Igoris Belovas

This research builds upon our previous work on efficient algorithms for calculating and visualizing fractal structures associated with zeta functions, shifting the focus from two-dimensional to three-dimensional structures. Specifically, we introduce Zetabulbs – a class of Mandelbulbs (three-dimensional analogues of Mandelbrot sets) derived from the zeta functions. The visualization of Mandelbulbs poses substantial computational and algorithmic challenges, while also carrying practical relevance in areas such as digital visual effects, where Mandelbulb-based structures have been used in the production of high-budget films. By introducing Zetabulbs, we expand the landscape of zeta-function–driven fractal geometry and open new opportunities for its application in both artistic visualization and scientific exploration.

Based on primary source data, the paper examines the development of admissions to mathematical studies at Vilnius University's Faculty of Physics and Mathematics (1945–1965), Faculty of Mathematics and Mechanics (1966–1977), and Faculty of Mathematics (1978–1990).

Assessing credit risk is essential when making financial decisions, especially investing in debt securities. As the bond market is the largest securities market in the world, a great demand exists for tools to assess issuer creditworthiness. Furthermore, information describing the probability of default is also useful in other areas, such as risk management. In the era of machine learning and big data, new techniques have emerged that allow for automated risk assessment based on large amounts of data. Traditional creditworthiness assessment methods may be inaccurate, as the investor could be biased or misinterpret available information. A review and comparison of modern tools that would allow intelligent processing of large amounts of information will help assess the issuer's credit risk as objectively as possible.

The study investigates the general admission indicators of Vilnius University and its faculties during the 2000–2026 academic years. AR, ARIMA, and exponential smoothing models are applied for data analysis and forecasting. Using correlation analysis, the study aims to assess the impact of demographic factors and determine whether their influence on admission results is statistically significant.

The study examines the trends in student admissions to undergraduate mathematics and informatics programs at the Faculty of Mathematics (1991–1999) and the Faculty of Mathematics and Informatics (1999–2024) of Vilnius University. The review is based on data drawn from primary sources.

The prime zeta function is one of the most under-researched varieties of the class. Very little is known about the irregular distribution of its zeros. The presented study aims - albeit partially - to fill the gap in our understanding of the subject. We consider the zero-free region of the prime zeta function and verify statistically certain conjectures regarding the distribution patterns of the zeroes of the prime zeta function.

It is conjectured that every admissible k-tuple matches infinitely many positions in the sequence of prime numbers. The investigations of this hypothesis have led to many important results; however, the problem remains unsolved. In this work, the problem is studied from the experimental mathematics side. Integer sequences associated with the distribution of admissible prime k-tuples in the intervals (s^n; s^{n+1}] are studied experimentally, using the probabilistic Miller-Rabin primality test and parallel computing technologies. The obtained result gives us one more argument in favor of the infinitude of admissible prime k-tuples conjecture.

Aukštasis mokslas yra vienas iš svarbesnių veiksnių, teikiančių ne tik asmeninę naudą, bet ir prisidedančių prie geresnės, sveikesnės visuomenės kūrimo. Lietuvoje aukštojo mokslo prieinamumui išaugus, šalis tapo viena labiausiai išsilavinusių visoje Europos Sąjungoje. Ženklus universitetų studentų skaičius mažėjimas 2021–2022 metais stabilizavosi ir pradėjo rodyti teigiamą dinamiką. Vilniaus universitete, kurį pasirenka didžiausia stojančiųjų į universitetus dalis (2023–2024 metais jį sudarė 42–43 %), nuo 2023 metų priimtųjų studijuoti skaičius tik augo ir 2024 metais Vilniaus universitete studijas pradėjo didžiausias per 2019–2024 metų laikotarpį pirmakursių skaičius. Darbe nagrinėjami Vilniaus universiteto XXI amžiaus pirmo ketvirčio priėmimo rodikliai. Galimų ateities tendencijų įvertinimui bei analizei yra taikomas ARIMA modelis. Prognozės rezultatai rodo, kad stojančiųjų rodiklis išliks stabilus. Taip pat darbe nustatoma, jog ARIMA modelis tiksliau įvertina stojančiųjų skaičių už anksčiau naudotą AR modelį.

Currently, the problem of generating synthetic financial documents is particularly acute. Extending recent research on the topic, we present an enhanced tool for invoice generation. The primary motivation is the need for invoice corpora for machine learning in accounting automation. The generation produces synthetic invoices with randomized layouts and contents. As content fields are generated, annotations for supervised machine learning are saved along with the generated invoice, thus solving the problem of labor-intensive annotation tasks. The content and layout diversity is evaluated and compared to empirical and synthetic invoice corpora using SELF-BLEU, Alignment, and Overlap metrics. We have validated the stability of the modeling statistically. The modeling is consistent and reproducible. The final assessment is that the diversity of the generated invoices is on par with the real-world ones and, by most metrics, exhibits superiority over the foregoing ones.