Quasiparticle bandstructures of covalent semiconductors and their surfaces

The exchange-correlation self-energies and quasiparticle shifts are calculated for band states of covalent materials (diamond, silicon) and their (001) 2×1 surface in order to solve the bulk and surface band-gap problem of the LDA. The screening properties are described by a model dielectric function taking into account the spatial nonlocality in the surface case assuming specular electron reflection. The wave functions are expanded in terms of localized orbitals. The quasiparticle bandstructures obtained are in reasonable agreement with experimental results.     

Nonlinear Rayleigh-Taylor instability in magnetic fluids with uniform horizontal and vertical magnetic fields

A weakly nonlinear evolution of two dimensional wave packets on the surface of a magnetic fluid in the presence of an uniform magnetic field is presented, taking into account the surface tension. The method used is that of multiple scales to derive two partial differential equations. These differential equations can be combined to yield two alternate nonlinear Schrödinger equations. The first equation is valid near the cutoff wavenumber while the second equation is used to show that stability of uniform wave trains depends on the wavenumber, the density, the surface tension and the magnetic field. At the critical point, a generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. From the latter equation, the various stability crteria are obtained.     

1,3-diallyl-5-[ω-(diphenylphosphino)alkyl] isocyanurates in reactions of complex formation with palladium(ii) dichloride

The reactions of phosphine derivatives of diallyl isocyanurates with palladium(ii) dichloride lead to the formation of complexes, whose structure, composition, and stability depend on the length of the methylene chain between the isocyanurate and diphenylphosphine fragments in the ligand. 1,3-Diallyl-5-[5′-(diphenylphosphino)pentyl and 10′-(diphenyl-phosphino)decyl] isocyanurates with PdCl₂ form monomeric L₂PdCl₂ trans-complexes in which P atoms of the ligands participate in coordination with the metal. 1,3-Diallyl-5-[2′-(diphenylphosphino)ethyl] isocyanurate with PdCl₂ forms a dimeric (LPdCl₂)₂ complex, which decomposes in a solution to the monomer including solvent molecule into the coordination sphere of the metal. The reactions of 1,3-diallyl-5-[4′-(diphenylphosphino)butyl] isocyanurate and 1,3-diallyl-5-[6′-(diphenylphosphino)hexyl] isocyanurate with PdCl₂ give monomeric chelate LPdCl₂ complexes in which one of the allyl groups of the isocyanurate cycle participates in coordination with the central ion along with the phosphorus atom. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1859–1865, September, 1998.     

Dynamics of phase separation in mesomorphic mixtures

We describe the dynamics of phase separation and transition processes, in binary mesomorphic mixtures with the help of a system of two coupled partial derivative equations. We emphasize, both analytically and numerically, that, depending on the regions of the phase diagram, the dynamical behaviour may result either from a two step process (first the phase transition, then the phase separation) or from a process showing salient features of the Cahn-Hilliard spinodal decomposition (bicontinuous periodic networks in the transient stages). The dynamics of evolution of the domain patterns are illustrated with the help of numerical simulations in which homeotropic and planar anchorages are visualized.     

Generating well-behaved utility functions for compromise programming

The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programming. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum.Thanks are due to the reviewers for their helpful suggestions. The English editing by Ms. Christine Méndez is appreciated. The authors have been supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT), Madrid, Spain.     

X-ray study of the superionic phase transition in CuCrS2

The temperature disorder of copper ions in the CuCrS₂ superionic conductor was studied by X-ray analysis. It is shown that the average square deviations of atoms sharply increase and become comparable with the distance between neighbouring tetrahedral sites when CuCrS₂ transforms into the superionic phase. It is also established that the direction of maximum deviation of atoms is close to the direction connecting the tetrahedral positions.     

Rapid multielemental analysis of Chinese reference soils by laser ablation inductively coupled plasma-source mass spectrometry

Summary Laser ablation inductively coupled plasma-source mass spectrometry has been used to determine thirty elements (Na, Mg, Al, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, As, Rb, Sb, Cs, Ba, La, Ce, Nd, Sm, Eu, Dy, Ho, Yb, Hf, Ta, W, Th, U) in seven Chinese reference soils. The Surrey prototype spectrometer was employed with sample ablation by a free-running ruby laser. Concentrations in the soils (GSS-2 to GSS-8) were calculated from elemental responses and sensitivities derived from another soil in the series, namely GSS-1. Comparisons with previous neutron activation analyses are made. Rapid semiquantitative analyses are proved feasible. About eighty percent of the LA-ICP-MS determined concentrations were within a factor of two of the concentrations measured by INAA, and many were considerably closer than this. Precisions were typically in the range 2–10% RSD, but some were considerably poorer for elements present at trace levels.     

Coherence of synchrotron radiation

Gal'tsov et al. [Vestn. Mosk. Gos. Univ., Fiz., Astron.,14, No. 5, 614 (1973)] studied the radiation spectrum of N equally spaced charges moving along a circle. In particular, it was shown that as N the intensity of the radiation from the system of charges vanishes. The present study will consider the radiation spectrum of N charges moving along an arbitrary closed curve, randomly distributed in the vicinity of equally spaced points. The coherency factor will be found for the assumption that: a) the distributions of individual charges are not intercorrelated; b) the charge distribution is such that in the vicinity of a given point only one charge is found. It will be shown that as N the radiation intensity tends to a finite limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 8–11, March, 1988.     

Density estimation and adaptive control of markov processes: Average and discounted criteria

We consider a class of discrete-time Markov control processes with Borel state and action spaces, and ^d i.i.d. disturbances with unknown distribution . Under mild semi-continuity and compactness conditions, and assuming that is absolutely continuous with respect to Lebesgue measure, we establish the existence of adaptive control policies which are (1) optimal for the average-reward criterion, and (2) asymptotically optimal in the discounted case. Our results are obtained by taking advantage of some well-known facts in the theory of density estimation. This approach allows us to avoid restrictive conditions on the state space and/or on the system's transition law imposed in recent works, and on the other hand, it clearly shows the way to other applications of nonparametric (density) estimation to adaptive control.Research partially supported by The Third World Academy of Sciences under Research Grant No. MP 898-152.     

A strange pigeon-hole principle

Using Ramsey theory, we establish the following pigeon-hole type principle: From a large number of random variables (functions, vectors, etc.) one can always select two, X and Y, such that P(X < Y) 1/2. We apply the principle for a poset problem.