XII Всеукраїнська наукова конференцiя молодих математикiв
Permanent URI for this collection
До збірника увійшли тези наукових доповідей молодих вчених, котрі брали участь в роботі конференції. Автори опублікованих матеріалів несуть відповідальність за їх зміст. Тези друкуються в авторській редакції.
Browse
Browsing XII Всеукраїнська наукова конференцiя молодих математикiв by Subject "conference abstracts"
Now showing 1 - 8 of 8
Results Per Page
Sort Options
Item Boolean network optimization by stochastic rewiring(2024) Cherevko, ChristinaIn today’s rapidly evolving technological world, the demand for smaller yet more powerful computers is escalating at an unprecedented pace, driving a significant need for research in circuit optimizations. This surge in demand underscores the critical role of logic synthesis, which lies at the heart of digital circuit design. Logic synthesis serves as a pivotal stage in converting a high-level functionality description into an efficient hardware implementation. It is key to meeting the ever-increasing demands for miniaturization and performance enhancement in modern electronics.Item Fractal dimension of the boundary of cantorvals(2024) Karvatskyi, DmytroWe say that a Cantorval 𝑋 is achievable if there exists a convergent positive series Σ︀ 𝑢𝑛 such that 𝑋 = 𝐸(𝑢𝑛). Taking into account the above theorem, there naturally arises the question: Is the boundary 𝑋𝐶 for an arbitrary Cantorval 𝑋 a fractal set?Item Generalized solvability of pseudo-parabolic integro-differential equations(2024) Nazarchuk, VictoriaIn our work, we prove the theorem 1 without requiring the fulfillment of conditions (3)–(5). Thus, it is demonstrated that the theorems regarding the well-possedned of the initial-boundary value problem and the existence of optimal control from [2] remain valid under weaker assumptions.Item Hybrid random fields(2024) Zhydok, Fedir; Chornei, RuslanHybrid Random Fields is a class of graphical probabilistic models and it combines Bayesian Networks and Markov Random Fields models. Due to certain assumptions and properties of Hybrid Random Fields, it can simplify the calculation of joint distribution for a certain set of random variables and conditional probability densities for each of the random variables.Item One generalization of the special linear group and matrix equations(2024) Skuratovskii, Ruslan; Zakolenko, OlhaWe generalize the group of unimodular matrices and find its structure. For this goal we propose one extension of the special linear group. Let SL2(Fp) denotes the special linear group of degree 2 over a finite field of order p.Item Solving classical (systems of) linear algebraic equations using non-classical methods of computer mathematics(2024) Tsukanova, AlisaSince the beginning of time people have made some optimal, more or less, decision, based only on pure human experience. Over time it was no longer possible to realize this action without special mathematical methods that carry out global search for necessary optimum. Nowadays, in crazy time of global computerization, these methods allow us to take, in fact, innovative look at some complicated problems of classical mathematics. The given paper presents basic results of analysis of well known classical Gauss method (or Gaussian elimination method) and new optimization method of gradient descent for solving general systems of linear algebraic equations, obtained after testing our own program, written in "Visual Basic for Applications".Item Strong consistency of discrete estimators for drift parameters in the Cox–Ingersoll–Ross model(2024) Prykhodko, O.; Ralchenko, KostiantynThe Cox–Ingersoll–Ross model is important and popular. It is used in many areas, for example, in the pricing of interest rate derivatives and as a model of stochastic volatility. Thus parameter estimation is significant for the practical application of this model. We are interested in developing theoretical estimators for parameters (𝑎, 𝑏) when 𝜎 is known for models based on discrete observations. Additionally, we aim to explore how estimators designed for continuous data can be adapted for the case of discrete observations. Therefore in this study we investigate the discrete counterparts of the strongly consistent estimators introduced in [2, Theorem 5].Item Strong law of large numbers for pairwise independent identically distributed random variables(2024) Lohvynov, DmytroConsider the case of a two-dimensional {𝑋𝑖,𝑗}𝑖,𝑗∈N sequence of pairwise independent and identically distributed random variables and let’s investigate the strong law of large numbers employing multi-indexed sums.