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 effect of geoacoustic characteristics of the bottom on the long-range sound propagation in an inhomogeneous ocean

The long-range sound propagation from a deep ocean to a receiving system located on the shelf is modeled. The waveguide model is constructed on the basis of the data of an acoustic-oceanographic experiment carried out in the northwestern Pacific. The sensitivity and the frequency dependence of the difference in the sound field levels at the crossing of the frontal zone on the geoacoustic characteristics of the bottom of the shelf and the continental slope are investigated. It is shown that the level difference decreases by 8.2 dB as the velocity of longitudinal waves increases by 100 m/s in the range within 1490–1820 m/s.     

Factor and term ranks for matrix union over semirings

We consider the arithmetic properties of the factor-rank and term-rank functions for matrices over semirings. In particular, we investigate the sets of matrices that satisfy the extremes of inequalities for these rank functions of matrix union. The classification of the linear transformations that keep these sets invariant is obtained. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 175–197, 2003.     

On entire nonnegative solutions of quasilinear inequalities of elliptic type that vanish on a set of positive measure

In the article, it is proved that any nonnegative solution of an elliptic quasilinear inequality that vanishes on a subset of positive measure is trivial. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 112–118, 2005.     

Prognostication of aging of polymeric composite materials

Experimental data demonstrate that a study of accelerated aging can enable prognostication of the working capacity and storage life of polymeric formulations used in aircraft components on the basis of changes in thermogravimetric constants of these polymeric formulations.     

A Symmetric-Impulse Approximation Applied to the Faddeev Theory on the Charge Transfer Amplitude

Off-the-shell anomalous factors of the two-body Coulomb transition matrices appear in the integral form of the Faddeev second-order nuclear-electronic amplitude, for proton-hydrogen charge transfer scattering in a typical nlm → n′l′m′ transition. A symmetric-impulse approximation (SIA) is applied to eliminate these factors and an induction method is proposed to analytically calculate the remaining integrals. The nuclear-electronic amplitude is derived for the general case, and for totally symmetric collisions, in terms of generalized hypergeometric functions of two variables, F ₄, and of one variable, ₃ F ₂, respectively. The angular distribution of the second-order nuclear-electronic charge transfer amplitude shows the Thomas mechanism as a peak or a hump for symmetric and asymmetric collisions. There also exists a peak in the forward angular distribution of the second-order nuclear-electronic amplitude, which partly cancels the kinematic peak in the angular distribution of the charge transfer differential cross sections.     

Fundamental aspects of initiated oxidation of tridecane and polyethylene in solutions

Specific features of the initiated oxidation of polyethylene and its low-molecular-weight analogue tridecane, associated with the occurrence of the process in the short-chain mode, were studied.