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Applying A.G. Postnikov’s Formula in Algebraic Number Fields 在代数数域中应用 A.G. 波斯特尼科夫公式
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-20 DOI: 10.1134/S1064562424601185
Hafez Al-Assad
{"title":"Applying A.G. Postnikov’s Formula in Algebraic Number Fields","authors":"Hafez Al-Assad","doi":"10.1134/S1064562424601185","DOIUrl":"10.1134/S1064562424601185","url":null,"abstract":"<p>We present a new result on the generalisation of A.G. Postnikov’s formula to the case of powers of 2. This, together with the original work of A.G. Postnikov and some structural theorems on reduced residue systems modulo prime-power ideals, is used to obtain estimates for certain character sums in algebraic number fields.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509585","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
Sub-Lorentzian Geometry on the Martinet Distribution 马蒂内分布上的亚洛伦兹几何学
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-20 DOI: 10.1134/S1064562424702053
Yu. L. Sachkov
{"title":"Sub-Lorentzian Geometry on the Martinet Distribution","authors":"Yu. L. Sachkov","doi":"10.1134/S1064562424702053","DOIUrl":"10.1134/S1064562424702053","url":null,"abstract":"<p>Two problems of sub-Lorentzian geometry on the Martinet distribution are studied. For the first one, the reachable set has a nontrivial intersection with the Martinet plane, while a trivial intersection occurs for the second problem. Reachable sets, optimal trajectories, and sub-Lorentzian distances and spheres are described.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530063","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
Bernstein–Riemann Interpolation Formula for Arbitrary Continuous Functions on an Interval 区间上任意连续函数的伯恩斯坦-黎曼内插法公式
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-10 DOI: 10.1134/S1064562424702028
A. N. Agadzhanov
{"title":"Bernstein–Riemann Interpolation Formula for Arbitrary Continuous Functions on an Interval","authors":"A. N. Agadzhanov","doi":"10.1134/S1064562424702028","DOIUrl":"10.1134/S1064562424702028","url":null,"abstract":"<p>For arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on some uniform grid. No additional assumptions about the functions are required. The construction of such a formula is connected with the properties of local Bernstein polynomials and the Riemann zeta function. Numerical results for the interpolation of functions of the Riemann, Weierstrass, Besicovitch, and Takagi types are presented.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141362717","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 Quantitative Assessment of Chirality: Right- and Left-Handed Geometric Objects 关于手性的定量评估：左右手几何物体
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-10 DOI: 10.1134/S106456242470203X
Yu. A. Kriksin,  V. F. Tishkin
{"title":"On Quantitative Assessment of Chirality: Right- and Left-Handed Geometric Objects","authors":"Yu. A. Kriksin,&nbsp; V. F. Tishkin","doi":"10.1134/S106456242470203X","DOIUrl":"10.1134/S106456242470203X","url":null,"abstract":"<p>Two methods for quantitatively assessing the chirality of a set are considered. As a measure of the noncoincidence between two sets, one method uses the area of the symmetric difference between them, and the other, the Hausdorff distance between them. It is shown that these methods, generally speaking, do not provide a correct quantitative estimate for a fairly wide class of sets, such as bounded Borel sets. Using examples of flat triangles and convex quadrangles, we consider the problem of dividing geometric objects into right- and left-handed ones. For triangles, level lines of two versions of the chirality measure are calculated on the plane of angular parameters. For a spatial helix, the values of two versions of the chirality index are found by calculating the mixed product of vectors and the Hausdorff distance between two sets, respectively.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141361699","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 Boyarsky–Meyers Estimate for the Gradient of the Solution to the Dirichlet Problem for a Second-Order Linear Elliptic Equation with Drift: The Case of Critical Sobolev Exponent 论带漂移的二阶线性椭圆方程迪里夏特问题解梯度的博雅斯基-梅耶斯估计：临界索波列夫指数情况
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-10 DOI: 10.1134/S1064562424701990
Yu. A. Alkhutov, A. G. Chechkina
{"title":"On the Boyarsky–Meyers Estimate for the Gradient of the Solution to the Dirichlet Problem for a Second-Order Linear Elliptic Equation with Drift: The Case of Critical Sobolev Exponent","authors":"Yu. A. Alkhutov,&nbsp;A. G. Chechkina","doi":"10.1134/S1064562424701990","DOIUrl":"10.1134/S1064562424701990","url":null,"abstract":"<p>Increased integrability of the gradient of the solution to the homogeneous Dirichlet problem for the Poisson equation with lower terms in a bounded Lipschitz domain is established. The unique solvability of this problem is also proved.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141364372","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
Multi-vortices and Lower Bounds for the Attractor Dimension of 2D Navier–Stokes Equations 二维纳维-斯托克斯方程的多旋涡和吸引维下限
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-10 DOI: 10.1134/S1064562424702016
A. G. Kostianko, A. A. Ilyin, D. Stone, S. V. Zelik
{"title":"Multi-vortices and Lower Bounds for the Attractor Dimension of 2D Navier–Stokes Equations","authors":"A. G. Kostianko,&nbsp;A. A. Ilyin,&nbsp;D. Stone,&nbsp;S. V. Zelik","doi":"10.1134/S1064562424702016","DOIUrl":"10.1134/S1064562424702016","url":null,"abstract":"<p>A new method for obtaining lower bounds for the dimension of attractors for the Navier–Stokes equations is presented, which does not use Kolmogorov flows. By applying this method, exact estimates of the dimension are obtained for the case of equations on a plane with Ekman damping. Similar estimates were previously known only for the case of periodic boundary conditions. In addition, similar lower bounds are obtained for the classical Navier–Stokes system in a two-dimensional bounded domain with Dirichlet boundary conditions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141365244","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
Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets 伪凸集合上定义的拉顿变换的反演问题
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-06-10 DOI: 10.1134/S1064562424702004
D. S. Anikonov, D. S. Konovalova
{"title":"Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets","authors":"D. S. Anikonov,&nbsp;D. S. Konovalova","doi":"10.1134/S1064562424702004","DOIUrl":"10.1134/S1064562424702004","url":null,"abstract":"<p>Some questions concerning the inversion of the classical and generalized integral Radon transforms are discussed. The main issue is to determine information about the integrand if the values of some integrals are known. A feature of this work is that a function is integrated over hyperplanes in a finite-dimensional Euclidean space and the integrands depend not only on the variables of integration, but also on some of the variables characterizing the hyperplanes. The independent variables describing the known integrals are fewer than those in the unknown integrand. We consider discontinuous integrands defined on specifically introduced pseudoconvex sets. A Stefan-type problem of finding discontinuity surfaces of the integrand is posed. Formulas for solving the problem under study are derived by applying special integro-differential operators to known data.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141364464","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
Erratum to: Expanded Personality as the Main Entity and Subject of Philosophical Analysis: Implications for Education 勘误：作为哲学分析的主要实体和主体的扩展人格：对教育的影响
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-16 DOI: 10.1134/S1064562424010010
A. L. Semenov, K. E. Ziskin
{"title":"Erratum to: Expanded Personality as the Main Entity and Subject of Philosophical Analysis: Implications for Education","authors":"A. L. Semenov,&nbsp;K. E. Ziskin","doi":"10.1134/S1064562424010010","DOIUrl":"10.1134/S1064562424010010","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412058","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
Erratum to: Computer Experiment in Teaching Mathematics 勘误：数学教学中的计算机实验
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-16 DOI: 10.1134/S1064562424010022
G. B. Shabat,  A. L. Semenov
{"title":"Erratum to: Computer Experiment in Teaching Mathematics","authors":"G. B. Shabat,&nbsp; A. L. Semenov","doi":"10.1134/S1064562424010022","DOIUrl":"10.1134/S1064562424010022","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412057","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
Description of Turbulent Flows Using a Kinetic Model 使用动力学模型描述湍流
IF 0.5 4区 数学
Doklady Mathematics Pub Date : 2024-05-13 DOI: 10.1134/S1064562424701953
B. N. Chetverushkin, A. E. Lutsky, E. V. Shilnikov
{"title":"Description of Turbulent Flows Using a Kinetic Model","authors":"B. N. Chetverushkin,&nbsp;A. E. Lutsky,&nbsp;E. V. Shilnikov","doi":"10.1134/S1064562424701953","DOIUrl":"10.1134/S1064562424701953","url":null,"abstract":"<p>A closed system of equations for describing turbulent flows is obtained. Additional equations for the cross pulsation moments <span>(rho overline {Delta {{u}_{i}}Delta {{u}_{k}}} )</span> are derived using a balanced kinetic equation, which was previously used to obtain a quasi-gasdynamic system of equations. Numerical results for the problem of a two-dimensional mixing layer between two flows are presented.</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":"140941770","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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