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Item Properties of the ideal-intersection graph of the ring Zn(2023) Utenko, YelizavetaIn this paper we study properties of the ideal-intersection graph of the ring 𝑍𝑛. The graph of ideal intersections is a simple graph in which the vertices are non-zero ideals of the ring, and two vertices (ideals) are adjacent if their intersection is also a non-zero ideal of the ring. These graphs can be referred to as the intersection scheme of equivalence classes (See: Laxman Saha, Mithun Basak Kalishankar Tiwary "Metric dimension of ideal-intersection graph of the ring 𝑍𝑛" [1] ). In this article we prove that the triameter of graph is equal to six or less than six. We also describe maximal clique of the ideal-intersection graph of the ring 𝑍𝑛. We prove that the chromatic number of this graph is equal to the sum of the number of elements in the zero equivalence class and the class with the largest number of element. In addition, we demonstrate that eccentricity is equal to 1 or it is equal to 2. And in the end we describe the central vertices in the ideal-intersection graph of the ring 𝑍𝑛.Item Risk modelling approaches for student-like models with fractal activity time(2021) Solomanchuk, Georgiy; Shchestyuk, NataliiaThe paper focuses on value at risk (V@R) measuring for Student-like models of markets with fractal activity time (FAT). The fractal activity time models were introduced by Heyde to try to encompass the empirically found characteristics of read data and elaborated on for Variance Gamma, normal inverse Gaussian and skewed Student distributions. But problem of evaluating an value at risk for this model was not researched. It is worth to mention that if we use normal or symmetric Student‘s models than V@R can be computed using standard statistical packages. For calculating V@R for Student-like models we need Monte Carlo method and the iterative scheme for simulating N scenarios of stock prices. We model stock prices as a diffusion processes with the fractal activity time and for modeling increments of fractal activity time we use another diffusion process, which has a given marginal inverse gamma distribution. The aim of the paper is to perform and compare V@R Monte Carlo approach and Markowitz approach for Student-like models in terms of portfolio risk. For this purpose we propose procedure of calculating V@R for two types of investor portfolios. The first one is uniform portfolio, where d assets are equally distributed. The second is optimal Markowitz portfolio, for which variance of return is the smallest out of all other portfolios with the same mean return. The programmed model which was built using R-statistics can be used as to the simulations for any asset and for construct optimal portfolios for any given amount of assets and then can be used for understanding how this optimal portfolio behaves compared to other portfolios for Student-like models of markets with fractal activity time. Also we present numerical results for evaluating V@R for both types of investor portfolio. We show that optimal Markowitz portfolio demonstrates in the most of cases the smallest possible Value at Risk comparing with other portfolios. Thus, for making investor decisions under uncertainty we recommend to apply portfolio optimization and value at risk approach jointly.Item Аналіз програмних систем підтримки розумного будинку(2019) Глибовець, Андрій; Моголівський, ВіталійПроведено аналіз досліджень у сфері "розумного будинку". Визначено ключові проблеми галузі. Розглянуто наявні Saas системи, здійснено порівняння між ними та знайдено сильні та слабкі сторони кожної із систем. Визначено ключові характеристики системи підтримки "розумного будинку".