Analysis of the structure of an amorphous sediment obtained upon decomposition of potassium oxofluroniobate in water

An amorphous sediment was prepared by the decomposition of potassium oxofluoroniobate K_{2 ? x} Nb₄O₃(O, F)₃F in water. For this sediment, the atomic radial distribution function was analyzed with the use of a fragment model, which allows one to interpret expanded coordination spheres as being formed by first several strongest diffusion maxima. These spheres carry the most reliable information on the structure. It is shown that the amorphous sediment consists of the randomly packed Nb(O,F)₆-octahedra with interatomic distances close to those observed in the ordered region in the N-Nb₂O₅ structure. During decomposition in water, the initial K_{2 ? x} Nb₄O₃(O, F)₃F phase loses KF-layers, whereas Nb₆ clusters with metal bonds are destroyed.     

On the possibility of a radical decrease in the strength of many-body interactions in the organic metal α-(BETS)<Subscript>2</Subscript> KHg(SCN)<Subscript>4</Subscript>

Behavior of the de Haas-van Alphen (dHvA) oscillations depending on the angle between the magnetic field direction and the perpendicular to conducting layers in the quasi-two-dimensional organic metal α-(BETS)₂ KHg(SCN)₄ was studied in detail. The angular dependence of the dHvA oscillation amplitude exhibits a series of minima (at ±43.2°, ±64.6°, and ±72.0°) related to the “zero spin” effect, through which it is possible to estimate the splitting factor. An analysis of this value suggests that many-body interactions in the compound studied are either absent or at least radically weakened.     

Application of hydroacoustic radiators for the generation of seismic waves

To excite seismic waves with a high coherence, powerful hydroacoustic radiators placed in a natural reservoir were used. Theoretical estimates and the test data demonstrate a high efficiency of the proposed method of seismic wave excitation. The calculations are in good agreement with the results of measurements. The results of phasing the radiation with the use of two monopole sources separated by a quarter-wave distance are presented. It is shown that the use of the proposed scheme of excitation makes it possible to control the radiation pattern while obtaining a high coherence of seismic waves.     

On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.     

Spectral problems for pencils of polynomial matrices. Methods and algorithms. V

Methods and algorithms for the solution of spectral problems of singular and regular pencils D(λ, μ)=A(μ)-λB(μ) of polynomial matrices A(μ) and B(μ) are suggested (the separation of continuous and discrete spectra, the computation of points of a discrete spectrum with the corresponding, Jordan chains, the computation of minimal indices and a minimal basis of polynomial solutions, the computation of the determinant of a regular pencil). Bibliography: 13 titles. Translated by V. N. Kublanovskaya Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 26–70     

Asymptotic expansions of solutions to singularly perturbed systems

Under the condition that a degenerate system has an exponentially stable integral manifold, an asymptotic expansion of the Cauchy problem that generalizes the well known Vasil'eva expansion is constructed for a perturbed system.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 552–560, April, 1993.     

Determination of the boiling point distribution of sulfur compounds in light cycle oil using GC with a flame photometric detector and pyrolyzer

A method has been developed to determine the boiling point distribution of sulfur compounds in light cycle oils (LCO'S). The method chosen for this analysis was GC with a flame photometric detector (FPD) and pyrolyzer. Tests were carried out to evaluate the recovery efficiency, repeatability, and accuracy of the method. Repeatabilities within 2% were obtained. The recovery of benzothiophenes and dibenzothiophenes was close to 100%; this was important because these are the major sulfur components in LCO's. No hydrocarbon or solvent interferences were observed with the use of the pyrolyzer, even for a 95% solvent level. Comparison with results from other techniques showed that the method accurately determined the levels of sulfur compounds in the LCO boiling point range.