Varieties whose countable embeddability skeletons are semilattices

Translated fromAlgebra i Logika, Vol. 32, No. 3, pp. 288–307, May–June, 1993.     

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.     

Sample-path optimization of convex stochastic performance functions

In this paper we propose a method for optimizing convex performance functions in stochastic systems. These functions can include expected performance in static systems and steady-state performance in discrete-event dynamic systems; they may be nonsmooth. The method is closely related to retrospective simulation optimization; it appears to overcome some limitations of stochastic approximation, which is often applied to such problems. We explain the method and give computational results for two classes of problems: tandem production lines with up to 50 machines, and stochastic PERT (Program Evaluation and Review Technique) problems with up to 70 nodes and 110 arcs. Sponsored by the National Science Foundation under grant number CCR-9109345, by the Air Force Systems Command, USAF, under grant numbers F49620-93-1-0068 and F49620-95-1-0222, by the U.S. Army Research Office under grant number DAAL03-92-G-0408, and by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. Sponsored by a Wisconsin/Hilldale Research Award, by the U.S. Army Space and Strategic Defense Command under contract number DASG60-91-C-0144, and the Air Force Systems Command, USAF, under grant number F49620-93-1-0068. Sponsored by the National Science Foundation under grant number DDM-9201813.     

Propagation of electromagnetic waves in the earth-ionosphere waveguide with a gradual periodic inhomogeneity of the ionospheric upper-boundary impedance

We study the influence of a gradually inhomogeneous periodic disturbance of the upper-wall impedance of a plane Earth-Ionosphere waveguide on the radiation of a vertical electric dipole immersed in the waveguide channel. We consider the case where the disturbance amplitude is commensurable with the undisturbed value of the impedance. An expression is obtained for the Hertz potential when the source and the observation point are located at the lower wall of the waveguide. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 374–383, March, 1998.     

Recurrent solar wind streams

A new approach to investigating the statistical relationship between certain solar features and recurrent wind streams is presented. This approach is based, on a comparative analysis of the distributions of lifetimes of a set of solar features, recurrent geomagnetic disturbances, and geomagnetic “calms.” Correlation coefficients of 0.81, 0.85, 0.79, and 0.77 are found for the distributions of several solar features—filaments, large-scale magnetic fields, coronal features, and coronal holes, respectively—and recurrent geomagnetic disturbances. A correlation factor of 0.97 between the distributions of geomagnetic “calms” and active regions is found. The combined evidence indicates that no specific type of solar feature is responsible for the recurrent stream activity. Rather, the configuration of the large-scale magnetic field of the Sun appears to control the permanently existing corpuscular activity. Since prominences trace polarity division lines of the large-scale magnetic field structure of the Sun, they have been checked as a possible general predictor of recurrent corpuscular activity; their parameters could present the most reliable indices that relate closely with trends in geomagnetic disturbances. A comparative analysis of cyclic variations of sunspot numbers, the total number of prominences, the relative number of low-height (<-20″) prominences, and recurrent geomagnetic storms is made for solar cycle N16. The relative number of low-height prominences is found to correlate broadly (0.83) with recurrent wind streams. P. K. Shternberg State Astronomical Institute, Moscow, Russia; National Solar Observatory, Sacramento Peak, U.S. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 145–151, February, 1998.     

States of surface V(IV)-bearing groups in phosphorus-vanadium oxide and titanium-vanadium oxide silica gels made by molecular epitaxy

ESR shows that V(IV) may occur in isolated or interacting vanadium-oxygen groups on the surfaces of catalytically active P-V and Ti-V-bearing silica gels; there is a relationship between the V(IV) content and the phthalic anhydride selectivity in the oxidation of o-xylene.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 3, pp. 277–282, May–June, 1992.     

Symmetry algebra of nonlinear integrable equations

The complete symmetry algebras of the Veselov-Novikov equation and of the modified Kadomtsev-Petviashvili equation are constructed. Some related questions are discussed.P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 34–41, April, 1993.