Optical manipulation of particle ensembles in air

We demonstrate that airborne light-absorbing particles can be photophoretically trapped and moved inside an optical lattice formed by multiple-beam interference. This technique allows simultaneous three-dimensional manipulation of multiple micro-objects in gases.     

Large deviations in the many-body problem

Translated from Matematicheskie Zametki, Vol. 57, No. 1, pp. 133–137, January, 1995.     

Heterocyclic enamines. Derivatives of 3a,4, 5,6-tetrahydro-3H-pyrazino[1,2,3-1 m]carbazole

Reduction of 5, 6-dihydro-4H-pyrazino[1, 2, 3-lm]carbazole alkiodides with sodium in alcohol affords 3a, 4, 5, 6-tetrahydro-3H-pyrazino[1, 2, 3-lm]carbazoles, which are heterocyclic enamines. Some reactions of these compounds are examined.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1244–1248, September, 1970.     

Relation between the structure and extracting power of higher tertiary amines

The effect of the composition and structure of higher tertiary amines on their efficiency in extracting nitric acid has been examined. The ionization constants of the amines in methanol have been determined by potentiometric titration. The extraction constants for nitric acid have been determined at constant ionic strength in the aqueous phase (μ=1). The dependence of these constants upon the concentrations and the degree of association of the amine salts in the organic phase has been examined. For the cases in which the role of steric factors is negligible it has been shown that at low amine salt concentrations in the organic phase there are quantitative regularities between the ionization constants of the amines in methanol, their extraction constants for nitric acid and the inductive effects of the substituents on the nitrogen atom.     

Synthesis of pyrrolo[1,2-a]pyrimidine derivatives

8-Cyanopyrrolo[1,2-a]pyrimidines, the cyano group of which is eliminated when they are heated with phosphoric acid, were obtained by reaction of 2-amino-3-cyanopyrroles with acetylacetone.Compounds Ia, c-g were described earlier in [3], while Ib, h are described in the present work.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1677–1681, December, 1976.     

Asymptotics of the density matrix for a system of a large number of identical particles

The Wigner equation is considered for a system of a large numberN of identical particles with interaction factor of the order of 1/N. In both the Bose and the Fermi cases, we construct the asymptotics of the solution of the Cauchy problem for this equation with regard to the exchange effect for the case in which the Planck constant is of the order ofN ^−1/d , whered is the space dimension. This asymptotics is interpreted in terms of the theory of the complex germ on a curved phase space equivalent to the space of functions with values on the Riemann sphere in the Fermi case and on the Lobachevskii plane in the Bose case. The classical equations of motion in both cases are reduced to the Vlasov equation; since the phase space is infinite-dimensional, the complex germ is subjected to additional conditions depending on the type of statistics. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 84–106, January, 1999.