Doklady Mathematics最新文献

{"title":"Nontransitive Dice with Equal Means and Variances","authors":"A. N. Yakusheva","doi":"10.1134/S1064562426700134","DOIUrl":"10.1134/S1064562426700134","url":null,"abstract":"<p>This study aims to investigate the nontransitivity of the stochastic precedence relation. The dice were taken as an example of discrete random variables with a finite set of values. The means and variances of the dice were assumed those of the classical dice. The whole variety of nontransitive sets containing three or four dice were found in case of one or two tosses and various ways to determine the advantage. The sets that reveal the strongest property of nontransitivity were obtained according to the specific function. The hypothesis has been tested about the emergence of nontransitivity after two tosses of dice in originally transitive sets.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 3","pages":"111 - 119"},"PeriodicalIF":0.8,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149222778","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}

{"title":"Dynamic Game-theoretical Models of Innovation Management in Universities Taking into Account Opportunistic behavior","authors":"V. Yu. Kalachev,&nbsp;G. A. Ougolnitsky,&nbsp;A. B. Usov","doi":"10.1134/S1064562426700146","DOIUrl":"10.1134/S1064562426700146","url":null,"abstract":"<p>The article studies the issues of innovation implementation in universities. A three-level hierarchically organized model is proposed to describe the process of innovation implementation in universities. The model includes agents (followers, in whose role teachers act), supervisors (subjects of middle-level management, universities) and a principal (leader, the state). The principal (the state) is the first to announce its behavior strategy. Supervisors choose their management strategies when the principal’s choice is already known, but the agents’ choice is not yet known. Agents (teachers) make their choice when the management strategies of the other subjects are already known. Supervisors, like agents, make their choice independently of each other. The principal subsidizes the innovative development of higher education institutions by allocating funds for the development of new electronic courses. The new electronic courses being developed are considered as innovative products that contribute to the innovative development of higher education institutions. Supervisors receive subsidies from the principal for the development and implementation of innovative products. They determine the required volume of new courses issued by agents. Agents develop new electronic training courses for subsequent sale and implementation in the educational process. Supervisors keep part of the subsidies received from the principal for themselves, and transfer part to agents. Agents receive subsidies, the amount of which depends on the demand for the courses they develop, and manage the quality of the courses they develop, improving their qualifications. The possibility of corruption in the system is provided for and methods for combating it are defined. Lower and middle management entities may be subject to corruption. Agents may offer bribes to supervisors, in exchange for which they inflate the portion of subsidies transferred to agents. An analysis is conducted of how the presence of corruption affects the innovative development of universities. Thus, a dynamic three-level model is constructed, in which the dynamics are described by a difference equation reflecting the change in the general innovative level of the education system depending on the agents’ controls. Algorithms for constructing a solution for different combinations of Stackelberg games with and without feedback on control between the state and universities and between universities and teachers are indicated. In a non-antagonistic game of universities among themselves, as in a game of teachers, a Nash equilibrium is built. The results of numerical experiments are presented, their analysis is given. A number of meaningful conclusions and recommendations are made.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 3","pages":"102 - 110"},"PeriodicalIF":0.8,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149222777","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}

{"title":"Validation Technology for Autonomous Navigation Methods of Unmanned Aerial Vehicles Based on SLAM Algorithms","authors":"P. A. Ukhov,&nbsp;K. A. Stenin","doi":"10.1134/S1064562426700122","DOIUrl":"10.1134/S1064562426700122","url":null,"abstract":"<p>The article proposes a technology for validating autonomous navigation methods for unmanned aerial vehicles based on simultaneous mapping and localization (SLAM) algorithms. The proposed technology is based on experimental studies using real flight data and includes the design of validation scenarios, synchronization and spatial alignment of trajectories, as well as the calculation of a set of quantitative metrics characterizing global and local accuracy, drift accumulation, and the stability of the navigation solution. As a demonstration example, the technology was evaluated using the VINS-Fusion visual-inertial algorithm using recordings of real UAV flights. The obtained results show that the proposed approach allows comparing different SLAM solutions under the same conditions and identifying flight modes that are most sensitive to error accumulation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 3","pages":"84 - 94"},"PeriodicalIF":0.8,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149222779","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}

