On the radical for some class of Banach algebras

Let A be a complex Banach algebra. It is well known that the second dual A** of A can be equipped with a multiplication that extends the original multiplication on A and makes A** a Banach algebra. We show that Rad(A) = ^⊥(A ^* · A) and Rad(A ^**) = (A ^* · A)^⊥ for some classes of Banach algebras A with scattered structure space. Some applications of these results are given.     

Dynamics of electron beams in plasmas

The characteristic features of the relaxation of the energy and momentum distribution functions of the electrons in a plasma produced by a low-voltage beam discharge in helium are investigated. It is established that, contrary to widely held opinion, the energy of an intense electron beam may relax due to the wave excitation. The critical currents corresponding to a jumplike transition from one relaxation mechanism to another are measured. The density of metastable helium atoms is determined from the comparative analysis of theoretical and experimental results on the structure of the energy spectrum of the electrons of an intense beam. An intense electron beam is found to become more isotropic in the course of its interaction with Langmuir waves in a collisionless plasma. The cross section for quasi-elastic collisions between the electrons and Langmuir plasmons is estimated. The wave nature of the beam-plasma mechanism for the relaxation of the anisotropic electron energy distribution function is demonstrated, and the mechanism itself is shown to come into play when the discharge current exceeds a certain critical level. The experimental threshold criterion for the energy relaxation of an intense monoenergetic beam is obtained for the first time. It is shown that the relaxation occurs in two stages: the isotropization stage, in which the beam energy decreases insignificantly, is followed by the stage in which the beam relaxes to a state with a plateau-like energy distribution function. The threshold criterion for the relaxation of the anisotropic electron energy distribution function is universal in character regardless of the cause of anisotropy.     

Energy spectrum and effective mass of carriers in the InSe/GaSe superlattice

Within an effective mass approximation the energy spectrum and mass of carriers in the InSe/GaSe superlattice have been calculated. The superlattice belongs to type II: electrons are primarily confined to the InSe layers whereas the holes are mosfly confined to the GaSe layers. The characteristic feature of electronic structure of the superlattice is the existence of minibands of light carriers at the θ point of the Brillouin zone and minibands of heavy carriers at theM point. The dependence of the miniband structure on thickness of layers has been computed. It is shown that the minibands of light and heavy carriers compete with one another in energy. A general conclusion is made concerning the influence of the competition between the minibands on optic and kinetic properties of the superlattice.     

Application of finite perturbation method in calculating g-factors of free radicals

Institute of Chemical Kinetics and Combustion, Siberian Branch of the Academy of Sciences of the USSR. Institute of Catalysis, Siberian Branch of the Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 28, No. 5, pp. 41–48, September–October, 1987.     

Oxidative polymerization of pyrrole in polymer matrix

The oxidative matrix polymerization of pyrrole (Py) by Ce(IV) in the presence of Polyacrylic acid (PAA) has been studied to obtain water-soluble and insoluble products. The role of the PAA, Pyrrole, and Ce(IV) concentration, order of component addition, the structure of polymer matrix (PAA, Hydroxy Ethyl Cellulose (HES), Poly-N-vinylpyrrolidone (PVP)], and model unit of PAA (propionic acid), on the polymerization system were investigated. Interaction of PAA with insoluble polypyrrole (PPy) and the interpolymer complex formation were investigated along with the aggregation of PPy onto the matrix polymer followed by spectral shifts. FTIR results of insoluble products obtained from the PAA–Py–Ce(IV) system and solubility of the system is explained in light of the mechanism of the polymerization of pyrrole on the polymer matrix. © 1995 John Wiley & Sons, Inc.     

Dehydrohalogenation of haloalkylarenes in the synthesis of alkenylaromatic hydrocarbons

Russian Journal of Organic Chemistry -     

Calculation of an unsteady moving-boundary flow in a porous medium by the generalized method of integral relations

Dorodnicyn’s generalized method of integral relations is used to compute a Verigin-type single-phase unsteady flow in a porous medium. This problem describes the pumping of a gas through a gallery in a bounded horizontal aquifer and is associated with underground gas storage in aquifers. The case of an isothermal process and an ideal gas are considered. The viscosity of the gas is neglected. Sines are used as smoothing functions. The results obtained in the first and third approximations are presented and analyzed. The solution is compared with a finite-difference solution and that produced by the method of integral relations. The results are given in a table.     

Slowing down of the growth of a crack of variable width under the influence of a temperature field

This paper touches upon changes in the temperature field near the ends of a crack of variable width under the action of an inhomogeneous stress field. The solution of the boundaryvalue problem on the equilibrium of the crack with partially contacting edges (there is adhesion of the edges on a certain part of the contact zone and slippage on another one) under the action of the outer inhomogeneous stress field, temperature field, and efforts on the contacting surfaces of the crack of variable width comparable with displacements in an elastic state is reduced to the problem of linear conjugation of analytic functions.