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Item Homogeneous Linear Recurrent Games [Articol](2024) Lazari, AlexandruGames defined on deterministic systems with homogeneous linear recurrent dynamic are studied. It is proved that they represent homogeneous linear recurrent systems and an efficient method for determining the generating vector is proposed. This enables the usage of the advanced properties of homogeneous linear recurrences for their algebraic characterization.Item Characteristic Function of the Markov Random Flight in Higher Dimensions [Articol](2024) Kolesnik, Alexander D.Two series representations of the characteristic function of the multidimensional symmetric Markov random flight, are presented. These series are the decompositions of the characteristic function with respect to Bessel functions and with respect to time variable, whose coefficients are given by recurrent relations, as well as in the form of special determinants. Basing on these series representations, an asymptotic formula for the second moment function of the process, is obtained.Item Some Analytical Properties of the Laplace Transform of the Characteristic Function of the Three-Dimensional Markov Random [Articol](2024) Kolesnik, Alexander D.The analytical properties of the Laplace transform of the characteristic function of the three-dimensional symmetric Markov random flight, are studied. The only singular point (ordinary pole) and the residue at this point are evaluated, which gives the first coefficient (by the negative power of complex variable) in the Laurent decomposition of the Laplace-Fourier transform of the transition density of the process.Item Data Parallelization for Solving Bimatrix Games [Articol](2024) Hâncu, Boris; Turcanu, CalinContemporary decision-making problems are very complex and require the processing of a very large volume of data. Thus, for the mathematical modelling of these processes, it is necessary to take into account the big data problems. The data is too big to be stored and processed by a single machine. In many large-scale solutions, data is divided into partitions that can be managed and accessed separately. In order to solve such problems in real time, parallel algorithms are built and then implemented on various types of parallel computing systems. In this paper, we will analyze the ways to build parallel algorithms, and especially, data parallelization, for a class of noncooperative games, bimatrix games.Item Transportation Problems, the Braess Paradox and Network Coordination [Articol](2024) Gorbachuk, Vasyl; Dunaievskyi, Maksym; Havrylenko, SerhiyTraveling through the transport network or sending information packets via the Internet is implicitly based on game-theoretic considerations: a specific decision-maker (DM), choosing his or her route, takes into account the probability of congestion depending on all DMs, that is, other routes. Based on similar considerations, it is possible to develop models for network traffic. These models explain some paradoxical observations where increasing the capacity of a given network can slow down its traffic under certain circumstances.Item Algorithm to Minimize the Worst-Case Regret Function [Articol](2024) Godonoaga, Anatol; Chumakov, BorysThis paper examines mathematical model of decision-making under conditions of uncertainty, when Savage’s regret function is used as the objective function. Numerical algorithm for solving the corresponding problems are proposed, based on the implementation of parallel minimization of indicators for each state of nature and the indicator of greatest regret. The algorithms are developed based on the generalized gradient projection method.Item Strong Edge-Colorings of Some Lexicographic Products of Graphs [Articol](2024) Drambyan, AramThe edge-coloring of a graph G is strong if edges at distance 0 or 1 receive different colors. The minimum number of colors required for a strong edge-coloring of G is called strong chromatic index of G and denoted by χ′ s(G). In this paper, we determine the exact value of the strong chromatic index of lexicographic products of graphs G and H when Δ(G) ≤ 2 and H is an arbitrary graph, and provide an upper bound on χ′ s(G[H]) when Δ(G) = 3 and H is an arbitrary graph.Item Semi-Markovian Networks [Articol](2024) Damian, IuliaIn stochastic networks, a series of new problems appear, because the output flow of messages from one node forms the input flow to another node (or other nodes), which is not Poisson, and the serving of messages in the nodes of these networks is no longer exponential type. Such networks are called semiMarkovian networks and, therefore, the mathematical analysis of semi-Markovian networks is complicated and requires the application of some modern departments of mathematics.Item Experimental Closed-Loop Identification of the Third Order Inertial Systems with Time Delay [Articol](2024) Cojuhari, Irinan this paper, it is analysed the problem of mathematical identification in the closed-loop and it is proposed an approach for experimental identification, based on the undamped step response of the closed-loop control system. According to the proposed procedure, the dynamics of the control object is proposed to be approximated with transfer function with inertia third order and time delay. The obtained results are verified by computer simulation in MATLAB software package.Item Collocation Method for Solving Singular Integral Equations with Discontinuous Coefficients [Articol](2024) Capcelea, Maria; Capcelea, TituThe paper presents an efficient method for solving the Cauchy singular integral equation, which is defined on a closed and smooth contour in the complex plane. The coefficients and the right-hand side of the equation are piecewise continuous functions, numerically defined on a finite set of points along the contour.