The matrix equation AX-YB=C and related problems

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23.     

On decomposition of continuity

Summary The main purpose of this paper is to introduce the concepts of η-sets, ηζ-sets,η-continuity and ηζ-continuity and to obtain a decomposition of continuity.     

Electrochemical Recovery of Silver from Lead Alloys in Chloride Melts

Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry.     

On the problem of calculating the optical film parameters from the measured transmission spectra

The procedure for calculating the dispersion of the refractive and absorption indices and thickness of an optical film, based on measurements of spectral dependence of the transmittance, is described. The film parameters are calculated using a solution of the approximation problem. The effect of the film model on the calculated values of the refractive and absorption indices is analyzed.     

Continuum Limit of the Volterra Model, Separation of Variables and Non-Standard Realizations of the Virasoro Poisson Bracket

The classical Volterra model, equipped with the Faddeev-Takhtajan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so-called separated variables. Taking the continuum limit of these formulae, we obtain the Virasoro generators written as determinants of infinite matrices, the elements of which are constructed with a set of points lying on an infinite genus Riemann surface. The coordinates of these points are separated variables for an infinite set of Poisson commuting quantities including L ₀. The scaling limit of the eigenvector can also be calculated explicitly, so that the associated Schroedinger equation is in fact exactly solvable.     

Energy losses of dipoles traveling relative to a moving medium

We consider the radiation from nonoscillating dipoles traveling with constant velocity directed parallel or antiparallel to the velocity of a homogeneous transparent moving medium. It is assumed that the medium in its rest frame is isotropic and has no spatial dispersion. We obtain expressions for the radiative energy losses and estimate the polarization energy losses of electric and magnetic dipoles of different orientations. In particular, it is shown that the energy loss of a source is negative if it moves in the direction of the medium motion and the source velocity is less than the medium velocity. Estimates for the energy losses of dipoles in the cases of an electron beam and a flow of a weakly dispersive medium are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 502–512, June 2006.     

Reaction of methyl bromopropiolate with diamines as a method of synthesis of imidazolidine derivatives

A convenient method of synthesis of 2-(methoxycarbonylmethylene)-substituted imidazolidines and imidazolidinium bromides, and also of bicyclic diazo compounds has been developed starting from methyl bromopropiolate and ethylenediamine and its derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1205–1208, September, 1991.     

Measurement of the Seperation between Atoms beyond Diffraction Limit

We propose a scheme to obtain the distance of two identical atoms placed inside the standing wave field by monitoring the collective resonance fluorescence spectrum emitted by the two particles. We find three different parameter ranges, depending on the distance of the atoms as compared to the transition wavelength. For large interparticle distances, dipole-dipole coupling is negligible, and the main system evolution arises from the interaction with the standing wave field. In the small-distance limit, the dynamics is dominated by the dipole-dipole interaction. Finally, in the intermediate region, a rich interplay of the various couplings arises, which however is lifted for strong driving laser fields. The present measurement procedure allows us to distinguish the three cases. In each of the cases, we show how to determine the distance of the two particles and their respective positions relative to the nodes of the standing wave field with fractional-wavelength precision.     

Standard enthalpy of formation of La2CoO4(cr)

The enthalpies of reactions of La₂CoO₄(cr) and CoCl₂(cr) with hydrochloric acid were measured with an isothermal-jacket calorimeter. The results obtained and the available literature data were used to calculate the standard enthalpy of formation of La₂CoO₄(cr) at 298.15 K, Δ_f H ^o = ?2179 ± 7 kJ/mol.