Bound diffusion of ultrafine particles in generalized anharmonic potential

Bound diffusion of ultrafine particles of ferric hydroxide precipitated inside the polymeric cross-linkage degree the experimental spectra reveal a striking broadening up to hundreds of mm/s. This is a consequence of the crossover from the diffusion of a Brownian oscillator to free diffusion in restricted volume, the spatial displacements of the particles depending on the cross-linkage and changing from 0.1 to 0.6 Å.     

Synthesis and mechanism of the formation of bis(methylamides) of pyrazoledicarboxylic acids

The reaction of ethoxymethyleneoxaloacetic ester with phenylhydrazine and methylhydrazine has been studied. It has been established that the addition of phenylhydrazine takes place to the ethoxy group through the -nitrogen atom, and the addition of methylhydrazine to the ethoxy group predominantly through the -nitrogen atom. Several derivatives of -alkyl(aryl)hydrazinomethyleneoxaloacetic esters have been obtained. A series of bis(methylamides) and several diamides of 1-alkyl(aryl)pyrazoledicarboxylic acids have been synthesized. Their structure has been determined on the basis of their UV spectra and their breakdown by hydrolysis to known acids. It has been found that in the alkylation of an ester of 3,4-pyrazoledicarboxylic acid with alkyl halides followed by amidation, two isomeric bis(methylamide)s are formed, apparently with the predominance of derivatives of 1-alkyl-3, 4-pyrazoledicarboxylic acids. It has been established that the bis(methylamide)s of 1-alkyl-3,4-pyrazoledicarboxylic and of 1-alkyl-4, 5-pyrazoledicarboxylic acids have characteristic UV spectra differing from one another. The bis(methylamide)s obtained are pharmacologically active substances.     

Discontinuous Steklov operators in the problem of uniform approximation of derivatives on an interval

With the help of discontinuous Steklov operators, families of integral operators are constructed, which are used to obtain uniform approximations to derivatives of an arbitrary order for a function given on an interval.     

A family of operators with discontinuous ranges and approximation and restoration of continuous functions

A class of operators whose construction is similar to but simpler than the construction of Landau operators is the basis for the design of a modified family of operators with discontinuous ranges. This family has good approximation properties with respect to approximation and restoration problems for continuous functions.     

Adsorption of cesium atoms at structural defects on sapphire surfaces

Results are presented from an experimental study of the adsorption of cesium atoms on sapphire surfaces and their photostimulated desorption. The adsorbed atoms are found to form chains on the surface which are localized near one-dimensional structural defects of the surface. One-dimensional adsorption is analyzed theoretically with different assumptions regarding the mobility of adsorbed atoms along a chain. A comparison of the theories with experimental data favors localized adsorption described in terms of a one-dimensional lattice gas model. The energy of adsorption for an isolated atom on a linear surface structural defect is 0.58 eV, while the energy of attraction between neighboring atoms in the chain is 26 meV. Zh. éksp. Teor. Fiz. 112, 362–370 (July 1997)     

The Riesz bases consisting of eigen and associated functions for a functional differential operator with variable structure

We consider a functional differential operator with variable structure with an integral boundary condition. We prove that its eigen and associated functions form a Riesz basis with brackets in the space L ₂³[0, 1].