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Differentiation, Efficiency, and Inflation in Economic Theory 经济理论中的分化、效率和通货膨胀
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S106456242570005X
B. I. Nigmatulin,  R. I. Nigmatulin
{"title":"Differentiation, Efficiency, and Inflation in Economic Theory","authors":"B. I. Nigmatulin,&nbsp; R. I. Nigmatulin","doi":"10.1134/S106456242570005X","DOIUrl":"10.1134/S106456242570005X","url":null,"abstract":"<p>The paper proposes four parameters to measure the efficiency of investments and their inflation. These parameters were calculated individually for 49 relatively large countries with a fairly advanced level of economic development, for the rest of the world within three international economic associations (OECD, Old EU countries, and New EU countries), and for the world (as a whole) in two time ranges: (1996–2008) and (2009–2023). Based on the calculated parameters, ratings of the efficiency of investments and broad money supply (M3 aggregate) and their inflation are constructed for these 53 subjects, which include all countries of the world. The necessary conditions for ensuring GDP growth in modern Russia above the global average while maintaining macroeconomic stability are shown.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"151 - 154"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371602","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 Some Class of Extreme Points of the Unit Ball of a Hardy–Lorentz Space Hardy-Lorentz空间单位球的几类极值点
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562425700036
S. V. Astashkin
{"title":"On Some Class of Extreme Points of the Unit Ball of a Hardy–Lorentz Space","authors":"S. V. Astashkin","doi":"10.1134/S1064562425700036","DOIUrl":"10.1134/S1064562425700036","url":null,"abstract":"<p>We consider the problem of characterizing the set of extreme points of the unit ball in a Hardy–Lorentz space <span>(H(Lambda (varphi )))</span>, posed by E.M. Semenov in 1978. New necessary and sufficient conditions under which a normalized function <i>f</i> in <span>(H(Lambda (varphi )))</span> belongs to this set are found. The most complete results are obtained in the case when <i>f</i> is the product of an outer analytic function and a Blaschke factor.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"95 - 98"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371612","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
Unique Strong Solvability of the Initial Boundary Value Problem for Inhomogeneous Incompressible Kelvin–Voigt Fluid Model 非齐次不可压缩Kelvin-Voigt流体模型初边值问题的唯一强可解性
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562425700073
V. G. Zvyagin, M. V. Turbin
{"title":"Unique Strong Solvability of the Initial Boundary Value Problem for Inhomogeneous Incompressible Kelvin–Voigt Fluid Model","authors":"V. G. Zvyagin,&nbsp;M. V. Turbin","doi":"10.1134/S1064562425700073","DOIUrl":"10.1134/S1064562425700073","url":null,"abstract":"<p>The existence and uniqueness of a strong solution for an inhomogeneous incompressible Kelvin–Voigt fluid motion model is proved. It is not assumed that the initial value of the fluid density is separated from zero. To prove the existence of a solution, an approximation problem is considered, its solvability is proved, and strong a priori estimates independent of the approximation parameter are established for its solutions. After that, passing to the limit as the approximation parameter tends to zero, we show that the solutions of the approximation problem converge to a strong solution of the original problem as the approximation parameter tends to zero. The uniqueness of the solution is established using the Gronwall–Bellman inequality.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"110 - 113"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371599","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
Exact Solutions and Reductions of the Nonlinear Schrödinger Equation of General Form 广义非线性Schrödinger方程的精确解与约简
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562425700061
A. D. Polyanin, N. A. Kudryashov
{"title":"Exact Solutions and Reductions of the Nonlinear Schrödinger Equation of General Form","authors":"A. D. Polyanin,&nbsp;N. A. Kudryashov","doi":"10.1134/S1064562425700061","DOIUrl":"10.1134/S1064562425700061","url":null,"abstract":"<p>We investigate a nonlinear Schrödinger equation of general form in which the chromatic dispersion and the potential are given by two arbitrary functions. The equation is a natural generalization of a wide class of related nonlinear partial differential equations that are often encountered in various fields of theoretical physics and mechanics, including nonlinear optics and plasma physics. For several general nonlinear Schrödinger equations, new exact solutions in implicit form are found, which are expressed in terms of elementary and arbitrary functions. One-dimensional reductions are described, which reduce the considered partial differential equation to simpler ordinary differential equations or systems of such equations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"134 - 137"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371614","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 a Combinatorial Application of Ultrafilter Theory: A New Construction of Triangle-Free Graphs with Arbitrarily Large Chromatic Number 超滤理论的组合应用：任意大色数无三角形图的新构造
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S106456242460249X
N. L. Polyakov
{"title":"On a Combinatorial Application of Ultrafilter Theory: A New Construction of Triangle-Free Graphs with Arbitrarily Large Chromatic Number","authors":"N. L. Polyakov","doi":"10.1134/S106456242460249X","DOIUrl":"10.1134/S106456242460249X","url":null,"abstract":"<p>The paper describes a new method for constructing triangle-free graphs with an arbitrarily large chromatic number. The method is substantiated using properties of various types of ultrafilter extensions of functions and predicates.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"126 - 133"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371613","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
