SCI Библиотека

This paper addresses the time-optimal control problem of the Dubins car, which is closely related to the problem of constructing the shortest curve with bounded curvature between two points in a plane. This connection allows researchers to apply both geometric methods and control theory techniques during their investigations. It is established that the time-optimal control for the Dubins car is a piecewise constant function with no more than two switchings. This characteristic enables the categorization of all such controls into several types, facilitating the examination of the solutions to the control problem for each type individually. The paper derives explicit formulas for determining the switching times of the control signal. In each case, necessary and sufficient conditions for the existence of solutions are obtained. For certain control types, the uniqueness of optimal solutions is established. Additionally, the dependence of the movement time on the initial and terminal conditions is studied.

In this paper, the seminormed Cesàro difference sequence space ℓ(j, q, g, r,μ, Δ(s)t,) is defined by using the generalized Orlicz function. Some algebraic and topological properties of the space ℓ(j, q, g, r,μ, Δ(s)t,) are investigated. Various inclusion relations for this sequence space are also studied.

На примере информационно-образовательного проекта«Правовой десант», реализуемого в Санкт-Петербургской академии Следственного комитета, рассматриваются современные способы профилактики противоправного поведения подростков.

In this article, we establish a refined extension of the above integral inequality by using the polar derivative instead of the ordinary derivative consisting of the leading coefficient and the constant term of the polynomial. Besides, our result also yields other intriguing inequalities as special cases.

For the class of bounded in l2-norm interpolated data, we consider a problem of interpolation on a finite interval [a, b] ⊂ ℝ with minimal value of the L2-norm of a differential operator applied to interpolants. Interpolation is performed at knots of an arbitrary N-point mesh ΔN: a ≤ x1 < x2 < < xN ≤ b. The extremal function is the interpolating natural -spline for an arbitrary fixed set of interpolated data. For some differential operators with constant real coefficients, it is proved that on the class of bounded in l2-norm interpolated data, the minimal value of the L2-norm of the differential operator on the interpolants is represented through the largest eigenvalue of the matrix of a certain quadratic form.

В настоящей статье рассмотрено перспективное направление криминологических исследований - ролевая концепция преступного поведения. Данное направление имеет огромную практическую пользу как для раскрытия преступлений, так и для анализа и прогноза преступности в целом и отдельных видов. Предложено авторское определение понятия «ролевая концепция преступного поведения», а также рассмотрены теоретические понятия, которые могут быть положены в основу данной концепции.

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.