AVERAGED CONTROLLABILITY OF THERMOELASTICITY EQUATIONS. AVERAGE STATE OF A RECTANGULAR PLATE

The concept of averaged controllability has been introduced relatively recently aiming to analyse the controllability of systems or processes containing some important parameters that may affect the controllability in usual sense. The averaged controllability of various specific and abstract equations has been studied so far. Relatively little attention has been paid to averaged controllability of coupled systems. The averaged state of a thermoelastic rectangular plate is studied in this paper using the well-known Green's function approach. The aim of the paper is to provide a theoretical background for further exact and approximate controllability analysis of fully coupled thermoelasticity equations which will appear elsewhere.

MOMENTUM OF AN ELECTROMAGNETIC WAVE IN TIME-VARYING DIELECTRIC MEDIA

In the context of the Abraham–Minkowski controversy, the problem of the propagation of electromagnetic waves in a linear dielectric medium with a time-varying dielectric constant is considered. It is shown that the momentum of an electromagnetic wave in the form of Minkowski is preserved with an instantaneous change in the dielectric permittivity of the medium. At the same time, the Abraham momentum is not conserved, despite the spatial homogeneity of the problem. This circumstance is interpreted as a manifestation of the Abraham force.

PARAMETER ESTIMATION FOR OSCILLATORY SYSTEMS

Simple harmonic motion was investigated of a rotational oscillating system. The effect of dumping and forcing on motion of the system was examined and measurements were taken. Resonance in a oscillating system was investigated and quality factor of the dumping system was measured at different damping forces using three different methods. Resonance curves were constructed at two different damping forces. A probabilistic model was built and system parameters were estimated from the resonance curves using Stan sampling platform. The quality factor of the oscillating system when the additional dumping was turned off was estimated to be $Q = \num{71 \pm 1}$ and natural frequency $\omega_0 = \num{3.105 \pm 0.008}\, \si{\per\second}$.

THE RADIATIVE CORRECTIONS ACCOUNTING IN THE REACTION NEAR-THRESHOLD OF $J/\psi$ PHOTOPRODUCTION

The use of the method developed in the CLAS collaboration (Jefferson Lab, USA) of improving leptons momentum for more correct studies of final state selection of quasi-real photoproduction resulting from the reaction to near threshold photoproduction of the $J/\psi$ meson is described. The radiation photons that were detected in electromagnetic calorimeter were studied with electrons and positrons accompanied them in very narrow angles. The method of radiated photon selection of $e^+ e^- p^{\prime}(e^{\prime})$ reaction is given, where $e^+ e^-$ lepton pair is formed during the decay of $J/\psi$ meson.

INTERVAL EDGE-COLORINGS OF TREES WITH RESTRICTIONS ON THE EDGES

An edge-coloring of a graph $G$ with consecutive integers $c_1,\ldots,c_t$ is called an interval t-coloring, if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if it has an interval t-coloring for some positive integer $t$. In this paper, we consider the case, where there are restrictions on the edges of the tree and provide a polynomial algorithm for checking interval colorability that satisfies those restrictions.

