In order to encourage research work in mathematics, the Department of Fundamental Sciences held its annual **competition for the best papers in mathematics and physics among those published in 2021 by the staff of Bauman Moscow State Technical University. **

After much deliberation, the winner and top rankings for the papers in mathematics were determined as follows:

**1st place **for the best 2022 scientific publication in mathematics is awarded to **Chetverikov Vladimir Nikolaevich**, D. Sc. (Phys. Math.), Professor of the FN-12 Department

for the paper "Orbital decompositions and integrable pseudosymmetries of control systems", published in Automatica (Q1, Scopus).

The paper aims to determine the conditions for orbital decomposition of affine systems in terms of their pseudosymmetries. It provides a constructive algorithm of orbital decomposition and a description of pseudo-symmetries. Several examples are considered. The results obtained are original and important for both fundamental research and solving real-world control problems.

The remaining top rankings in the 2022 competition for the best scientific publication in mathematics include:

2nd place

**Gordeev Eduard Nikolaevich**, D. Sc. (Phys. Math.), Professor of the IU-8 Department

for the paper "On the Number of Solutions to the Linear Diophantine Equation and Frobenius Problem" in Computational Mathematics and Mathematical Physics (Q2, Scopus).

The paper considers the issues concerning solvability of linear Diophantine equations and the number of solutions to those. Beside the general case, the paper focuses on the combinatorial characteristics of the number of solutions and the mean number of solutions to equations of a special type. One type of equation represents the partition of a natural number into natural terms. The other type is a linear equation in two variables, usually investigated in connection with the Frobenius problem. Three aspects are considered in particular detail. The first aspect concerns investigating whether the Diophantine equation exists and what number of solutions it may have in the case of problem parametrization with respect to the right-hand side. The paper presents formulas and estimates for calculating this number for the general case as well as for specific cases. The second aspect deals with the partition problem. The third aspect concerns the well-known Frobenius problem. The results obtained are stated as proven theorems and represent advances in the field of Diophantine equations.

3rd place

**Fetisov Dmitriy Anatolyevich**, D. Sc. (Phys. Math.), Professor of the FN-12 Department

For the paper "On A-Orbital Linearization of Three-Dimensional Single-Input Affine Systems" in Differential Equations (Q2, Scopus).

The investigation established the conditions for A-orbital linearizing feedback and equivalence of three-dimensional affine systems to linear controllable systems in the vicinity of the equilibrium position. The paper presents the necessary and sufficient conditions obtained in the form of a theorem and provides its proof. In addition, a linearization algorithm is described and an example is analyzed. The results of the work are important for both fundamental research and solving real-world stabilization problems.

Congratulations to the winners!