On a characterization of a convolution of Gaussian and idempotent distributions

We prove some analogues of the well-known Skitovich-Darmois and Heyde characterization theorems for a second countable locally compact Abelian group X under the assumption that the distributions of the random variables have continuous positive densities with respect to a Haar measure on X and the coefficients in the linear forms considered are topological automorphisms of the group X.     

Thermodynamics of a gas-coal massif and a nonuniform gas distribution in a coal bed

The thermodynamic potential of a coal bed is calculated, and the gas pressure in the crack-pore system of the bed is shown to be nonuniformly distributed. This pressure is high in “weak“ regions in the bed, i.e., at the sites of a high porosity, low elastic moduli, and low solubility, as well as at high bearing pressure sites. All these phenomena are caused by the elastic interaction of a gas with a solid-state coal frame and the possibility of the formation of a solid solution in the coal. The relative increase in the gas pressure at these sites is estimated. The results obtained can be used to predict the localization of explosive and outburst regions in coal beds.     

Isoperimetric constants of manifolds with small handles

Mathematische Zeitschrift -     

Dipole relaxation in normal aliphatic alcohols

A new mechanism of dipole relaxation and molecular motion in normal aliphatic alcohols is suggested, based on the assumption of the existence of consequent reorientations of the molecules in chains It is shown that the experimental data obtained by different methods of dielectric spectroscopy, including TDS. can be described accurately within the framework of the model.     

A better step-off algorithm for the knapsack problem

The knapsack problem, maximize Σ^m_{i = 1}c_ix_i when Σ^m_{i = 1}a_ix_i?b for integers x_i?0, can be solved by the classical step-off algorithm. The algorithm develops a series of feasible solutions with ever-increasing objective values. We make a change in the problem so that the step-off algorithm produces a series of solutions of not necessarily increasing objective values. A point is reached when no better solutions can be found and the calculation is stopped.     

Intranuclear-Cascade model calculation of photofission probabilities for actinide nuclei

We have calculated the fission probabilities for ²³⁷Np, ^{233, 235, 238}U, ²³²Th, and ^natPb following the absorption of photons with energies from 68 MeV to 3.77 GeV using the RELDIS Monte Carlo code. This code implements the cascade-evaporation-fission model of intermediate-energy photonuclear reactions. It includes multiparticle production in photoreactions on intranuclear nucleons, pre-equilibrium emission, and the statistical decay of excited residual nuclei via competition of evaporation, fission, and multifragmentation processes. The calculations show that in the GeV energy region the fission process is not solely responsible for the entire total photoabsorption cross-section, even for the actinides. The fission probabilities are 80-95% for ²³³U, ²³⁵U, and ²³⁷Np, 70-80% for ²³⁸U, and only 55-70% for ²³²Th. This is because certain residual nuclei that are created by deep photospallation at GeV photon energies have relatively low fission probabilities. The results of those model calculations are in reasonable agreement (at the 10% level) with recent experimental data on relative photofission cross-sections for ²³⁷Np and ^{233, 235, 238}U (but not for ²³²Th or ^natPb) from the Saskatchewan and Jefferson Laboratories over a very wide range in photon energy. Using our calculated fission probabilities plus the total photoabsorption cross-sections per nucleon, estimated from previous cross-section data for nuclei from C to Pb, we can infer absolute photofission cross-sections for the actinide nuclei and compare them with the SAL and JLab results. The resulting discrepancies, however, clearly demonstrate the need for direct measurement of the total photoabsorption cross-sections for the heavy actinides.     

Dragmacidin E synthesis studies. Preparation of a model cycloheptannelated indole fragment

[reaction: see text] The conversion of N-2,2-dichloropropionyl indole methyl ester into a tetracyclic cycloheptannelated indole model compound for the synthesis of dragmacidin E was accomplished in 10 steps. Key reactions include a Witkop cyclization to fashion a C-C bond at C(4) of the indole nucleus and a subsequent Dieckmann cyclization to deliver the desired cycloheptanoid ring.