[en] The prerelativistic history of the equivalence principle (EP) is presented briefly. Its role in history of the general relativity theory (G.R.T.) discovery is elucidated. A modern idea states that the ratio of inert and gravitational masses does not differ from 1 at least up to the 12 sign after comma. Attention is paid to the difference of the gravitational field from electromagnetic one. The difference is as follows, the energy of the gravitational field distributed in space is the source of the field. These fields always interact at superposition. Electromagnetic fields from different sources are put together. On the basis of EP it is established the Sun field interact with the Earth gravitational energy in the same way as with any other one. The latter proves the existence of gravitation of the very gravitational field to a heavy body. A problem on gyroscope movement in the Earth gravitational field is presented as a paradox. The calculation has shown that gyroscope at satellite makes a positive precession, and its axis turns in an angle equal to α during a turn of the satellite round the Earth, but because of the space curvature - into the angle two times larger than α. A resulting turn is equal to 3α. It is shown on the EP basis that the polarization plane in any coordinate system does not turn when the ray of light passes in the gravitational field. Together with the historical value of EP noted is the necessity to take into account the requirements claimed by the EP at description of the physical world

[en] Concepts of physical reality and the wave function determinism form are considered. Discussion of the last years showed that in case of following the quantum ensemble theory, such ensembles must be attributed to unusual properties, that are not consistent with the standard probability theory. Thse properties are not seen in a single particle and may be detected in correlation effects. Similar to non-Euclidean geometry, necessary for description of the rate space in special relativity theory, quantum mechanics gives rise to non-Kolmogorov probability theory. The author considers this to be the essence of analysis of quantum ensemble properties

[en] A detailed derivation of T-coefficient representations is given. A connection is established between the T-coefficients and the sigmasub(j)-symbols. It is proved that the T-coefficients of the tree method are analytically continued sigmasub(j)-symbols of angular moment theory

No abstract available

[en] Two methods for derivation of a transformation coefficient of the basis function in the six-dimensional space which corresponds to a three-body problem are shown. The second method of replacement of the overlapping integral by a matrix element of a certain exponential function makes it possible to summarize different coefficients in the angular momentum theory. The calculated matrix element completes the series of transformation coefficients of so-called trees functions. Together with T-coefficients obtained elsewhere which realize transformations between different ''trees'', the coefficient (j'sub(1)j'sub(2)/jsub(1)jsub(2))sup(PHI)sub(KJ) gives all the factors of the Vigner function for different linear transformations of the wave-function of a three-particle system

[en] A new method is proposed for obtaining the coefficient < j'₁j'₂/j₁j₂>sub(KJM)sup(PHI) corresponding to transformations of the three-body basis function in the six-dimensional space. This method generalizes the previously suggested methods. Theoretical group representation is applied. The result obtained includes as particular case expressions for transformation coefficients known earlier

No abstract available

[en] By a diagrammatic method of construction of spherical hrmonics, the transition matrices between the Cartesian and hyperspherical bases of a multidimensional isotropic oscillator are calculated. The transition matrices are shown to be expressed in terms of the Klebsch-Gordan coefficients for SU(2) group, continued onto moments multiple to 1/4. A diagrammatic method is proposed for construction of these matrices for an arbitrary hyperspherical tree

No abstract available

[en] On the basis of two-dimentional oscillator Wigner functions (OWF) the arbitrary dimentional OWF are derived and development of the diagram technique permitting to determine relatively easy the obvious dependence of these functions on Eulerian angles is developed. Wigner functions are studied for the isotropic oscillator of arbitrary dimension. Cartesian wave functions being chosen as the basis