An evolution operator in semiclassical electrodynamics

An evolution operatior is described, which acts on the operators of a problem to take it into the solutions of the corresponding problem of semiclassical electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 66–69, November, 1981.     

Systematic investigations of the multi-element preconcentration from copper by precipitation of the matrix as copper(I) oxide and copper(I) thiocyanate

Two methods for multi-element preconcentration from copper by reductive matrix precipitation are presented. In systematic investigations on the coprecipitation behaviour of Ag, Al, Au, Bi, Cd, Co, Cr, Fe, Ga, In, Mn, Mo, NJ, Pb, Sb, Se, Sn, Te and Zn during precipitation of the copper matrix as Cu₂O or CuSCN, the separation parameters were optimized. By combination with a hexamethyleneammonium hexamethylenedithiocarbamate collector precipitation, a concentration of 8 elements (Cu₂O precipitation) or 13 elements (CuSCN precipitation) in a small volume was achieved. The limits of detection of the procedures are, depending on the element, 0.1–5 μg g^?1 for flame atomic absorption spectrometry (AAS) and 0.01–0.1 μg g^?1 for graphite furnace AAS. The relative standard deviations are about 3%. The analytical performance of the procedures is compared with that of an electrolytic copper separation.     

Numerical analysis of near electromagnetic fields of a parabolic cylinder and a paraboloid of revolution

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 119–127.     

Applications of coupled LC-GC: A review

Although coupled liquid chromatographygas chromatography (LC-GC) was first demonstrated ten years ago, only in the last few years has there been a sudden surge of interest in the technique. Approximately 70% of the total number of LC-GC applications have been published in the last two years (1987–88) alone. This review categorizes LC-GC publications into four main application areas: fossil fuels, foods, environmental samples, biologiical/pharmaceutical samples, and miscellaneous samples. Multidimensional separations carried out using other coupled-column chromatographic techniques (such as supercritical fluid chromatography (SFC) with GC, and on-line trace enrichment-GC) have also been included in this review.     

A transfer map for singular fibrations

Using a new group of singular chains on polyhedra, a transfer map is defined on the chain level for fibrations with singularities. These include usual transfer on homology as well as Oliver transfer and other cases.     

Positive definite functions on the Heisenberg group

Work supported in part by the NSF     

On the optimal allocation of two active redundancies in a two-component series system

Components C₁ and C₂ form a series system. Suppose we can allocate the spare R₁ in parallel with C₁ and the spare R₂ in parallel with C₂, or otherwise, allocate R₁ with C₂ and R₂ with C₁. In this paper, we compare these two options using hazard rate ordering.     

Hybrid reordering strategies for ILU preconditioning of indefinite sparse matrices

Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.     

Scattering of solitons for the Schrödinger equation coupled to a particle

We establish soliton-like asymptotics for finite energy solutions to the Schrödinger equation coupled to a nonrelativistic classical particle. Any solution with initial state close to the solitary manifold converges to a sum of a travelling wave and an outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and the symplectic projection onto the solitary manifold in the Hilbert phase space.