Discrete and Continuous Models and Applied Computational Science

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This work presents an intensive study of a single server finite-capacity queueing model with impatience timers which depend on the server’s states, feedback, and a single working vacation policy operating under an \(N\)-policy discipline. We examine the scenario where the server must wait for the number of customers to reach \(N\) to start a regular busy period; otherwise, the server will initiate a working vacation or switch to the dormant state if the number of customers increases. By applying the Markov recursive method, the steady-state probabilities were derived. Various performance metrics were visually depicted to assess diverse system parameter configurations. After constructing the expected cost function of the model, Grey Wolf Optimization (GWO) algorithm is utilized to determine the optimum values of the service rates \(\mu^{*}\) and \(\mu_{v}^{*}\). Numerical examples are provided to validate the theoretical findings, offering insights into this intricate system.

Systems of linear algebraic equations with multi-diagonal coefficient matrices may arise after many different scientific and engineering problems, as well as problems of the computational linear algebra where finding the solution of such a system of linear algebraic equations is considered to be one of the most important problems. This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of the algorithm is formulated and proven. Formula for the complexity of the multidiagonal numerical algorithm is obtained.

The motivation of this paper was the development of computer geometry course for students of mathematical specialties. The term “computer geometry” hereafter refers to the mathematical foundations of machine graphics. It is important to emphasize separately that this course should be designed for second-year students and, therefore, they can only be required to have prior knowledge of a standard course in algebra and mathematical analysis. This imposes certain restrictions on the material presented. When studying the thematic literature, it was found out that the de facto standard in modern computer graphics is the use of projective space and homogeneous coordinates. However, the authors faced a methodological problem-the almost complete lack of suitable educational literature in both Russian and English. This paper was written to present the information collected by the authors on this issue.

Effective application of artificial intelligence (AI) models in various fields in the field of financial risks can increase the speed of data processing, deepen the degree of their analysis and reduce labor costs, thereby effectively improving the efficiency of financial risk control. The application of AI in the field of financial risk management puts forward new requirements for the system configuration and operation mode of financial supervision. With the rapid growth of computer and network technologies, the increase in the frequency of market transactions, the diversification of data sources, and the development and application of big data, this creates new problems for financial risk management based on big data. This paper analyzes the role of artificial intelligence in promoting the reform and growth of the financial industry, and proposes countermeasures for the rational use of AI in the field of financial risk management.