved. It is shown that for an odd <i>m</i> non-trivial kernels of all realizations <b>H</b><sub><i>B</i></sub> with scalar <span>(B = alpha I)</span> are two-dimensional. Besides, for arbitrary realizations <span>((B ne alpha I))</span> the estimate <span>(dim (ker {{{mathbf{H}}}_{B}}) leqslant m - 1)</span> is proved, and all invariant realizations of the maximal dimension <span>(dim (ker {{{mathbf{H}}}_{B}}) = m - 1)</span> are described. One of them is the Krein realization, which is the minimal positive extension of the operator <span>({{Delta }_{X}})</span>.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"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
{"title":"Induced Forests and Trees in Erdős–Rényi Random Graph","authors":"M. B. Akhmejanova,&nbsp;V. S. Kozhevnikov","doi":"10.1134/S1064562424701886","DOIUrl":"10.1134/S1064562424701886","url":null,"abstract":"<p>We prove that the size of the maximum induced forest (of bounded and unbounded degree) in the binomial random graph <span>(G(n,p))</span> for <span>({{C}_{varepsilon }}{text{/}}n &lt; p &lt; 1 - varepsilon )</span> with an arbitrary fixed <span>(varepsilon &gt; 0)</span> is concentrated in an interval of size <span>(o(1{text{/}}p))</span>. We also show 2-point concentration for the size of the maximum induced forest (and tree) of bounded degree in <span>(G(n,p))</span> for <i>p</i> = const.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884741","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
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
{"title":"A Joint Logic of Problems and Propositions","authors":"S. A. Melikhov","doi":"10.1134/S1064562424701916","DOIUrl":"10.1134/S1064562424701916","url":null,"abstract":"<p>In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper <i>On the interpretation of intuitionistic logic</i> “was written in hope that with time, the logic of solution of problems [i.e., intuitionistic logic] will become a permanent part of a [standard] course of logic. A unified logical apparatus was intended to be created, which would deal with objects of two types—propositions and problems.” We construct such a formal system as well as its predicate version, QHC, which is a conservative extension of both the intuitionistic predicate calculus QH and the classical predicate calculus QC. The axioms of QHC are obtained as a result of a simultaneous formalization of two well-known alternative explanations of intiuitionistic logic: (1) Kolmogorov’s problem interpretation (with familiar refinements by Heyting and Kreisel) and (2) the proof interpretation by Orlov and Heyting, as clarified and extended by Gödel.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140884550","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
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