Vanadium oxide surface studies

The vanadium oxides can exist in a range of single and mixed valencies with a large variety of structures. The large diversity of physical and chemical properties that they can thus possess make them technologically important and a rich ground for basic research. Here we assess the present status of the microscopic understanding of the physico-chemical properties of vanadium oxide surfaces. The discussion is restricted to atomically well-defined systems as probed by surface techniques. Following a brief review of the properties of the bulk oxides the electronic and geometric structure of their clean single crystal surfaces and adsorption studies, probing their chemical reactivity, are considered. The review then focuses on the growth and the surface properties of vanadium oxide thin films. This is partitioned into films grown on oxide substrates and those on metal substrates. The interest in the former derives from their importance as supported metal oxide catalysts and the need to understand the two-dimensional overlayer of the so-called “monolayer” catalyst. On the single crystal metal substrates thin oxide layers with high structural order and interesting properties can be prepared. Particular attention is given to ultrathin vanadium oxide layers, so-called nano-layers, where novel phases, stabilised by the substrate, form.     

Structural and electronic comparative analysis of aminopyridazines showing anti-GABA activity. Crystal structure of 2-(carboxy-3′-propyl)-3-amino-6-cyclohexylpyridazinium bromide.Ab initio Mulliken population analysis of the 6-phenyl-substituted analog compared to GABA

The crystal structure of 2-(carboxy-3-propyl)-3-amino-6-cyclohexylpyridazinium bromide has been determined by single-crystal X-ray diffraction techniques and refined by full-matrix least squares. The compound crystallized in the tri-clinic space groupP ¯1 witha=10.275(1),b=11.215(1),c=7.082(1) Å,=91.84(1),=102.21(1), =106.77(1)°, andZ=2. FinalR-factor is 0.045. The main structural results are very similar to the ones observed for the 6-phenyl analog. These two compounds are GABA-A antagonists.Ab initio molecular orbital calculations, with STO-3G and 4-31G basis sets, suggest that the exocyclic nitrogen accurately mimics the nitrogen atom of GABA.     

Beryllium diffusion across GaAs/(Al,Ga)As heterojunctions and GaAs/AlAs superlattices during MBE growth

Beryllium diffusion during MBE growth of (Al, Ga)As layers, (Al, Ga)As/GaAs heterojunctions and GaAs/AlAs superlattices has been studied by electrochemical C-V and secondary ion mass spectrometry (SIMS) concentration profiling, in conjunction with transmission electron microscopy. Diffusion times were comparatively short since they were limited to part of the growth sequence, so non-equilibrium effects had a significant influence. The results are consistent with an interstitial-substitutional mechanism in which lattice site incorporation becomes more difficult with increasing band gap enthalpy. Incorporation involves a kick-out reaction which leads to the observed disordering of the superlattices.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

Some inequalities for partial orders

We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most maximal chains, if some antichain has cardinality v, and if there are ₁ chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ₁v (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).This paper was written while the authors were visitors at the Laboratoire d'algèbre ordinale, Département de Mathématiques, Université Claude Bernard, Lyon 1, France.Research supported by NSERC grant # A5198.     

Local products for relativistic quantum fields

A definition of local functions of generalized free fields is suggested. Their concrete form is determined in a fairly general setting by analysing realizations of locality. A huge class of new models of relativistic quantum fields results in this way.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Density of the set of attractive compacta

A compact set K in a smooth closed manifold M is said to be attractive, if on M there exists a system of differential equations, for which K is an asymptotically stable invariant set. It is proved that the set of attractive compacta is dense and its complement contains a dense set of type G in the space of all compacta of the manifold M endowed with two natural topologies.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 143, pp. 170–175, 1985.     

Errors of solutions of linear algebraic systems

Error estimates are derived for the following methods: the sweepout method for tridiagonal systems, the method of square roots, the bordering method, and the method of reflection matrices. The book of S. K. Godunov is devoted to the last method; he altered the method so that it takes any matrix into a bidiagonal matrix; a considerable part of that book is devoted to the error of this alteration. In the present paper the method of reflection matrices is studied in the form in which it is expounded in the familiar book of D. K. Faddeev and V. N. Faddeeva. Recurrent formulas are obtained for the sweepout method which make it possible to successively estimate errors of the components of the solution vector. In the method of square roots the error of the solution vector is estimated by the quantity Here _i and are small quantities; the first characterizes the accuracy of small arithmetics effects, and the second the round-off error in the reverse step. Further, A is the matrix of the system, m, is its order, f is the vector of free terms, and C and are constants with 0 <1. We shall not present here the rather involved estimates for the bordering method. The error of the solution vector obtained by the method of reflection matrices is estimated by the quantity (p_A is the conditioning number of the matrix A) All estimates are obtained up to terms of higher order of smallness than and ₁. The estimates themselves are related to the classification of errors of computing processes proposed by the author in recent years.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 94–110, 1984.