Associators as measures of memory for media with optical memory and the optimization problem

The interference of light in a medium with optical memory is discussed within the framework of a nonassociative algebra. It is shown that it is possible to introduce an energy coefficient of useful action K_e, an information coefficient of useful action K_int, and a coefficient characterizing the size of the memory of the medium D. The problem of optimizing the process over these parameters is considered. Graphs are given for K_e, K_int, and D as functions of a free parameter β that accounts for experimental conditions. Tbilisi State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 29–32, August, 1997.     

Enumeration of Full Graphs: Onset of the Asymptotic Region

A full graph on n vertices, as defined by Fulkerson, is a representation of the intersection and containment relations among a system of n sets. It has an undirected edge between vertices representing intersecting sets and a directed edge from a to b if the corresponding set A contains B;. Kleitman, Lasaga, and Cowen gave a unified argument to show that asymptotically, almost all full graphs can be obtained by taking an arbitrary undirected graph on the n vertices, distinguishing a clique in this graph, which need not be maximal, and then adding directed edges going out from each vertex in the clique to all vertices to which there is not already an existing undirected edge. Call graphs of this type members of the dominant class. This article obtains the first upper and lower bounds on how large n has to be, so that the asymptotic behavior is indeed observed. It is shown that when n > 170, the dominant class predominates, while when n < 17, the full graphs in the dominant class compose less than half of the total number of realizable full graphs on n vertices.     

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.     

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.     

Meta-Hamiltonian groups with elementary commutant of rank 2

This paper is concerned with the structure of periodic meta-Hamiltonian groups with elementary commutant of rank 2 that have complemented Miller Moreno subgroups. It is proved that there exist four types of such groups.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 168–175, February, 1990.The proof of this assertion will be given in another paper of the authors.     

Cubic surfaces in AG(3, q) and projective planes of order q 3

Spread sets of projective planes of order q ³ are represented as sets of q ³ points in A AG(3, q ³). A line through the origin in A can be interpreted as a space A ₀ AG(3, q), and the spread set induces a cubic surface L in A ₀. If the projective plane is a semifield plane of dimension 3 over its kernel, then L has the property that it misses a plane of A ₀. Determining all such surfaces L leads to a complete classification of the semifield planes of order q ³, whose spread sets are division algebras of dimension 3.An alternative proof of a result due to Menichetti, that finite division algebras of dimension 3 are associative or are twisted fields, follows with the classification.     

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Primitive points on constant elliptic curves over function fields

Letf:CE be a non-constant rational map between curves over a finite field, whereE is elliptic. We estimate the number of rational points ofC whose image underf generate the group of rational points ofE.     

Nonlinear properties of surface “screw” instability in symmetric semiconductor plates

For the first time we study the nonlinear properties of the surface screw instability (SSI) when waves are excited at both faces of a plate and the interaction between them must be taken into account. The nature of the SSI development and the stability of surface screw waves against modulation are examined. Diagrams of the regions where the SSI development is soft and explosive as well as the regions of modulated waves are given in the space of parameters characterizing the electro-hole plasma and external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 30–34, April 1990.