YSU scientists’ research works published in international prestigious scientific journals

Professor Grigori Karagulyan, Doctor of Physical and Mathematical Sciences at the Chair of Function Theory and Differential Equations, conducted joint research with Polish mathematician Anna Kamont and published the article titled "Wavelet polynomials and Weyl multipliers" in the American "Mathematical Analysis" journal with Q1 rating.

The Armenian professor is the author of more than 60 scientific articles, more than 10 of which were published in Q1 journals.

"My three research works published in 2021 are dedicated to the estimation of maximal for orthogonal sums of different natures. Anna Kamont proposed to consider similar problems for wavelet transforms. After a while, we started our joint remote discussions related to the problem. As a result of working actively for about two months, we managed to solve the proposed problem in its final version," said G. Karagulyan and informed that this work was published in 2023.

The main result of the work of Armenian and Polish researchers is an inequality that is related to one of the modern directions of mathematics - the theory of wavelets.

"In the work, it was applied in the study of some problems related to orthogonal series and wavelets. In particular, the exact asymptotics of the Weyl multipliers of the convergence of wavelet-polynomial series have been found, as well as the exact norm estimate of the maximum function generated from a finite number of wavelet transformations was presented," the professor noted while talking about the topic of the research.

Initially, the researchers were aimed at solving the Weyl multiplier problem for wavelet-polynomial systems, but the results exceeded expectations since much more general estimates were found with a variety of applications.

"The results of the work and proposed methods will have other applications in wavelets and related mathematical directions. The theory of wavelets is one of the modern directions of mathematics, the origins of which come from applied problems. Wavelets are widely used in fields such as quantum physics, geology, image processing and tomography," the professor noted and emphasized that although the amount of research directly related to everyday human problems is extremely small in mathematics, mathematics is a complete organism like a fruit tree and requires love and continuous attention to give abundant harvest.

The articles of Professor Viktor Ohanyan, Head of the Chair of the Theory of Probability and Mathematical Statistics of the Faculty of Mathematics and Mechanics and Doctor of Physical and Mathematical Sciences are also published in high-impact international journals with Q1 rating.

In 2023, Viktor Ohanyan, co-authored with his PhD student Davit Martirosyan, published his another research work titled "Intersection Probabilities of Four Lines inside a planar convex domain" in Cambridge University's "Applied Probability" journal.

The research on stochastic geometry and tomographic methods of geometric probabilities is aimed at solving the problem of recovery of convex bodies using probabilistic methods.

"It is noteworthy that this problem is solved for all cases, except for the three-dimensional case, which, in fact, is the most demanded in applications," said Professor Ohanyan.

Presenting the importance of his research in the context of solving problems encountered in everyday life, he emphasized that currently medical tomographic tools determine the shape and size of convex curves approximately (the measurement variation is unknown). Therefore, this research is also aimed at accurately determining the shape and size of convex curves using probabilistic tomographic methods.

Professor Ohanyan, summing up the speech, noted that probabilistic tomography is a broad concept, as it is possible to use different models when solving this problem: "Unfortunately, the issue of unity in the world has not been resolved to this day. Our latest article, published in the Contemporary Mathematical Analysis Journal with Q3 rating in 2024, in the continuation of that research."

Professor Viktor Ohanyan, Head of the Chair of the Theory of Probability and Mathematical Statistics of the Faculty of Mathematics and Mechanics and Doctor of Physical and Mathematical Sciences is the author of more than 100 scientific articles.