On the analysis of coordinate-dependent diffusion

Coordinate-dependent diffusion in solids, in which case the probability of presence of a vacancy, φ, and the probability of migration, γ, depend on coordinate x is analyzed. The coordinate dependence of parameters φ and γ is shown to cause the drift component of the diffusion flux. In the presence of this component, the direction of atomic motion may coincide (enhanced diffusion) or not coincide (retarded diffusion and up-diffusion) with the direction of the diffusion component. The criteria of enhanced diffusion, retarded diffusion, and up-diffusion are established. These criteria are specified by the behavior of function F(x)=φ(x)/γ(x).     

Negative molecular ions of azafullerenes and their hydrogenated derivatives

The formation and decay of negative molecular ions of azafullerenes and their hydrogenated derivatives are investigated by mass spectrometry. The mechanisms of resonant electron capture and the lifetimes of negative molecular ions with respect to the electron autodetachment in azafullerene molecules are discussed. A comparative analysis of the data obtained for azafullerenes and hydrogenated fullerene derivatives is carried out.     

Nonlinear optical parameters and optical limitation in cobalt-doped polyvinylpyrrolidone solutions

Nonlinear optical parameters (nonlinear refractive indices and nonlinear absorption coefficients) of solutions of polyvinylpyrrolidone doped by cobalt to various concentrations are measured at the lasing and second-harmonic wavelengths of a picosecond Nd:YAG laser (λ=1064 and 532 nm, respectively, and τ=35 ps). Data on optical limitation in these solutions are presented. The absence of nonlinear absorption in the IR spectral range and its significant effect in the visible range are demonstrated. Optical limitation at a wavelength of 1064 nm is related to defocusing, whereas at 532 nm, this effect is caused by two-photon absorption and partially by inverse saturated absorption and defocusing. Nonlinear optical parameters of metal-polymer complexes are reported.     

Measurement of thermal lensing effects in high power thin disk laser

Two different experimental methods for disk characterization in thin disk lasers are investigated in this paper. First method is based on the stability regions in optical resonator and the second method is based on using an expanded probe beam. Both of the mentioned techniques are used to determine the thermal lensing effects in high power thin disk laser. The results of the experiments are presented and analyzed. Also the advantages and disadvantages of each method are explained.     

A Tranversality Theorem for Holomorphic Mappings and Stability of Eisenman-Kobayashi Measures

We show that Thom's Transversality Theorem is valid for holomorphic mappings from Stein manifolds. More precisely, given such a mapping from a Stein manifold to a complex manifold and given an analytic subset of the jet space can be approximated in neighborhoods of compacts by holomorphic mappings whose -jet extensions are transversal to . As an application the stability of Eisenman-Kobayshi intrinsic -measures with respect to deleting analytic subsets of codimension is proven. This is a generalization of the Campbell-Howard-Ochiai-Ogawa theorem on stability of Kobayashi pseudodistances.

     

Maximum principle in the problem of time optimal response with nonsmooth constraints : PMM vol. 40, n 6, 1976, pp. 1014–1023

The problem of optimal response [1, 2] with nonsmooth (generally speaking, nonfunctional) constraints imposed on the state variables is considered. This problem is used to illustrate the method of proving the necessary conditions of optimality in the problems of optimal control with phase constraints, based on constructive approximation of the initial problem with constraints by a sequence of problems of optimal control with constraint-free state variables. The variational analysis of the approximating problems is carried out by means of a purely algebraic method involving the formulas for the incremental growth of a functional [3, 4] and the theorems of separability of convex sets is not used.Using a passage to the limit, the convergence of the approximating problems to the initial problem with constraints is proved, and for general assumptions the necessary conditions of optimality resembling the Pontriagin maximum principle [1] are derived for the generalized solutions of the initial problem. The conditions of transversality are expressed, in the case of nonsmooth (nonfunctional) constraints by a novel concept of a cone conjugate to an arbitrary closed set of a finite-dimensional space. The concept generalizes the usual notions of the normal and the normal cone for the cases of smooth and convex manifolds.     

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED3

Elementary-particle Physics and Field Theory

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED₃     

Synthesis of submicron CaZrO<Subscript>3</Subscript> in combustion reactions

Submicron CaZrO₃ powder is obtained in combustion reactions (solution combustion synthesis—SCS) with glycine. It is found that SCS reduces the sintering temperature of CaZrO₃ powders. The dielectric properties of calcium zirconate ceramics are studied by the electrochemical impedance method. It is shown that a ceramics of powders obtained by the SCS method has high dielectric characteristics.     

Dynamics of nanodefects on a loaded gold surface

The dynamics of defects with linear dimensions from ≈1 to ≈100 nm on a Au surface under load have been studied by means of tunnelling microscopy. It is found that the origin, growth, and resorption of the defects is caused by displacements of bands of material from 5 to 50 nm wide, parallel to the {111} slip planes. The defects can be separated into two groups: nonsteady-state defects, whose lifetime does not exceed 15 min, while the depth is ⩽20 nm, and quasi-steady-state defects, with a lifetime three orders of magnitude greater than the first. It is assumed that the nonsteady-state defects are formed when the ensemble of dislocations is being reconstructed, while the quasi-steady-state defects are formed at the instant of formation of dislocation substructures during the creep of the loaded metal. Fiz. Tverd. Tela (St. Petersburg) 40, 2180–2183 (December 1998)     

Effect of a thermal radiation field on the γ-luminescence of alkali-silicate glass

We revealed the changes in the γ-luminescence spectra under the influence of a thermal radiation field on high-purity alkali-silicate glasses (I) and those with addition of Fe³⁺ ions (II). We explain the obtained results within the framework of the L-model of edge absorption and electron-hole recombination processes. Samarkand State University, 15, Universitetskii Bul., Samarkand, 703004, Republic of Uzbekistan. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 453–455, May–June, 1998.