Nonuniform estimates of the stability of the normal law under random perturbations of the scale parameter and some of their applications

Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei. Trudy Seminara, 1988, pp. 84–92.     

Synthesis of methyl ethers of methyl 2-acetamido-2-deoxy-α-D-glucopyranoside

A convenient method is proposed for the synthesis of all the individual methyl ethers of methyl 2-acetamido-2-deoxy-α-D-glucopyranoside based on the partial methylation of 2-acetamido-2-deoxy-α-D-glucopyranoside with dimethyl sulfate in an alkaline medium followed by preparative liquid column chromatography on silica gel of the resulting mixture of methyl ethers.     

The matrix equation AX-YB=C and related problems

The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23.     

Isotopic families of contact manifolds for elliptic PDE

A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

     

Analysis of packing factors of crystalline polymers in terms of the glass transition to melting temperature radio

An expression for the ratio of the glass transition temperature to the melting temperature, T _g/T _m, was derived with allowance for fluctuations of the packing factor in the amorphous state. This relationship made it possible to describe the actual range of variation in T _g/T _m depending on a change in the packing factor in the crystalline state k _{o, cr}. The proposed approach forms the basis for the method of determination of increments in the packing ratio k _{o, cr} and formulation of the principles of selection of experimental data for calculations. The glass transition temperatures in polyethylene depending on the type of unit cell were calculated.     

CONCEPTUAL DESIGN STUDIES OF AN 84 GHz, 500 kW, CW GYROTRON

The feasibility of an 84 GHz, 500 kW, CW gyrotron for ECRH on an experimental tokamak will be presented in this paper. Mode competition and mode selection procedures are carefully investigated by considering various candidate modes and the TE_10,4 mode is chosen as the operating mode. A conventional cylindrical cavity resonator with weak input and output tapers and parabolic roundings is considered for interaction studies. Self-consistent, both single mode and time-dependent, calculations are carried out and power and efficiencies are computed for a typical set of beam parameters. The results show that an output power of well over 500 kW, CW and efficiency around 40% can be reached without a depressed collector.