Nash Equilibria,Variational Inequalities,and Dynamical Systems

In this paper, we introduce some relationships between Nash equilibria, variational equilibria, and dynamical equilibria for noncooperative games.     

How to find the Lax pair from the Yang-Baxter equation

We show explicitly how to construct the quantum Lax pair from the Yang-Baxter equation. We demonstrate the new method by applying it to the Heisenberg XYZ model.Supported by DOE contract DE-FG02-88ER25053     

Screw dislocation in spherical particle

The elastic fields generated by a straight-line screw dislocation axially arranged in a spherical particle have been calculated and analyzed. Some features of the distribution of elastic fields in this case and in the case of a screw dislocation lying along the axis of a cylindrical whisker are similar. The elastic energies per unit dislocation length differ slightly in the two cases. This corroborates the validity of application of some of the results obtained for screw dislocations in elastic cylinders to the study of properties of screw dislocations in equiaxed particles.Authors are very indebted to dr. A. B. Lebedev for his kind support.     

Determination of the rate of nonradiative relaxation,processes on excitation of electronic states in YAG:Nd3+

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 2, pp. 229–233, February, 1991.     

Anisotropic field of background internal waves on a sea shelf and its effect on low-frequency sound propagation

The space-time spectral characteristics of the field of background internal waves (IW) are obtained for two oceanic shelf regions (the Atlantic shelf of the United States and the Kamchatka shelf) and analyzed. Within the framework of a numerical experiment, it is shown that the observed anisotropy of the IW field may considerably affect the low-frequency sound fluctuations in the aforementioned regions and, in particular, may change the interference invariant of the sound field.     

Absorption and emission dynamics in concentrated optical ensembles under laser excitation

A new theoretical model describing the emission and absorption dynamics in an ensemble of molecules under intense coherent pulsed pumping is developed on the basis of the concepts of cooperative light-induced luminescence (CLIL). The CLIL development is described within the framework of formalism of the system density matrix in the space of photon wave functions. It is shown that the fast growth of CLIL relates to the development of coherent states of the quantum field in the area of efficient cooperative interactions of molecules (coherence volume). A system of equations for the calculation of CLIL energy, population of excited states, and optical absorption of the system in dependence on the laser pump energy density is solved. The theoretical results obtained are in good agreement with the experimental data.     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -     

Minimax detection of a signal in the heteroscedastic Gaussian white noise

We consider the problem of signal detection in the heteroscedastic Gaussian white noise when the set of alternatives is essentially nonparametric. In this setting, we find a family of asymptotically minimax tests. The results are extended to the case of testing a parametric hypothesis against nonparametric sets of alternatives. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 54–68.     

Characteristic features of carbazole phosphorescence quenching by benzophenone molecules in toluene at 77 K

We have studied the characteristic features of carbazole phosphorescence quenching by benzophenone in toluene at 77 K. We have shown that the decrease in the relative phosphorescence intensity for carbazole (energy donor) by a greater factor than we see for the relative change in its decay time is due to the fact that a change in the phosphorescence decay time occurs only for carbazole molecules participating in triplet-triplet energy transfer, while the substantial decrease in the phosphorescence intensity for carbazole with no change in the phosphorescence decay time is connected with quenching of its singlet states. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 554–556, July–August, 2006.