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On Solvability in Gevrey Classes for the Cauchy Problem for an Equation with Weyl Fractional Derivative 一类带Weyl分数阶导数方程的Cauchy问题在Gevrey类中的可解性
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700127
S. A. Alimov
{"title":"On Solvability in Gevrey Classes for the Cauchy Problem for an Equation with Weyl Fractional Derivative","authors":"S. A. Alimov","doi":"10.1134/S1064562425700127","DOIUrl":"10.1134/S1064562425700127","url":null,"abstract":"<p>An alternative definition of Weyl fractional derivatives is given, and their effect on functions from Gevrey classes is studied. For a partial differential equation with Weyl derivatives, conditions for the solvability of the Cauchy problem in Gevrey classes are found.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"160 - 162"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706224","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 Certain Spanning Subgraphs of Random Graphs 关于随机图的若干生成子图
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700176
O. I. Serkova
{"title":"On Certain Spanning Subgraphs of Random Graphs","authors":"O. I. Serkova","doi":"10.1134/S1064562425700176","DOIUrl":"10.1134/S1064562425700176","url":null,"abstract":"<p>An improvement of Riordan’s result on the threshold probability of the occurrence of a spanning subgraph in a random graph is obtained for some classes of subgraphs. In particular, this result implies an improved bound for the maximum power of a Hamiltonian cycle in a random graph. Moreover, a sharp asymptotic threshold probability for a random graph to contain spanning subgraphs from a wide class of <span>(k)</span>-degenerate graphs is found.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"195 - 198"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706221","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
An Approach to Obtaining Perturbation Bounds for Continuous-Time Markov Chains 连续时间马尔可夫链摄动界的一种获取方法
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562424601410
A. I. Zeifman, I. A. Usov, Ya. A. Satin, A. L. Kryukova, V. Yu. Korolev
{"title":"An Approach to Obtaining Perturbation Bounds for Continuous-Time Markov Chains","authors":"A. I. Zeifman,&nbsp;I. A. Usov,&nbsp;Ya. A. Satin,&nbsp;A. L. Kryukova,&nbsp;V. Yu. Korolev","doi":"10.1134/S1064562424601410","DOIUrl":"10.1134/S1064562424601410","url":null,"abstract":"<p>Homogeneous Markov chains with continuous time are considered. A new approach is proposed that makes it possible to obtain accurate perturbation bounds for such chains with respect to perturbations of infinitesimal characteristics. It is shown how the results can be applied to stationary queuing systems of several classes and to some nonstationary systems.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"175 - 181"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706216","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
Algorithmic Properties of Basic Categorial Grammars with Unique Category Assignment 具有唯一类别分配的基本范畴语法的算法性质
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700188
M. E. Vishnikin
{"title":"Algorithmic Properties of Basic Categorial Grammars with Unique Category Assignment","authors":"M. E. Vishnikin","doi":"10.1134/S1064562425700188","DOIUrl":"10.1134/S1064562425700188","url":null,"abstract":"<p>This work examines basic categorial grammars and categorial grammars with the unique type assignment condition. For the first formalism, it is proven that determining for an arbitrary context-free language <span>(L)</span> whether it is generated by some grammar from this class is algorithmically undecidable. It is also proven that, for any two grammars of this class, the problem of determining the emptiness of the intersection of the languages generated by these grammars is algorithmically undecidable. For the second formalism, it is proven that, for any two categorial grammars with unique type assignment, the problem of determining language inclusion is algorithmically undecidable.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"167 - 171"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706225","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 Sizes of k-Subgraphs of the Binomial Random Graph 二项随机图的k-子图的大小
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700206
Yu. N. Yarovikov
{"title":"On the Sizes of k-Subgraphs of the Binomial Random Graph","authors":"Yu. N. Yarovikov","doi":"10.1134/S1064562425700206","DOIUrl":"10.1134/S1064562425700206","url":null,"abstract":"<p>Consider the set <span>(mathcal{E}(G,k))</span> of all sizes (numbers of edges) of induced subgraphs of size <i>k</i> in a given graph <span>(G)</span> on <span>(n)</span> vertices. For the binomial random graph <span>(G = G(n,p))</span>, we prove that, for each <span>(alpha &gt; 0)</span> and <span>(varepsilon )</span> small enough, the set <span>(mathcal{E}(G,k))</span> with high probability contains a long interval for all <i>k</i> such that <span>({{(ln n)}^{{1 + alpha }}} &lt; k &lt; varepsilon n)</span>. We also find the asymptotic length of this interval.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"199 - 201"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706222","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
Numerical Solution of Integro-Differential Equations of Viscoelasticity with Kernels of Exponential and Rabotnov Types 指数核和Rabotnov型粘弹性积分微分方程的数值解
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700164
I. B. Petrov, D. A. Prikazchikov, N. I. Khokhlov
