Absorptive corrections to structure functions at small-x

The role of corrections due to the interactions between different branches of parton (gluon) cascades is studied. It is shown that at HERA energies these interactions increase the absorptive (two-Pomeron cut) contributions by about 60 to 80% compared with the Gribov-Levin-Ryskin equation.This work was supported, in part, by a Soros Foundation Grant awarded by the American Physical Society     

Temperature dependence of the efficiency at which electrons are captured into axial channeling

A procedure for calculating the efficiency at which electrons are captured into axial channeling with a realistic axis potential is discussed. That region in the space of the electron's total transverse energy E and angular momentum L (integrals of motion) which corresponds to stable bound states of the electron with an atomic row is found. The temperature dependence of the capture coefficient is analyzed. As the crystal temperature is increased, the capture coefficient decreases, to a particularly noticeable extent for beams making a small angle with the crystallographic axis and for crystals having a high atomic number z.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–74, May, 1988.     

Infrared reflection spectra in contactless nondestructive measurements of the electron density and mobility in indium phosphide

On the basis of numerical calculations and experimental studies we analyze the possibilities of measuring the electrophysical parameters of indium phosphide by means of infrared reflection spectra at wavelengths ranging from 5 to 200 m. We demonstrate that contactless nondestructive measurements of the electron density in the range 10¹⁶–10²⁰ cm^–3 can be made with a relative error not exceeding 15%, and of mobility with a relative error not exceeding 25%. A nomogram method is presented for rapid conversion of data from infrared reflection spectra into the parameters being measured.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 22–27, January, 1988.     

Experimental study of regions of reversed magnetization in an amorphous layer of Co70Fe5Si10B15

The characteristics of the distribution of magnetization and remagnetization of microsections of the surface in the amorphous alloy Co₇₀Fe₅Si₁₀B₁₅, prepared in the form of thin ribbons, were studied by the magnetooptical method. It was found that the magnetization I on the surface of the amorphous ribbon studied was strongly nonuniform. It was established that heat treatment (HT) of the sample leads to the appearance of regions of reversed magnetization in the surface layer of the ribbon, while thermomagnetic annealing reduces the nonuniformity of I. The conservation of the transverse component in the HT sample in fields where the magnitude of the component of magnetization parallel to the length of the ribbon remains virtually unchanged suggested that a domain structure of the magnetization ripple type, owing to the strong microdispersion of the magnetic anisotropy, is realized in this sample.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 89–94, March, 1988.     

Coherence of synchrotron radiation

Gal'tsov et al. [Vestn. Mosk. Gos. Univ., Fiz., Astron.,14, No. 5, 614 (1973)] studied the radiation spectrum of N equally spaced charges moving along a circle. In particular, it was shown that as N the intensity of the radiation from the system of charges vanishes. The present study will consider the radiation spectrum of N charges moving along an arbitrary closed curve, randomly distributed in the vicinity of equally spaced points. The coherency factor will be found for the assumption that: a) the distributions of individual charges are not intercorrelated; b) the charge distribution is such that in the vicinity of a given point only one charge is found. It will be shown that as N the radiation intensity tends to a finite limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 8–11, March, 1988.     

Multivariate cardinal interpolation with radial-basis functions

For a radial-basis function?∶?→? we consider interpolation on an infinite regular lattice , tof∶? ⁿ→?, whereh is the spacing between lattice points and the cardinal function , satisfiesX(j)=δ _oj for allj∈? ⁿ. We prove existence and uniqueness of such cardinal functionsX, and we establish polynomial precision properties ofI _h for a class of radial-basis functions which includes \(\varphi (r) = r^{2q + 1} \) , \(\varphi (r) = r^{2q} \log r,\varphi (r) = \sqrt {r^2 + c^2 } \) , and \(\varphi (r) = 1/\sqrt {r^2 + c^2 } \) whereq∈? ₊. We also deduce convergence orders ofI _hf to sufficiently differentiable functionsf whenh→0.     

Problem without initial conditions for some classes of nonlinear parabolic equations

Questions of uniqueness and existence of solutions of the problem without initial conditions for quasilinear parabolic equations of arbitrary order with monotone spatial part, equations of nonstationary filtration type, and operator differential equations of parabolic type are studied. The cases when restrictions are and are not imposed on the behavior of solutions as t– are considered here.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 14, pp. 3–44, 1989.     

The minimum area of a surface with prescribed boundary contour in a pseudoeuclidean space

LetE ^{n, k} be a pseudoeuclidean space with linear elementdx ₁ ² ++dx _n–k ² –dx _n–k ^+1/2 ––dx _n ² . The area of a smooth two-dimensional surface inE ^{n, k} is defined by , whereE, F, andG are the coefficients of the first fundamental form of the surface andD is the region of variation of the parametersu andv. The following theorem is proved: LetL be a piecewise smooth closed curve inE ^{n, k} (1kn–1). Then there exists a two-dimensional piecewise smooth surface of arbitrarily small area bounded by the curveL. 3 figures.Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 18–22.