Entangled state generation and modulation of vacuum squeezing by classical optical fields in birefringent fiber

Evolution of the vacuum fluctuations in the two-wave mixing of the optical fields propagating in a birefringent fiber is studied. The two-wave mixing in the birefringent fiber was suggested as a possible scheme for the entangled-state generation. Our treatment in studying the entangled-state generation uses depleted pump approximation and enables one to trace the influence of the input conditions of classical optical fields on the evolution of vacuum squeezing. We report the periodical modulation of the vacuum squeezing when the input relative phase of coherent waves varies. The measure of nonclassical correlations imposed on the generated light is calculated.     

Foliations by complex curves and the geometry of real surfaces of finite type

We show that if the Levi form of a smooth CR manifold is de-generate in every conormal direction, then on a dense open set, the manifold is foliated by complex curves. As a consequence we show that every real analytic manifold of finite D'Angelo type can be stratified so that each stratum locally is contained in a Levi nondegenerate hypersurface. Received in final form: 11 June 2001 / Published online: 28 February 2002     

Simulation of time-resolved vibronic spectra and the possibility of analyzing molecules with similar spectral properties

The possibility of using time-resolved vibronic spectroscopy for spectral analysis of mixtures of chemical compounds with similar optical properties, when traditional methods (based on stedy-state spectra) are inefficient, is demonstrated by using the method of computer simulation. The analysis is carried out by the example of molecules of a series of polyenes (butadiene, hexadiene, octatetraene, decapentaene, and decatetraene), their various cis-and trans-rotational isomers, and phenyl-substituted polyenes. Ranges of relative concentrations of molecules similar in their spectral properties, where reliable interpretation of time-resolved spectra of mixtures and both qualitative and quantitative analyses are possible, are determined. The use of computer simulation methods for optimizing full-scale experiments in femtosecond spectroscopy is shown to hold much promise.     

A microeconomic simulation model of reproduction

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 152–184, 1989.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.