The paper analyzes average integral payoff indices for trajectories of the dynamic equilibrium and replicator dynamics in bimatrix coordination games. In such games, players receive large payoffs when choosing the same type of behavior. A special feature of a 2 × 2 coordination game is the presence of three static Nash equilibria. In the dynamic formulation, the trajectories of coordination games are estimated by the average integral payoffs for a wide range of models arising in economics and biology. In optimal control problems and dynamic games, average integral payoffs are used to synthesize guaranteed strategies, which are involved, among other things, in the constructions of the dynamic Nash equilibrium. In addition, average integral payoffs are a natural tool for assessing the quality of trajectories of replicator dynamics. In the paper, we compare values of average integral indices for trajectories of replicator dynamics and trajectories generated by guaranteed strategies in constructing the dynamic Nash equilibrium. An analysis is provided for trajectories of mixed dynamics when the first player plays a guaranteed strategy, and the behavior of replicator dynamics guides the second player.
In this paper, we prove certain Littlewood-Tauberian theorems for general matrix summability method by imposing the Tauberian conditions such as slow oscillation of usual as well as matrix generated sequence, and the De la Vallée Poussin means of real sequences. Moreover, we demonstrate (N, pn) and (C, 1) - summability methods as the generalizations of our proposed general matrix method and establish an equivalence relation connecting them. Finally, we draw several remarks in view of the generalizations of some existing well-known results based on our results.
В статье анализируются вопросы правового регулирования долевого строительства. Освещаются этапы становления института долевого строительства при осуществлении конституционного права на жилье как альтернативны широко используемых договоров подряда, простого товарищества (о совместной деятельности), уступки требования (цессии) и других. Рассматриваются реформы в федеральном законодательстве о долевом строительстве, а также проблемные аспекты практической реализации долевого участия в строительстве жилья.
The main aim of this paper is to present and explore some of properties of the concept of -statistical convergence in measure of complex uncertain sequences. Furthermore, we introduce the concept of -statistical Cauchy sequence in measure and study the relationships between different types of convergencies. We observe that, in complex uncertain space, every -statistically convergent sequence in measure is -statistically Cauchy sequence in measure, but the converse is not necessarily true.
В статье исследуется динамика колебаний соотношения вынесенных в судебном порядке административных штрафов относительно общего количества рассмотренных судами дел об административных правонарушениях за 2012-2022 гг., выявляется и объясняется корреляция указанного соотношения и общего количества рассматриваемых судебных решений. Устанавливаются причины невыявления корреляции в отдельные годы, предлагаются возможные способы ее применения в деятельности государственных органов.
Clustering is a strategy for discovering homogeneous clusters in heterogeneous data sets based on comparable structures or properties. The number of nodes or links that must fail for a network to be divided into two or more sub-networks is known as connectivity. In addition to being a metric of network dependability, connectivity also serves as an indicator of performance. The Euler graph can represent almost any issue involving a discrete arrangement of objects. It can be analyzed using the recent field of mathematics called graph theory. This paper discusses the properties of clustered networks like connectivity and chromaticity. Further, the structure of the antipodal graph in the clustered network has been explored.
В статье автор утверждает, что любые реформы разрешают назревшие противоречия мирным путем, смягчают острые конфликты в обществе, являются итогом разумных компромиссов, при этом реформирование местного самоуправления не является исключением. Уделяя особое внимание периодизации исторических преобразований местного самоуправления в Российской империи, в статье предложена авторская периодизация. Проанализированы особенности территориального деления и устройства государства, сочетающие в себе признаки как политико-территориальной, так и административно-территориальной организации. Автономия и самостоятельность в решении вопросов местного значения отграничивают местное самоуправление от локального управления, а в зависимости от особенностей сочетания местного и локального управления выделяются два типа муниципальных систем. Автором определена потребность в формировании новой модели местного самоуправления с учетом современных реалий и богатейшего исторического наследия в области местного самоуправления периода Российской империи.
The notion of f-statistical convergence in topological space, which is actually a statistical convergence’s generalization under the influence of unbounded modulus function is presented and explored in this paper. This provides as an intermediate between statistical and typical convergence. We also present many counterexamples to highlight the distinctions among several related topological features. Lastly, this paper is concerned with the notions of sf-limit point and sf-cluster point for a unbounded modulus function f.
We consider finite deterministic automata such that their alphabets consist of exactly one letter of defect 1 and a set of permutations of the state set. We study under which conditions such an automaton is completely reachable. We focus our attention on the case when the set of permutations generates a transitive imprimitive group.
A graph G is splittable if its set of vertices can be represented as the union of a clique and a coclique. We will call a graph H a {splittable ancestor} of a graph G if the graph G is reducible to the graph H using some sequential lifting rotations of edges and H is a splittable graph. A splittable r-ancestor of G we will call its splittable ancestor whose Durfey rank is r. Let us set s=(1/2)(sumtl(λ)−sumhd(λ)), where hd(λ) and tl(λ) are the head and the tail of a partition λ. The main goal of this work is to prove that any graph G of Durfey rank r is reducible by s successive lifting rotations of edges to a splittable r-ancestor H and s is the smallest non-negative integer with this property. Note that the degree partition dpt(G) of the graph G can be obtained from the degree partition dpt(H) of the splittable r-ancestor H using a sequence of s elementary transformations of the first type. The obtained results provide new opportunities for investigating the set of all realizations of a given graphical partition using splittable graphs.