Heat pulses in the second-sound regime

At low temperatures, heat propagates in crystals in the form of collective excitations—second-sound waves. How the parameters of the phonon system of the crystal can be determined from the shape of the heat pulse is considered here. Fiz. Tverd. Tela (St. Petersburg) 40, 126–127 (January 1998)     

Some wide-sense analogs of characteristic properties of the normal distribution

Wide-sense analogs of a series of well-known characteristic properties of the normal distribution are adduced.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 61, pp. 59–67, 1976.     

Photochemistry with circularly polarized light—III : Synthesis of helicenes using bis(arylvinyl) arenes as precursors

A systematic study of the photochemical ring-closure of bis(arylvinyl)arenes, using circularly polarized light, is described and commented. In the two series of compounds 5a–e and 6a–e, the observed optical yields follow a similar trend; no asymmetric syntheses were observed in the case of the higher benzologues of [10] helicene, using a 290–370 nm irradiation band, circularly polarized at 313 nm.     

Carrying capacity and deformation properties of glass-reinforced plastic pipes of various construction

Glass-reinforced plastic pipe under internal hydrostatic pressure starts to sweat at loads lower than the mechanical strength of the material. It is established that the life of such pipes is well described by an exponential law. The leakage mechanism is mainly controlled by the deformation properties of the reinforcement and resin. The period of reliable service can be estimated from the time of development of the strain corresponding to the end of the phase of steady-state creep. It is shown that for pipe made with cross-wound glass rovings, the winding angle and the number of roving ends have a considerable influence on the creep and life.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1082–1088, 1967     

Admissibility of the estimate of least squares. Unusual property of the normal law

It is shown that in the linear-regression scheme, the estimates of the squares of parametric vector-functions are admissible in the class of unbiased estimates if and only if the observations obey a normal law. Here, the covariation matrix (non-negative definite) serves as a measure of the quality of the estimate.Translated from Matematicheskie Zametki, Vol. 6, No. 1, pp. 81–89, July, 1969.     

Quantum diffusion of muons in bismuth

A muon spin relaxation rate in a super-pure sample of bismuth has been measured. The experimental data and the theory of coherent diffusion in crystalline lattices with shifted levels are compared.     

The problem of “thermal explosion” in spin-polarized atomic hydrogen gas

The exponential character of the depolarization-rate temperature dependence in spin-polarized atomic hydrogen gas results in a “thermal explosion” phenomenon with increasing density. The inhomogeneous heating is stimulated by the three-body recombination, which in allowance for dipole-dipole interaction takes place at arbitrary spin states of colliding particles. The critical gas density is found to be in the range of 10¹⁸–10¹⁹ cm^?3 for the real parameters of the system.     

Canonical decomposition of projective and affine killing vectors on the tangent bundle

For an affine connection on the tangent bundle T(M) obtained by lifting an affine connection on M, the structure of vector fields on T(M) which generate local one-parameter groups of projective and affine collineations is described. On the T(M) of a complete irreducible Riemann manifold, every projective collineation is affine. On the T(M) of a projectively Euclidean space, every affine collineation preserves the fibration of T(M), and on the T(M) of a projectively non-Duclidean space which is maximally homogeneous (in the sense of affine collineations) there exist affine collineations permuting the fibers of T(M).Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 247–258, February, 1976.