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.     

Semi-Classical Asymptotic of Spectral Function for Some h-Admissible Operators

In this paper the results from [7, 8], concerning the asymptotic behaviour of the spectral function on the diagonal for Schrodinger operators h →0, are extended to the case of some h-admissible operators, acting in Rⁿ, no 2.     

Rotation of the universe

We study the problem of a possible rotation of the observable Universe (Metagalaxy) from the point of view of the general-relativistic theory of gravitation. We employ the concept of a hierarchical structure of reality, based on the existence of Eddington-Dirac large numbers. From the Einstein equations in their Landau-Raichaudhuri form we derive expressions for the angular momentum and angular velocity of the rotation of the Metagalaxy. These expressions give an coinciding in order of magnitude with the observed one. Using the formulas obtained, and using the hierarchy relation (large number relation), we obtain the Stanyukovich formula S N^3/2 which relates the number of nucleons in the Metagalaxy N and its angular momentum S. We show that the angular velocity may decrease in inverse proportionality to the scale factor, which may explain its small value at this time. We show that the source of rotation in cosmology can be space-time torsion, induced by the spin of fermionic matter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 12–16, March, 1987.The authors are grateful to V. F. Panov for the discussion of this paper and valuable comments.     

Self-activated luminescence of zinc sulfide

The nature of the luminescence of zinc sulfide in the spectral range (360), 380–420 nm (SAL) at 80K is analyzed. It is shown that the appearance of SAL radiation is accompanied by additional absorption in the region (350) 365–370 nm at 80K. The low-temperature spectra of sphalerite, exposed to different radiation and subjected to different treatment, are studied. The multiband luminescence of the isoelectronic sulfur impurity in ZnO deposits in the region 383–640 nm is discussed. It is concluded that SAL luminescence is attributable to the localization of excitons in ZnS on clusters, whose formation precedes the precipitation of the ZnO·S phase. The formation of oxygen clusters and deposits on dislocations in ZnS is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 60–66, February, 1987.     

Self-avoiding random walk: A Brownian motion model with local time drift

Summary A natural model for a self-avoiding Brownian motion inR ^d, when specialised and simplified tod=1, becomes the stochastic differential equation , where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that exists almost surely, and to identify the limit.     

A subjective Bayesian approach to the theory of queues II — Inference and information in M/M/1 queues

This is a sequel to Part I of A Subjective Bayesian Approach to the Theory of Queues. The focus here is on inference and a use of Shannon's measure of information for assessing the amount of information conveyed by the various types of data from queues. The notation and terminology used here is established in Part I.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

A Study of Composite Heuristic Algorithms

When faced with a difficult combinatorial problem whose optimization may be prohibitively expensive, researchers frequently turn to the study of fast heuristic algorithms in an effort to guarantee near-optimal results. An important aspect in the evaluation of such an algorithm is the determination of its worst-case behaviour, relative to an optimization rule. We here focus attention on schemes for combining two or more heuristics so as demonstrably to improve the worst case that can occur. We survey successful, illustrative examples of such composite algorithms, concentrating on problems of central significance from domains such as scheduling, packing and routeing. We also attempt to illuminate the conditions under which these strategies can be successful and why.     

The free loop space and the algebraic k-theory of spaces

Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let . Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces.