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On Interpretations of Presburger Arithmetic in Büchi Arithmetics 论<s:1> chi算术中普雷斯伯格算术的解释
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700655
A. A. Zapryagaev
{"title":"On Interpretations of Presburger Arithmetic in Büchi Arithmetics","authors":"A. A. Zapryagaev","doi":"10.1134/S1064562423700655","DOIUrl":"10.1134/S1064562423700655","url":null,"abstract":"<p>Büchi arithmetics <b>BA</b><sub><i>n</i></sub>, <span>(n geqslant 2)</span>, are extensions of Presburger arithmetic with an unary functional symbol <span>({{V}_{n}}(x))</span> denoting Presburger arithmetic the largest power of <i>n</i> that divides <i>x</i>. Definability of a set in <b>BA</b><sub><i>n</i></sub> is equivalent to its recognizability by a finite automaton receiving numbers in their <i>n</i>-ary expansion. We consider the interpretations of in the standard model of <b>BA</b><sub><i>n</i></sub> and show that each such interpretation has an internal model isomorphic to the standard one. This answers a question by A. Visser on the interpretations of certain weak arithmetical theories in themselves.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"89 - 92"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5139931","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: 1
On the Accuracy of Discontinuous Galerkin Method Calculating Gas-Dynamic Shock Waves 论不连续伽辽金法计算气体动力激波的精度
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700746
M. E. Ladonkina, O. A. Nekliudova, V. V. Ostapenko,  V. F. Tishkin
{"title":"On the Accuracy of Discontinuous Galerkin Method Calculating Gas-Dynamic Shock Waves","authors":"M. E. Ladonkina,&nbsp;O. A. Nekliudova,&nbsp;V. V. Ostapenko,&nbsp; V. F. Tishkin","doi":"10.1134/S1064562423700746","DOIUrl":"10.1134/S1064562423700746","url":null,"abstract":"<p>The results of a numerical calculation of gas-dynamic shock waves that arise in solving the Cauchy problem with smooth periodic initial data are presented for three variants of the discontinuous Galerkin (DG) method, in which the solution is sought in the form of a piecewise linear discontinuous function. It is shown that the DG methods with the Cockburn limiter used for monotonization have approximately the same accuracy in shock influence areas, while the nonmonotone DG method (with no limiter) has a significantly higher accuracy in these areas. Accordingly, it can be used as a basic method in the construction of a combined scheme that monotonically localizes shock fronts and maintains increased accuracy in the areas of their influence.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"120 - 125"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142529","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
Refined Mathematical Model of Economic Dynamics under High Inflation and Unstable Development 高通胀与不稳定发展下经济动力学的精细化数学模型
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700709
V. A. Sadovnichiy,  A. A. Akaev, A. I. Zvyagintsev, A. I. Sarygulov
{"title":"Refined Mathematical Model of Economic Dynamics under High Inflation and Unstable Development","authors":"V. A. Sadovnichiy,&nbsp; A. A. Akaev,&nbsp;A. I. Zvyagintsev,&nbsp;A. I. Sarygulov","doi":"10.1134/S1064562423700709","DOIUrl":"10.1134/S1064562423700709","url":null,"abstract":"<p>Previously, the authors proposed two mathematical models that describe the dynamics of economic development rates and forecasting inflation rates. The events that took place after February 2022 introduced an element of significant turbulence into the processes of macroeconomic dynamics in Russia, which required some correction of the previous models. This is reflected in this article. The processes simulated on the basis of new models show that a significant reduction in the interest rate and a steady increase in the money supply are required to restore economic growth and reduce inflation in the medium term. It is shown that, in the current era of geopolitical changes and the collapse of many liberal market dogmas, the role of the state and planning in managing economic processes is increasing.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"105 - 108"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142707","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: 1
The Problem of the Flow of One Type of Non-Newtonian Fluid through the Boundary of a Multiply Connected Domain 一类非牛顿流体通过多连通域边界的流动问题
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700722
V. G. Zvyagin, V. P. Orlov
{"title":"The Problem of the Flow of One Type of Non-Newtonian Fluid through the Boundary of a Multiply Connected Domain","authors":"V. G. Zvyagin,&nbsp;V. P. Orlov","doi":"10.1134/S1064562423700722","DOIUrl":"10.1134/S1064562423700722","url":null,"abstract":"<p>The existence of a weak solution of the initial boundary value problem for the equations of motion of a viscoelastic non-Newtonian fluid in a multiply connected domain with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is established. The study assumes Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to study the behavior of trajectories of a nonsmooth velocity field.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"112 - 116"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142530","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 One Approach to the Estimation of a Triangular Element Degeneration in a Triangulation 三角剖分中三角元退化估计的一种方法
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S106456242370076X
Yu. A. Kriksin,  V. F. Tishkin
{"title":"On One Approach to the Estimation of a Triangular Element Degeneration in a Triangulation","authors":"Yu. A. Kriksin,&nbsp; V. F. Tishkin","doi":"10.1134/S106456242370076X","DOIUrl":"10.1134/S106456242370076X","url":null,"abstract":"<p>A quantitative estimate for the quality of a triangular element—the triangle degeneration index—is proposed. To apply this estimate, a simple model triangulation is constructed in which the vertex coordinates are obtained as the sum of the corresponding node coordinates in a given regular grid and their random increments. For various parameter values, the empirical distribution function of the triangle degeneration index is calculated, which is considered a quantitative characteristic of the quality of triangular elements in the constructed triangulation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"126 - 129"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5139920","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
Elementary Invariants for Quantified Probability Logic 量化概率逻辑的初等不变量
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700667
S. O. Speranski
{"title":"Elementary Invariants for Quantified Probability Logic","authors":"S. O. Speranski","doi":"10.1134/S1064562423700667","DOIUrl":"10.1134/S1064562423700667","url":null,"abstract":"<p>Let QPL be the two-sorted probabilistic language proposed in [8], which expands the well-known ‘polynomial’ language described in [3], Section 6, by adding quantifiers over events. We show that all atomless spaces have the same QPL-theory, and this theory is decidable. Also we introduce the notion of elementary invariant for QPL and use it for obtaining exact complexity upper bounds for some interesting probabilistic theories.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"93 - 96"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142532","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
One Condition for Discreteness of the Spectrum and Compactness of the Resolvent of a Nonsectorial Sturm–Liouville Operator on a Semiaxis 半轴上非扇形Sturm-Liouville算子谱离散性和解紧性的一个条件
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700734
S. N. Tumanov
{"title":"One Condition for Discreteness of the Spectrum and Compactness of the Resolvent of a Nonsectorial Sturm–Liouville Operator on a Semiaxis","authors":"S. N. Tumanov","doi":"10.1134/S1064562423700734","DOIUrl":"10.1134/S1064562423700734","url":null,"abstract":"<p>The spectral properties of the Sturm–Liouville operator on a semiaxis in the case of a complex-valued potential with a range exceeding the half-plane have been poorly studied. The operator in this case can be nonsectorial: its numerical range can coincide with the entire complex plane. In this situation, conditions are proposed ensuring the discreteness of the spectrum and the compactness of the resolvent.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"117 - 119"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142533","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 Analogue of Mahler’s Transference Theorem for Multiplicative Diophantine Approximation 乘式丢番图近似的马勒转移定理的一个模拟
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700680
O. N. German
{"title":"An Analogue of Mahler’s Transference Theorem for Multiplicative Diophantine Approximation","authors":"O. N. German","doi":"10.1134/S1064562423700680","DOIUrl":"10.1134/S1064562423700680","url":null,"abstract":"<p>Khintchine’s and Dyson’s transference theorems can be very easily deduced from Mahler’s transference theorem. In the multiplicative setting an obstacle appears, which does not allow deducing the multiplicative transference theorem immediately from Mahler’s theorem. Some extra considerations are required, for instance, induction by the dimension. In this paper we propose an analogue of Mahler’s theorem which implies the multiplicative transference theorem immediately.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"101 - 104"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142527","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
Computers as a Novel Mathematical Reality: I. A Personal Account 计算机作为一种新颖的数学现实:1 .个人账户
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423700758
N. A. Vavilov
{"title":"Computers as a Novel Mathematical Reality: I. A Personal Account","authors":"N. A. Vavilov","doi":"10.1134/S1064562423700758","DOIUrl":"10.1134/S1064562423700758","url":null,"abstract":"<p>Much ink has been spilled in the last few decades on computer proofs, computer-assissted proofs, computer-verified proofs, etc. It is obvious that the advent and proliferation of computers have drastically changed the applications of mathematics. What is far less discussed, however, is how computers changed mathematics itself, as well as the stance of mathematicians in regard to mathematical reality, both as far as the possibilities to immediately observe it and the apprehension of what we can hope to prove. I am recounting my personal experience of using computers as a mathematical tool and the experience of similar use in the works of colleagues that I observed at close range. This experience has radically changed my perception of many aspects of mathematics; how it functions; and, especially, how it should be taught. This first introductory part consists mostly of reminiscences and some philosophical observations. Later parts describe several specific important advances in algebra and number theory that would had been impossible without computers.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"130 - 141"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142705","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: 4
Erratum to: A Model Zeta Function of the Monoid of Natural Numbers 对自然数单群的一个模型Zeta函数的勘误
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2023-08-30 DOI: 10.1134/S1064562423220027
N. N. Dobrovol’skii
{"title":"Erratum to: A Model Zeta Function of the Monoid of Natural Numbers","authors":"N. N. Dobrovol’skii","doi":"10.1134/S1064562423220027","DOIUrl":"10.1134/S1064562423220027","url":null,"abstract":"","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"142 - 142"},"PeriodicalIF":0.6,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5142522","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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