Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

Explosive Materials Combustion by Heated Wires

The knowledge of ignition parameters of explosive materials (EM) presents both the definite scientific interest for developing the ignition kinetics models and the practical interest from the point of view of their danger assessment. The present investigations, as opposed to the known technique for EMs ignition temperature determination, have been performed by using the model explosive material samples of high density which have been produced on the basis of HMX and TATB. Applying the technique of firing ballistic powders by a heated wire, the EM ignition temperature depending on the time (rate) of heating has been investigated. The technique makes it possible to calculate heat pulses and heat flows leading to ignition. By decreasing the heat flow, the time for the EM heating up to ignition increases and temperature falls thereby approaching the critical value, characterising the danger limit under accidents associated with heating. The ignition of EM based on HMX and TATB takes place in a different manner. With the EM on the basis of HMX and with great heat flows. The ignition beginning from the surface in the form of flash is typical but when achieving the critical parameters, the heated layer flash takes place that increases the probability of the explosion realisation. EM based on TATH always ignite in the form of combustion from the surface, independent of the heat flow that points to the higher extent of its safety. These data correlate well with the higher parameters of its ignition

The level of somatic health, sports specialization and qualification of an athlete as indicators of intermediate selection in the mixed martial arts

This article presents the results of experimental research to identify high-priority types of martial arts whose representatives successfully implement their skills in mixed martial arts, as well as the results of the study of somatic healt

Close combat and physical training in kickboxing

The aim of the study was to develop a technique for preparing blows in close combat and improving physical fitness in kickboxing over a period of 10 years (2011-2021

The effectiveness of taekwondo footwork in kickboxing

Modern types of martial arts are increasingly perceived as combinations of improved techniques of several types of wrestling, contributing to increased efficiency, endurance, increased speed and fitness of athletes. Therefore, the aim of the study was to develop a new, improved methodology for preparing effective taekwondo strikes in various sections of kickboxin