Quantum frequency standards based on the soliton state of a Bose-Einstein condensate

A method for stabilizing frequency based on using the soliton state of the Bose-Einstein condensate of alkali metal atoms as an atomic source was suggested. The critical total number of lithium condensate particles at which the existence of a quasi-one-dimensional soliton in the condensate was possible and the lifetime of such a soliton were estimated. The attainable accuracy of measuring reference transition frequencies in the suggested standard was shown to be substantially higher than with the known quantum frequency standards.     

Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application

Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics.     

Indeterminacy Criteria for the Stieltjes Matrix Moment Problem

In this paper, we obtain criteria for the indeterminacy of the Stieltjes matrix moment problem. We obtain explicit formulas for Stieltjes parameters and study the multiplicative structure of the resolvent matrix. In the indeterminate case, we study the analytic properties of the resolvent matrix of the moment problem. We describe the set of all matrix functions associated with the indeterminate Stieltjes moment problem in terms of linear fractional transformations over Stieltjes pairs.     

Synthesis of 2-substituted indoles by palladium-catalyzed heteroannulation with Pd-NaY zeolite catalysts

Various 2-substituted indoles were prepared by heteroannulation of o-iodoanilines and terminal alkynes in a one-pot reaction with a Pd(II)-NaY zeolite catalyst. The product formation largely depended on the solvent, base, and reaction temperature. The recycled catalyst showed good reusability in the heteroannulation reaction.     

Polarization fluctuations in a dipolar medium in an electrostatic field

Radio Engineering and Electronics Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1113–1124, September, 1989.     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.     

Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005     

A representation of acoustic waves in unbounded domains

Compact, time‐harmonic, acoustic sources produce waves that decay too slowly to be square‐integrable on a line away from the sources. We introduce an inner product, arising directly from Green's second theorem, to form a Hilbert space of these waves and present examples of its computation.¹ © 2005 Wiley Periodicals, Inc.