Needle Variations and Almost Lower Semicontinuous Differential Inclusions

It is shown that the construction of needle variations can be carried out for almost lower semicontinuous differential inclusions rather than for the case of ordinary single-valued continuously differentiable vector fields usually considered in the literature. The construction leads to needle variations whose flows are in general set-valued but still have good differentiability properties. The variations are constructed by using single-valued selections that are not necessarily continuous with respect to the state variable, but have instead a much weaker 'integral continuity' property, somewhat more general that the 'directional continuity' considered in previous work by A. Cambini and S. Querci, A. Pucci, and A. Bressan. The existence of many such selections is proved by slightly adapting an argument due to Bressan, extending it from the lower semicontinuous to the almost lower semicontinuous case, and strengthening it to yield not only directional continuity at all points but also full continuity at a specified point.     

Galactic model of element formation

A cosmological model is presented that produces He, C, O, D, Li, Be, and B in their observed abundances without a Big Bang. The elements are produced during the 1.5-Gy formation period of a galaxy, with C, O, and other heavy elements produced by stars of M>12 M₃ , He by stars of 6 M_s<M<12 M_s, and D, Li, Be, and B by cosmic-ray reactions in a nearly pure H plasma halo. Thus, the model shows that the major elements used in astrophysical studies can be produced during galactic formation by exactly the same processes known to function today at much lower rates     

Asymptotic integration of a problem of convection

Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 69–75, July–August, 1989.     

Self-broadening in the millimeter-wave spectrum of ozone

Self broadened widths of seven lines of ozone between 75 and 120 GHz have been measured at room temperature. The variation with temperature of the self-broadening parameter for three of these lines has been studied in the range 245–292°K.     

Method of linear prediction in the ultrasonic spectroscopy of rock

The possibility of using the resonant acoustic spectroscopy method for testing the internal state of rock is considered. This method can be used for the determination of the concentration of defects and their spatial distribution. A rock specimen with defects is characterized by a high loss of vibrational energy, which leads to the overlapping of the resonant responses. In this case, the complex resonant frequencies are determined as the parameters of a model that describes the measured transfer function of the response of the mechanical system. The linearity of the vibratory system is used as the a priori information for presetting the functional dependences of the model. An algorithm is developed for the determination of the parameters of the resonances in conditions of their partial overlapping. Examples are presented to demonstrate the possibility of analyzing the complex elastic constant tensor of rock by the acoustic spectroscopy method. The proposed method of experimental data processing provides the possibility for the determination of the weak anisotropy that occurs in the velocity of sound because of a partial fracture of rock.     

Conditional Time Before Ruin of an Insurance Company

The statistical characteristics of conditional time before ruin of an insurance company, including the distribution function of conditional time and its moments are examined.     

The Universe in the Logunov Metric

Exact solutions of the Lagrange equations in the Logunov metric are found in the context of classical gravitation theory.     

Boundary Problems for the Quantum Bose Gas

A relaxation kinetic equation that describes the behavior of a Bose gas is derived. The Kramers half-space problem on isothermal slip is treated. An analytical solution and the number-of-particle distribution function for particles flying toward a wall, in explicit form, are obtained. The dependence of the slip velocity on the parameter that is the ratio of the chemical potential to the product of Boltzmann's constant by the absolute temperature is analyzed. The influence of the quantum effects on the isothermal slip coefficient is evaluated for He⁴.