The DipolarCalc Software System for Assessing the Polarization of Biological Molecular Structures 用于评估生物分子结构极化的DipolarCalc软件系统
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562425600113
I. K. Il’in, Yu. A. Uss, M. V. Shamolin, L. A. Yan’ko
{"title":"The DipolarCalc Software System for Assessing the Polarization of Biological Molecular Structures","authors":"I. K. Il’in,&nbsp;Yu. A. Uss,&nbsp;M. V. Shamolin,&nbsp;L. A. Yan’ko","doi":"10.1134/S1064562425600113","DOIUrl":"10.1134/S1064562425600113","url":null,"abstract":"<p>The unique DipolarCalc software system is presented, which makes it possible to calculate the polarization of biomolecules through the total dipole moment of chemical bonds of “functional topological atoms” (FTA). The program implements a user-friendly interface that provides intuitive data entry and visualization of calculation results, as well as it uses analytical expressions that allow accurate calculations to be performed in real time. The presented software package is aimed at use in computational biology and provides a convenient tool for modeling intra- and intermolecular interactions of biological molecular structures.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"147 - 150"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371615","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
Notes on the Recurrence of Birkhoff Sums 关于Birkhoff和递归性的注解
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562425700085
N. V. Denisova
{"title":"Notes on the Recurrence of Birkhoff Sums","authors":"N. V. Denisova","doi":"10.1134/S1064562425700085","DOIUrl":"10.1134/S1064562425700085","url":null,"abstract":"<p>Given a compact metric space with Carathéodory measure, we consider ergodic transformations of the space that are measure-preserving, but not necessarily invertible. The behavior of the Birkhoff sums for integrable and almost everywhere bounded functions with zero mean value in terms of the Carathéodory measure is studied. It is shown that for almost all points of the metric space there is an infinite sequence of “time instants” along which the Birkhoff sums tend to zero and the trajectory points at the these instants approach their initial position as close as possible (as in the Poincaré recurrence theorem). As an example, we consider the transformation <span>(x mapsto 2x)</span> <span>(bmod 1)</span> of the unit interval <span>(0,leqslant ,x,leqslant ,1)</span> closely related to Bernoulli trials.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"144 - 146"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371601","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
Ordinary Differential Equations of Even Order with Integral Conditions 具有积分条件的偶阶常微分方程
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562425700048
R. A. Bayrash, A. L. Skubachevskii
{"title":"Ordinary Differential Equations of Even Order with Integral Conditions","authors":"R. A. Bayrash,&nbsp;A. L. Skubachevskii","doi":"10.1134/S1064562425700048","DOIUrl":"10.1134/S1064562425700048","url":null,"abstract":"<p>We consider an even-order ordinary differential operator with a spectral parameter and integral conditions. An a priori estimate of solutions to the problem is obtained for sufficiently large values of the spectral parameter. The discreteness and the sectoral structure of the spectrum of the corresponding operators are proved.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"99 - 102"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371616","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
Problems and Methods of the Theory Functional Differential Equations with Discontinuous Right Hand Side 右手边不连续的理论泛函微分方程的问题与方法
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562421100124
I. A. Finogenko
{"title":"Problems and Methods of the Theory Functional Differential Equations with Discontinuous Right Hand Side","authors":"I. A. Finogenko","doi":"10.1134/S1064562421100124","DOIUrl":"10.1134/S1064562421100124","url":null,"abstract":"<p>The main methods and approaches of the theory of discontinuous systems are used to construct the theory of functional differential equations with a discontinuous right-hand side. In particular, methods for describing sets of discontinuity points and sliding modes of discontinuous systems with delay are considered using a special class of invariantly differentiable functionals.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"138 - 143"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371600","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 Structure of the Solution Set of a Cauchy Problem for Fractional Differential Inclusions with an Upper Semicontinuous Right-Hand Side 右上半连续的分数阶微分内含物Cauchy问题解集的拓扑结构
IF 0.6 4区 数学
Doklady Mathematics Pub Date : 2025-10-27 DOI: 10.1134/S1064562424601823
G. G. Petrosyan
{"title":"Topological Structure of the Solution Set of a Cauchy Problem for Fractional Differential Inclusions with an Upper Semicontinuous Right-Hand Side","authors":"G. G. Petrosyan","doi":"10.1134/S1064562424601823","DOIUrl":"10.1134/S1064562424601823","url":null,"abstract":"<p>We study the topological structure of the solution set of the Cauchy problem for semilinear differential inclusions of fractional order <span>(alpha in (1,2))</span> in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by an upper semicontinuous multivalued operator of Carathéodory type. It is established that the solution set of the problem is an <span>({{R}_{delta }})</span>-set.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"111 2","pages":"121 - 125"},"PeriodicalIF":0.6,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145371610","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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