{"title":"Topologically Consistent Fuzzy Clustering in a Neurodynamic Model of the Traveling Salesman Problem","authors":"V. A. Sudakov","doi":"10.1134/S1064562426700110","DOIUrl":"10.1134/S1064562426700110","url":null,"abstract":"<p>A new neurodynamic model for joint optimization of the traveling salesman problem route and fuzzy cluster partitioning of a set of vertices is proposed. The model’s energy function includes three components: a Hopfield-Tank term encoding route feasibility constraints; a fuzzy means term ensuring geometric compactness of clusters; and a topological matching term penalizing for discontinuities in cluster membership between adjacent vertices along the route. An iterative minimization scheme is developed. The following convergence properties are proven: monotonic energy decrease and convergence of the energy sequence to a limit value. Computational experiments on a test example showed that the proposed model finds solutions that coincide with the global optimum, while the resulting clusters differ significantly from the results of the classical fuzzy c-means algorithm, reflecting the topology of the optimal route. The results of the study can be used for problems of delivery territory zoning, production operation planning, and condensation of large factor models.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 3","pages":"75 - 83"},"PeriodicalIF":0.8,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149222775","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}

{"title":"The Problem of Redistributing Quotas for Training between Structural Divisions of a Higher Educational Institution","authors":"V. Yu. Kalachev,&nbsp;G. A. Ougolnitsky,&nbsp;A. B. Usov","doi":"10.1134/S1064562426700158","DOIUrl":"10.1134/S1064562426700158","url":null,"abstract":"<p>The problem of redistributing quotas for training among structural divisions of a higher education institution is considered. The problem of redistributing quotas has a wide range of applications, in particular, in preventing environmental pollution. The article assumes that a higher education institution has several structural divisions. The management of the higher education institution allocates some quotas for training to structural divisions (SD). The head of each SD can give part of the quota of his SD to another division, receiving some compensation in return. In this case, if the quota is not given, it must be fully used in the joint venture to which it was allocated. The head of each joint venture strives to maximize his gain, expressed by his objective function. For simplicity, it can be considered that the goal of the head of each joint venture is to maximize the amount of funds accumulated in the centralized fund of this joint venture. In this case, the head of the joint venture can manage the share of the quota allocated to him, which he wants to give or receive from another joint venture. It is shown in which cases all structural divisions manage to receive optimal quotas for them as a result of redistribution. Three cases are considered: when the total value of the quota that the divisions want to give is greater than, less than or equal to the total value of the quota that other structural divisions want to acquire. Algorithms for redistributing quotas in each of these cases are proposed. The study is conducted analytically for a particular type of input functions, which are taken as power functions. Numerical examples are given and an analysis of the results obtained is given. A number of meaningful conclusions are made.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 3","pages":"95 - 101"},"PeriodicalIF":0.8,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149222776","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}

{"title":"Optimality Criterion in the Form of Maximum Principle in Control Problems for High-Order Hyperbolic Equations","authors":"M. B. Bulakina,&nbsp;A. M. Romanenkov","doi":"10.1134/S1064562426700092","DOIUrl":"10.1134/S1064562426700092","url":null,"abstract":"<p>An optimal control problem for a high-order linear pseudohyperbolic equation with a right-hand side control dependent only on time is considered. The equation is reduced to a system of two partial differential equations. The needle variation method is used to obtain necessary optimality conditions in the form of Pontryagin’s maximum principle. The uniqueness of a weak solution is established.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 2","pages":"53 - 58"},"PeriodicalIF":0.8,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148902620","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}