{"title":"Numerical Solution of Integro-Differential Equations of Viscoelasticity with Kernels of Exponential and Rabotnov Types","authors":"I. B. Petrov,&nbsp;D. A. Prikazchikov,&nbsp;N. I. Khokhlov","doi":"10.1134/S1064562425700164","DOIUrl":"10.1134/S1064562425700164","url":null,"abstract":"<p>Differential equations describing the behavior of continuous media with creep involve integral type operators, in accordance with Volterra’s linear theory, which is applicable to a wide range of materials with amorphous and heterogeneous structures. In these equations, the kernel of the integral operator is represented as a sum of exponentials or as a weakly singular kernel (Rabotnov function). Obtaining an analytical solution for the equations in question is problematic in some cases, so it is necessary to develop a numerical method and algorithm, taking into account the memory of the considered medium. In this paper, the equations are solved using the grid-characteristic method and dimensional splitting (for multidimensional problems). The approximation and stability of the proposed method are numerically investigated.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"202 - 207"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706217","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 Numerical Solution of the Three-Dimensional Neumann Problem for the Helmholtz Equation Using the Potential Method 用势法数值解亥姆霍兹方程三维诺伊曼问题
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700218
A. A. Kashirin,  S. I. Smagin
{"title":"On the Numerical Solution of the Three-Dimensional Neumann Problem for the Helmholtz Equation Using the Potential Method","authors":"A. A. Kashirin,&nbsp; S. I. Smagin","doi":"10.1134/S1064562425700218","DOIUrl":"10.1134/S1064562425700218","url":null,"abstract":"<p>The three-dimensional exterior Neumann problem for the Helmholtz equation is considered. Using the potential method, we reduce it to a weakly singular boundary Fredholm integral equation of the second kind, which is solved numerically. To improve the accuracy of the numerical solution algorithm and to reduce its computational complexity, we average the kernel of the integral operator and localize its singular part during discretization by applying simple analytical expressions. Examples of using this approach in the numerical solution of the original problem are given.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"208 - 212"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706218","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
Modification of the Discontinuous Galerkin Method Using Time-Dependent Basis Functions 时变基函数对间断伽辽金法的修正
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700140
M. E. Ladonkina,  V. F. Tishkin
{"title":"Modification of the Discontinuous Galerkin Method Using Time-Dependent Basis Functions","authors":"M. E. Ladonkina,&nbsp; V. F. Tishkin","doi":"10.1134/S1064562425700140","DOIUrl":"10.1134/S1064562425700140","url":null,"abstract":"<p>In this paper, we propose a modification of the discontinuous Galerkin method using time-dependent basis functions. The use of such basis functions allows one to naturally and stably calculate strong discontinuities.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"182 - 188"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706226","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 Energy Integrals of a Mixed Problem for a B-Hyperbolic Equation 一类b -双曲型方程混合问题的能量积分
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700152
L. N. Lyakhov
{"title":"On Energy Integrals of a Mixed Problem for a B-Hyperbolic Equation","authors":"L. N. Lyakhov","doi":"10.1134/S1064562425700152","DOIUrl":"10.1134/S1064562425700152","url":null,"abstract":"<p>A mixed problem for a B-hyperbolic equation in Euclidean domains with different locations relative to singular coordinate hyperplanes is considered. In each of these domains, energy integrals with respect to the Lebesgue–Kipriyanov integral measure with weak and strong singularities are introduced. It is proved that there is no energy flow through the singular coordinate hyperplanes, which are the internal boundary of mirror-symmetric domains in Euclidean space. If solutions to these problems exist, their uniqueness is proved.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"189 - 194"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706227","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 Primary Submodules in Modules of Entire Functions That Are Dual to Spaces of Ω-Ultradifferentiable Functions 对Ω-Ultradifferentiable函数空间对偶的全函数模中的主子模
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-12-09 DOI: 10.1134/S1064562425700115
N. F. Abuzyarova, Z. Yu. Fazullin
{"title":"On Primary Submodules in Modules of Entire Functions That Are Dual to Spaces of Ω-Ultradifferentiable Functions","authors":"N. F. Abuzyarova,&nbsp;Z. Yu. Fazullin","doi":"10.1134/S1064562425700115","DOIUrl":"10.1134/S1064562425700115","url":null,"abstract":"<p>We consider weighted modules of entire functions that are dual to general spaces of <span>(Omega )</span>-ultradifferentiable functions. We explore the local description problem for primary submodules in these modules. It is shown that there exist primary submodules that are not weakly localizable. Nontrivial conditions are obtained under which a local description is possible. All assertions can be reformulated as equivalent dual ones concerning the spectral synthesis problem for differentiation-invariant subspaces of <span>(Omega )</span>-ultradifferentiable functions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 3","pages":"155 - 159"},"PeriodicalIF":0.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145706219","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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