Calculation of the infrared spectrum and density of the vibrational states of an SiO2 melt by molecular dynamics

The density of the vibrational states of an SiO₂ melt under various PT conditions, the distributions of the Si-O-Si and O-Si-O angles in it, and its IR absorption spectra have been calculated by molecular dynamics with the use of a pairwise additive Born-Mayer potential. A comparison with the experimental data reveals that the ionic approximation selected is capable of basically reproducing the structural and spectroscopic properties of the melt, but the distributions of the bond angles are considerably broader than the experimentally determined distributions, and the absorption band caused by the stretching vibrations is not displayed in the calculated spectrum. The disparities indicated are apparently due to the isotropic nature of the potential of the interparticle interactions.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 467–470, July–August, 1991. Original article submitted October 12, 1990.     

Polarization dynamics of longitudinally monomode bipolarized microchip solid-state lasers

This paper is devoted to the polarization dynamics of a longitudinally monomode bipolarized Nd:YAG laser: the low-frequency polarization dynamics of a microchip laser is studied experimentally and theoretically. The intensities and the relaxation oscillation spectrum of orthogonally polarized modes versus the direction of pump polarization is observed. A phase-sensitive model of a longitudinally monomode bipolarized solid-state laser with linear polarized diode laser pump is developed to account for the experimental observations.     

Comparative study of the behaviour of 1H-indazoles and 1-(p-aminophenyl)indazoles under electron impact

The electron impact mass spectrometric fragmentation pathways for several 1H-indazoles and 1-(p-amino-phenyl)indazoles were investigated. An interesting relationship between the substitution pattern in the framework of the indazole derivatives and the fragmentation patterns was observed.     

Class of singular integral operators

A class of singular integral operators is studied from the point of view of the boundedness of their action from some symmetric spaces into other spaces.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 105–110, January, 1991.     

On the theory of isentropic solutions of quasilinear conservation laws

This paper studies isentropic solutions of quasilinear first-order equations with two independent variables and a flux function that is only continuous. The isentropic solutions are characterized by the requirement that the S. N. Kruzhkov entropy conditions hold for these solution with the equality sign. It turns out that the existence of a nonconstant isentropic solution imposes rather strong restrictions on the nonlinearity. In particular, it is shown that on the minimal interval containing the essential image of the isentropic solution, the flux function satisfies the local Lipschitz condition, and its generalized derivative is a function of locally bounded variation. Also, it is proved that when the flux function is nonlinear, any isentropic solution is continuous on nondegenerate intervals. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

Metric fluctuations,entropy, and the Wheeler-deWitt equation

Quantization using quantum potentials is described in terms of momentum fluctuations, and it is related to Fisher information and entropy. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 32–44, July, 2007.     

Object-oriented representation of hierarchical graphs

We introduce the concept of C₀-systems, which can be used to represent syntactic objects of graph-based formal systems with inheritance. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 159–170, 2004.