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Item The Synthesis Function Method for Solving the Multi-Criteria Linear-Fractional Model in Integers [Articol](2024) Tkacenko, AlexandraIn this paper, I will propose a method for solving the linearfractional multi-criteria optimization model with identical denominators in whole numbers. The solving procedure involves assigning utilities (weights) to each criterion, after which a singlecriterion linear-fractional optimization model is constructed and can be solved. By changing the utility values, we can determine a new optimal compromise solution(s). The algorithm is theoretically justified and it was tested successfully on several examples.Item Optimality Criterion and Algorithm for Solving the Traveling Salesman Problem [Articol](2024) Terzi, DmitriChanging the direction of research from exact methods to methods such as genetics, with heuristic approaches, is promising for creating the desired algorithm. To this end, the paper presents a method for solving the traveling salesman problem, considering it as a transportation-type problem that can be easily solved by a modified distribution method. The main results are related to the expansion of the application of the latest technology. The criteria for optimality of the solution are presented. A new algorithm has been developed, as well as a new, fairly general, test problem generator with a given optimal solution, which is consistent with the hypothesis about the need to conduct mass computational experiments to build an effective way to solve the traveling salesman problem.Item Using the Ellipsoid Method to Find Parameters of Lasso and Ridge Regressions [Articol](2024) Stetsyuk, Petro; Khomiak, OlhaWe consider the optimization problem for finding the parameters of a linear regression according to the criterion of the least moduli powered to p (1 ≤ p ≤ 2) with the regularization of parameters according to the criterion of the least moduli powered to q (1 ≤ q ≤ 2). Its partial cases are lasso regression and ridge regression, as well as least squares method and the least moduli method. An algorithm for solving the problem is developed based on the well-known ellipsoid method.Item Mathematical Modelling of Shock Wave Reflection from a Heat-Conducting Wall [Articol](2024) Secrieru, GrigoreIn this work, on the basis of the model of the Navier-Stokes equations, a study of the dynamics of the flow, which arises in the process of reflection of a normally incident shock wave from a heat-conducting wall, is carried out. At the weak intensity of the shock wave and moderate jump in the initial temperatures of gas and wall, analytical expressions for the perturbation of gas parameters, describing the main characteristic features of the reflected flow, are obtained. This allows us to evaluate the influence of viscosity, thermal conductivity and other physical effects on the formation of dissipative and ideal non-viscous and non-heat-conducting zones in the region of the arising flow.Item PERSIST: A New Probabilistic Model For Data Denoising [Articol](2024) Scrob, SergiuThe paper proposes a more efficient solution for reducing the data noise level, using probability estimation for radius-based spatial inference and sampling techniques.Item Informational Extended Games And Their Applications [Articol](2024) Novac, LudmilaIn this article, we analyse informational extended games, i.e., games in which the players choose their actions simultaneously, with assumption that they have some information about the future strategies which will be chosen by other players. For all informational extended games of this type we assume that players’ payoff functions are common knowledge. Under these assumptions we define the noncooperative informational extended games and analyse Nash equilibrium. As a particular case of the non-cooperative informational extended games, we analyse the class of bimatrix informational extended games and we present an example of game in order to show the possibility to use the information for this class of games.Item Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems [Articol](2024) Magnanti, Thomas L.; Stratila, DanWe introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. Using our technique, we obtain a 1.61-approximation algorithm for the concave cost facility location problem, an exact algorithm for the concave cost lot-sizing problem, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs.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.