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The Poincare-invariant equations without redundant components, describing the motion of a particle which can be in different spin and mass states are obtained. The quasi-relativistic equation for a particle with arbitrary spin in external electromagnetic field is found. The group-theoretical analysis of these equations in carried out.

It is well known that the electron motion in the external electromagnetic field is described by the relativistic Dirac equation. In this case, in the Foldy–Wouthuysen representation, the Hamiltonian includes the terms corresponding to the interaction of the particle magnetic moment with a magnetic field (∼ (1/m)(σH)) and the terms which are interpreted as a spin-orbit coupling (∼ (σ/m2){(p−eA)×E)). Apart from these constituents the Hamiltonian includes the Darwin term (∼ (1/m) divE) [1]. Such a description is in good accordance with the experimental data. It was shown by Bargman [2] that it is possible to introduce the particle spin in the nonrelativistic quantum mechanics by performing the central extension of the Galilei group. In connection with this Bargman result the problem of finding the motion equations, which are invariant with respect to the extended Galilei group G, arises naturally. Such a problem has been considered in [3–5]. The equations obtained in [5] have redundant components and, besides, these equations do not describe the spin-orbit and the Darwin couplings if one makes the replacement pμ → πμ = pμ − eAμ in them. The aim of this note is to find such motion equations for a particle with spin which are invariant relative to the group G, have no redundant components and describe the spin-orbit and the Darwin couplings of the particle with the field. It is reached by the supposition that the free nonrelativistic particle Hamiltonian has two energy signs just as the Dirac Hamiltonian. This is equivalent to the requirement that the theory (equations) be invariant under such a transformation

A number of papers dedicated to the description of free particles and antiparticles with zero mass and spin 12 has recently appeared [1–6]. A great many equations with different C, P , T properties have been proposed and the impression could be formed that there are many nonequivalent theories for zero-mass particles. The purpose or this paper is to show that it is not the case and to describe all nonequivalent equations. 1. First we shall formulate the result [1] obtained for a particle of spin 12 in such a form that all principal assertions will be valid for massless particles of arbitraly spin. It has been shown [1] that for a particle of spin 12 three types of nonequivalent twocomponent Poincare-invariant equations exist. These three of equations are equivalent to the Dirac equation

The methods of macro- and microstructural analysis are used to investigate the relation between the injection molding parameters, on the one hand, and the structure and physico-mechanical properties of the molded polypropylene block, on the other. It is shown that the structure takes the form of layers of different thickness and shape. Certain properties of molded products are determined not only by the spherulitic structure but also by the nature of the macrostructure of the polymer in the block.

The spectral dependence of the relative quantum yield of certain metals (Cu, Ag, Au, Al, In, Sn, Ti, Fe, Ni, Zr, Nb, Mo, Ta, W, Pt) and nonmetals (ThO2, ZrO2, HfO2, Sc2O3, Nb2O5, LiE, MgF2, SrF2, CsI, ZnS, SbS, BeO) has been investigated in the 95-20 nm region of the spectrum.

The "Minsk-22" computer was used to study the rhythm of cardiac contractions. The R - R intervals of ECG tracings were studied in 1000 to 2000 cardiac cycles. The measurement of these intervals was performed automatically by means of a special device - intervalmeter. The data input was done from a punch tape. Mathematical analysis of the cardiac rhythm consisted in calculating the mathematical expectance, excess and asymmetry of the distribution of the R - R intervals of ECG. This method was employed for the analysis of the sinus rhythm in normal individuals and in patients with atherosclerosis and rheumatic heart diseases. The rhythm was recorded at rest and during functional tests (administration of nitroglycerine, or single breath holding at the peak of inspiration). The asymmetry of the R - R intervals distribution is an index that helps to reveal the dynamics of the transitory processes, being in this respect superior to the intervalgramme. The excess index permits to evaluate quantitatively the stability of the rhythm and the peculiarities of its regulation. Employment of the described methods of cardiac rhythm analysis is expedient for various functional tests and the assessment of the pharmacological effects.

On 29/III in Novocherkassk, Prof. Vladimir Ivanovich Levchatkin, former director of the Kazan District Psychiatric Hospital, died.