Complete classification of stationary flows with constant total pressure of ideal incompressible infinitely conducting fluid

The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of the flow the system of magnetohydrodynamics (MHD) equations is reduced to a nonlinear vector wave equation extended by the incompressibility condition in a form of a generalized Cauchy integral. For flows with constant total pressure the wave equation is explicitly integrated, whereas the incompressibility condition is reduced to a scalar equation for functions, depending on different sets of variables. The central difficulty of the investigation is the separation of variables in the scalar equation, and integration of the resulting overdetermined systems of nonlinear partially differential equations. The canonical representatives of all possible types of solutions together with equivalence transformations, that extend the canonical set to the whole amount of solutions are represented

On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

Effect of audiovisual stimulation on the psychophysiological functions in track-and-field athletes

In 18- to 23-year-old athletes specialized in field-and-track athletics, the psychophysiological status (cognitive, psychoemotional, and neurodynamic indicators) and the spectral power of the main EEG rhythms, and the heart rate variability prior to and after the course of audiovisual stimulation (AVS) training (the experimental group) were studied as compared with athletes not receiving AVS (the control group). It has been shown that the AVS training sessions in the experimental group caused improvements to the psychoemotional (the levels of anxiety and neuroticism decreased, while the motivation to achieve success and the hardiness level increased), cognitive, and neurodynamic indicators (the volume of mechanical memory and the speeds of attention switching and simple visual-motor responses increased, while the variation of anticipatory and delayed responses to a moving object became reduced). Increases have also been recorded in the high-frequency EEG α2-subrange rhythm power and the parasympathetic nervous system activity, while the autonomic regulation contour activity was enhanced, and more efficient heart activity at rest was formed after the AVS training course in the experimental group compared to the control. This leads to the conclusion about a positive effect of the AVS training course received by athletes engaged in track-and-field athletics on their psychophysiological parameters and autonomic regulation mechanisms