LOCALLY-BALANCED $k$-PARTITIONS OF GRAPHS

In this paper we generalize locally-balanced $2$-partitions of graphs and introduce a new notion, the locally-balanced $k$-partitions of graphs, defined as follows: a $k$-partition of a graph $G$ is a surjection $f:V(G)\rightarrow \{0,1,\ldots,k-1\}$. A $k$-partition ($k\geq 2$) $f$ of a graph $G$ is a locally-balanced with an open neighborhood, if for every $v\in V(G)$ and any $0\leq i<j\leq k-1$ $$\left\vert \vert \{u\in N_{G}(v)\colon\,f(u)=i\}\vert - \vert \{u\in N_{G}(v)\colon\,f(u)=j\}\vert \right\vert\leq 1.$$ A $k$-partition ($k\geq 2$) $f^{\prime}$ of a graph $G$ is a locally-balanced with a closed neighborhood, if for every $v\in V(G)$ and any $0\leq i<j\leq k-1$ $$\left\vert \vert \{u\in N_{G}[v]\colon\,f^{\prime}(u)=i\}\vert - \vert \{u\in N_{G}[v]\colon\,f^{\prime}(u)=j\}\vert \right\vert\leq 1.$$ The minimum number $k$ ($k\geq 2$), for which a graph $G$ has a locally-balanced $k$-partition with an open (a closed) neighborhood, is called an $lb$-open ($lb$-closed) chromatic number of $G$ and denoted by $\chi_{(lb)}(G)$ ($\chi_{[lb]}(G)$). In this paper we determine or bound the $lb$-open and $lb$-closed chromatic numbers of several families of graphs. We also consider the connections of $lb$-open and $lb$-closed chromatic numbers of graphs with other chromatic numbers such as injective and $2$-distance chromatic numbers.

EXPLICIT FORM FOR THE FIRST INTEGRAL AND LIMIT CYCLES OF A CLASS OF PLANAR KOLMOGOROV SYSTEMS

In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form \begin{equation*} \left\{ \begin{array}{l} x^{\prime }=x\left( R\left( x,y\right) \exp \left( \dfrac{A\left( x,y\right) }{B\left( x,y\right) }\right) +P\left( x,y\right) \exp \left( \dfrac{C\left( x,y\right) }{D\left( x,y\right) }\right) \right) , \\ \\ y^{\prime }=y\left( R\left( x,y\right) \exp \left( \dfrac{A\left( x,y\right) }{B\left( x,y\right) }\right) +Q\left( x,y\right) \exp \left( \dfrac{V\left( x,y\right) }{W\left( x,y\right) }\right) \right) , \end{array} \right. \end{equation*} where $A\left( x,y\right)$, $B\left( x,y\right)$, $C\left( x,y\right)$, $D\left( x,y\right)$, $P\left( x,y\right)$, $Q\left( x,y\right)$, $R\left(x,y\right)$, $V\left( x,y\right)$, $W\left( x,y\right)$ are homogeneous polynomials of degree $a$, $a$, $b$, $b$, $n$, $n$, $m$, $c$, $c$, respectively. Concrete example exhibiting the applicability of our result is introduced.

LOSS FUNCTIONS AND DESCENT METHOD

In this paper, we showed that it is possible to use gradient descent method to get minimal error values of loss functions close to their Bayesian estimators. We calculated Bayesian estimators mathematically for different loss functions and tested them using gradient descent algorithm. This algorithm, working on Normal and Poisson distributions showed that it is possible to find minimal error values without having Bayesian estimators. Using Python, we tested the theory on loss functions with known Bayesian estimators as well as another loss functions, getting results proving the theory.

PATH FOLLOWING PROBLEM FOR UAV CARRYING PENDULUM

The linearized dynamics of a UAV is considered along with a pendulum hanging from it. The state trajectories of the center of mass of the UAV are given. Given the trajectory of the center of mass of the UAV and the state trajectory of its yaw angle, we have to find the control actions and conditions under which the UAV would follow the path while holding the pendulum stable around its lower equilibrium point. The problem is solved using the method for solving inverse problems of dynamics. All the state trajectories of the system and all the control actions are calculated. The condition is obtained under which a solution to the path following problem exists. A specified simple trajectory is chosen as an example for visualizing the results.

MEASUREMENT OF DISTANCE BETWEEN REGULAR EVENTS FOR MULTITAPE AUTOMATA BASED ON A NEW CHARACTERIZATION OF EQUIVALENCE CLASSES

In this paper several problems related to the implementation of the method for the approximate calculation of distance between regular events for multitape finite automata are considered and resolved. An algorithm of matching for the considered regular expressions is suggested and results of the algorithm application to some specific regular expressions are adduced. The proposed method can be used not only for the mentioned implementation, but also separately.