Vol. 42 No. 2 (216) (2008)

The present paper investigates the reasons of occurrence of known paradoxes in the intuitive set theory. We have proved that the process of formation of sets is non-finishing, and the reason of occurrence of paradoxes consists in representation of formation of sets as a finishing process (in other words, the reason of occurrence of paradoxes is the identification of concepts of a set and a class). The possibility of full formalization of the intuitive set theory is suspected.

In the paper the parametric representation for Hilbert spaces $b_\alpha^2(B)$ of functions harmonic in the unit ball $B\subset \mathbb R_n $ is obtained.

Using the Mellin transformation the solution of the Cauchy problem for one type degenerate a parabolic equation is constructed.

The paper studied the Fredholm criterion of Teoplits operators in some Hilbert spaces of analytic functions on the unit disk in the complex plane C. The index of those operators was calculated.

In this paper for one limit law from the theory of queues by methods of Fourie an integral representation and expansion in terms of convergent series for density is found.

The analysis of formation change of thin ring plates is carried out in case of large plastic deformations, in view of interconnected change of thickness of the material and deformation of hardening. It is established, that in case of isotropic hardening the equations of the plastic plane stress are reflected on a deviator plane of the cylinder of plasticity as simple dependence between speeds of radial stress and intensity of deformations.

In the light of recombination-enhanced motion of dislocations in semiconductors, we explored the process of thermal capture of an electron by a smooth kink on dislocation. Multi-phonon capture becomes possible due to carrier localisation on the kink. With the use of wave function of localized state we have found the multi-phonon capture cross-section for two limiting temperature cases corresponding to the thermally activated and quantum transition between vibronic terms.

By using the Lee–Low–Pines method the general properties of one dimensional Fröhlich polaron in a quantum wire in presence of electric field are investigated. Analytical expressions for polaron self-energy and the effective mass are obtained.

The adsorption of particles on membranes with taking into account change of structure of adsorption center was theoretically researched. It is shown that combined consideration of adsorption and change of structure of adsorption center leads to the necessity to examine the adsorption in the frame of nonlinear theory of dynamic system. Such approach allows to obtain plurality of stationary states of adsorption center, which brings to bistable regime of adsorption.

In this paper are presented the perspectives of investigation in CLAS detector at Jefferson Lab (TJNAF) of the physics of the quark propagation in cold QCD matter and the resulting hadronization process. The determination of the ''production time" and ''formation time" are given as well as their interpretation as quark energy loss resulting in transverse momentum broadening of the produced hadron and hadronic attenuation in the nuclear medium. A novel target setup was used for these measurements in CLAS where two targets were placed in the beam simultaneously and a newly developed $\pi ^+$ identification technique is presented from the EG2 experiment [1].

A high resolution S-band phase monitor for the 20 MeV electron linac’s RF system is proposed. The resolution gain is achieved by measurement transposition to the high RF harmonic region. The monitor’s main parameters as well as the proposed technical decisions are presented.

Relaxation processes are typical for polybromoprene, which are connected with the dipol-segmental mobility (α-processes), dipol-group (β-processes) and by chemical structure (γ-processes). In addition to these basic relaxation processes in certain conditions, other processes, which are connected with the overmolecular structure of the polymer, show themselves as well. These relaxation processes reflect the cooperativeness of thermal molecular mobility of separate types of macromolecular parts of intercrystalline fields. They are also connected with the mobility of kinetic elements of macromolecules of the amorphous polymer, which save information about the crystal condition.

Доказано неравенство, оценивающее норму в $L_2$ по строго внутренней подобласти градиента обобщенного (из $W^1_{2,loc}$ ) решения эллиптического уравнения второго порядка через нормы в $L_2$ самого решения и правой части уравнения.

In this paper one standard convolution identity of vector space is considered. This identity can be presented as a determinant of operators.