Gaussian samples, regular simplices, and exchangeability

The interchangeable Goodman—Pollack-type random finite sets are characterized. Received June 14, 1995, and in revised form October 16, 1995.     

Topology of rearrangements of non-smoothness sets of minimum functions in variational problems

Control Problems Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 3, pp. 62–63, July–September, 1990.     

Excitation of photoluminescence in Er-doped oxide and fluoride crystals

It has been established that laser excitation of infrared radiation (2.9 μm) in oxide and fluoride crystals doped by Er³⁺ ions gives rise to excitation of concomitant luminescence in the visible region according to the two-step nonlinear mechanism.     

Electret processes in disordered systems based on liquid dispersion media

Electret-thermal analysis (ETA) of disordered systems based on dispersed media is carried out. It is shown that the method of thermally stimulated currents makes it possible to estimate the structural changes occurring in a liquid dispersion medium. It is found that liquid water in a free state exhibits the electret properties. The observed multiple peaks on the thermally stimulated current curve are the evidence of the multicomponent nature of the ??free water?? system. The mechanisms of processes leading to the formation of the electret state in such systems are considered.     

An experimental and theoretical study of shock-wave propagation through reactive gases under conditions causing a transformation of the flow structure

Experimental observations of the transformation of the structure of shock waves entering the discharge gap of either a transverse or decaying glow discharge are presented. It is found that the total impulse of the shock wave pressure remains constant. A variation in the speed of sound, that is, the shock wave velocity, at which total dispersion of the wave occurs is found to be nonmonotonous across the discharge gap. The times over which the wave structure keeps changing after switching off the discharge have been more accurately determined. On the basis of the obtained experimental data and earlier results, a conclusion on the mechanism of this effect has been drawn. This mechanism is related to the dispersion of disturbances making up the wave structure in a relaxing medium (such as the glow discharge plasma). On the basis of a theory of this kind of dispersion, using the experimental data, and comparing energetic and temporal characteristics of the internal states of the plasma under study and the mode of sound disturbances (which according to the experiment, are responsible for the effect), we have succeeded in determining the O₂(a ¹Δ_g) state whose relaxation brings about this effect.     

A modified scheme for the synthesis of 1-benzyl-4,5-diamino-1,2,3-triazole

Conclusions A modified scheme was proposed for the synthesis of 1-benzyl-4, 5-diamino-1,2,3-triazole involving the use of high pressure (5–6 kbar) which permits a significant increase in the yield of this product.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2633–2634, November, 1985.     

Asymptotics of Damped Periodic Motions with Random Initial Speed

We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form αU + β, where U is a fixed random variable and α and/or β tend to infinity.     

Flood search under the California Split rule

We consider flood search on a line and show that no algorithm can achieve an average-case competitive ratio of less than 4 when compared to the optimal off-line algorithm. We also demonstrate that the optimal scanning sequences are described by simple recursive relationships that yield surprisingly complex behavior related to Hamiltonian chaos.     

Preparation of rhenium carbonyl chloride

Summary The reaction between iron pentacarbonyl and rhenium pentachloride in ethyl ether under a pressure of hydrogen and carbon dioxide forms rhenium carbonyl chloride in 30% yield. It was not possible by this method to prepare the total-rhenium carbonyl Re₂(CO)₁₀.