Vol 20, No 3 (2014)

In this paper, one-dimensional longitudinal vibration of a solid rod fixed at the ends by means of local masses and springs is studied. As a mathematical model we use Rayleigh rod. The existence and uniqueness of a generalized solution are proved.

The paper is devoted to invariant theory problems, in particular to the problem of finding generators of invariant fields in an explicit form. The set of generators is given for invariant field of unitriangular group concerning the ad-joint representation of GL(n, K) group. Moreover, the set of generators of Borel group for the field of invariants is constructed and their algebraic independence is proved.

Lie group;

adjoint representation;

field of invariant;

generators of the field of invariants;

Borel group;

In this article, we study a problem for a multimensional pseudohyperbolic equation of the fourth-order with an integral condition. Existence and uniqueness of a generalized solution is proved.

One of the well-known problems of algebraic K-theory is the Gersten conjecture. In this work we prove a variant of Gersten conjecture for Adzumaya algebras in equicharacteristic case. Geometrical case of this proposition was proved in the article by I. Panin and A. Suslin.

In the paper, we study an inverse problem for a hyperbolic equation with integral overdetermination condition. The existence of a generalized solution is proved.

In the paper the detailed review of the present-day results related to problems of continuum damage mechanics is given. The survey shows the development of ideas of Y.N. Rabotnov who together with L.M. Kachanov introduced damage and continuity variables which characterize the damage state. In the paper the recent studies in the elasticity, plasticity and creep theories accounting for damage accumulation processes are discussed.

The results of application of semi-conductor converters on the basis of silicon carbide as a sensitive super-high frequency signals recorder. It was also noted that this material is prospective in the development of such areas as medicine, aerospace equipment, high-speed communication lines. The necessity of silicon carbide is increasing for its application in nanoelectronics.

New technique, allowing to increase the accuracy of determination of molecularweight andboiling temperature of unknown components of analyzing mixture, in comparison with our work described in the journal ”Sorption and Chromatographic Processes” 2011, № 4. and based on information on sizes of indexes of retention of Van den Dool and Krats and indexes of the logarithm of constant of distribution in the system ”hexane - acetonitrile”is suggested.

This article proposes a chemism of the barium azide formation through monoazidometilat barium. The results obtained allowed to eliminate possible stops of the process due to formation of gelatinous mass by varying duration of the process.

The properties of spike activity of neurons of the suprachiasmatic nucleus during their membrane depolarisation in vitro are investigated on rat hypothalamic slices. Depolarisation of membrane caused an increase in activity of cells and a decrease in entropy log interspike interval distribution were used as a measure of spikes irregularity generation. Possible mechanisms of the effects are discussed.

With the use of technique of spirography it was shown that background values of breathing pattern parameters in students depend on their biorhythmological features and time of day. Most prominent changes in breathing during the day were found in students with ”intermediate” type of circadian activity, and less prominent - in students with late” type of activity. Significant differences in values of respiratory frequency and in duration of respiratory phases between students with ”early” and ”intermediate” circadian activity were found, and also the differences in frequency and volume parameters of breathingbetween persons with ”intermediate” and ”late” activity in the morning and in the evening were registered. The differences in dynamics of respiratory parameters between persons with ”early” and ”late” types of activity were not significant.

Registration of electroencephalogram (EEG) in the right-handed students during an exam revealed weakening of alpha rhythm in all areas of right and left cerebral hemispheres as well as increased beta rhythm in parietal and end-lobes of the right hemisphere. Simultaneously regular delta waves in the frontal leads ofboth hemispheres and theta waves in right frontal, occipitalis and temporal leads were marked. Offset of EEG slow wave activity in the right hemisphere in partial right-handers was marked in more noticeable way than in that of the true right-handers. The obtained data suggest that the distribution of EEG rhythms in condition of mental and emotional stress in right-handers depends on the type and severity of functional hemispheric asymmetry.