{"title":"Heat Transfer in a Locally Nonequilibrium Anisotropic Half-Space Based on a Generalized Wave Heat Transfer Law","authors":"B. A. Garibyan,&nbsp;V. F. Formalev","doi":"10.1134/S1064562426700109","DOIUrl":"10.1134/S1064562426700109","url":null,"abstract":"<p>Heat transfer in a thermodynamically nonequilibrium anisotropic half-space with transverse anisotropy is modeled using a generalized wave heat transfer law. The law retains the mathematical structure of the classical Fourier heat conduction equation, but incorporates a time argument delay equal to the relaxation time. The resulting governing equation is of parabolic type with a time delay corresponding to the relaxation time. For the three-dimensional unsteady heat conduction problem with tensorial transport coefficients, a novel analytical solution is derived by applying the double Fourier transform with respect to two spatial coordinates and the Laplace transform with respect to time. The computational results reveal that the isothermal surfaces are approximated by elliptic paraboloids with local inflection lines, while the temporal temperature profiles exhibit propagating fronts of jump discontinuities, thereby confirming the wave-like nature of heat transfer.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 2","pages":"47 - 52"},"PeriodicalIF":0.8,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148902619","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}

{"title":"Development of Stability Domains for Various Stationary Points in the Problem of an Aerodynamic Pendulum in a Medium Flow","authors":"D. Belyakov,&nbsp;A. Zinchenko","doi":"10.1134/S1064562426700079","DOIUrl":"10.1134/S1064562426700079","url":null,"abstract":"<p>This paper presents the construction and investigation of a mathematical model of an aerodynamic pendulum in a medium flow. To model the aerodynamic forces, the hypothesis of quasi-static flow around a plate by the medium is employed. The equations of motion are obtained in dimensionless variables, describing the regimes of small oscillations of the aerodynamic pendulum. A violation of uniqueness in determining the angle of attack is demonstrated. A graphical and numerical investigation of the solutions to the equilibrium equations is carried out, and various nontrivial stationary points are found. For the identified stationary points, stability regions are constructed using the Routh–Hurwitz method. A software package has been developed in the MATLAB mathematical environment, enabling the construction of stability regions and the numerical integration of the equations describing the body’s oscillations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 2","pages":"67 - 73"},"PeriodicalIF":0.8,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148902618","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}

{"title":"Optimization of GPU Ray Tracing Algorithm for Voxel Data Using a Tetrahexacontree Data Structure","authors":"V. D. Bakharev,&nbsp;S. S. Krylov","doi":"10.1134/S1064562426700080","DOIUrl":"10.1134/S1064562426700080","url":null,"abstract":"<p>An optimization of the traversal algorithm using tetrahexacontree data structure is presented, which improves raytracing performance in voxel scenes. In existing research on this data structure, the use of the classical 3DDDA method [1] was proposed for traversing the cells of the space partition without any additional modifications. This approach proved to be less efficient in terms of performance compared to the popular hierarchical voxel data structure—the octree [2]. The aim of this work is to justify and evaluate the application of optimization techniques to the tetrahexacontree traversal algorithm. By analyzing cell occupancy bitmaps, the ray can skip empty regions within the tree nodes, thereby reducing the number of ray steps and thus improving performance. The optimization incurs a small overhead in terms of processor time and requires a fixed amount of extra memory, but does not require any additional preprocessing of the input data. The optimization is compatible with both dense and sparse tree representations. On average, the algorithm optimization yields a 28% performance gain compared to naive tetrahexacontree traversal algorithm, and is 21% more efficient than an octree method.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 2","pages":"59 - 66"},"PeriodicalIF":0.8,"publicationDate":"2026-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148902621","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}

{"title":"On Computing the Gradient in a Control Problem for a Higher-Order Pseudoparabolic Equation","authors":"A. M. Romanenkov","doi":"10.1134/S106456242670002X","DOIUrl":"10.1134/S106456242670002X","url":null,"abstract":"<p>A control problem is considered for the solution to an initial-boundary value problem for a linear differential equation of pseudoparabolic type that is higher-order in the spatial variable. The existence of a generalized solution is studied, and a constructive approach to constructing this solution using the Galerkin method is proposed. The control problem is stated for an integral quadratic functional, for which a majorant functional is constructed. For the introduced functional, the gradient is explicitly computed, making it possible to use the gradient descent method for computations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 1","pages":"9 - 15"},"PeriodicalIF":0.8,"publicationDate":"2026-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380396","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}