Absorption and refraction phenomena in proton- and antiproton-nucleus scattering

The experimental data on the 180 MeV proton and 50, 180 MeV antiproton scattering by the nuclei¹²C,⁴⁰Ca and²⁰⁸Pb have been analysed on the basis of the phenomenological diffraction theory. The optical properties of the nuclei with regards to the incident protons and antiprotons are investigated. Various limiting cases of the proton- and antiproton-nucleus scattering are considered. The contribution of the Coulomb and the spin-orbit interactions to the differential cross sections of these processes has been also analysed.The authors are indebted to D.M. Skrypnik for assistance in preparing the English version of this paper.     

A universe of Friedmann type with pressure

We propose a method of obtaining homogeneous and isotropic cosmological models satisfying physical conditions for 0 and . The model obtained in this way describes a universe filled with matter, the equation of state of which changes in time from the asymptotically ultrarelativistic to the asymptotically dust state.Dnepropetrovsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 8–12, May, 1993.     

Non-Archimedean superfields

The component representation of superfields over non-Archimedean (and, in particular, p-adic) superalgebras with an infinite number of anticommuting generators is investigated. It is shown that supersmooth fields, nonpolynomial in anticommuting variables, exist in the non-Archimedean case (as opposed to the real or complex case). The superfield representation for the algebra of non-Archimedean supersymmetries is analyzed in the p-adic case (p 3 mod 4). New solutions of equations on a chiral superfield and other superfield equations are discovered in non-Archimedean theory.This work has been supported by the CNR Fund (Italy) and an Advanced Study of p-Adic Mathematical Physics Grant.Institute of Electronic Engineering, Moscow. Genova University, Italy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 35–38, November, 1993.     

Sulfur-containing derivatives of thiolan-1,1-dioxide 3. Reactions of salts of 2-(n,n-dialkyl)iminio-5,5-dioxoperhydrothieno[3,4-d]-1,3-dithiolans with bases

Salts of condensed 2-(N,N-dialkyl)iminio-1,3-dithiolan and 1,1-dioxothiolan rings are converted in alkaline media to 1,1-dioxothiolen esters of N,N-dialkyldithiocarbamic acids and into unsaturated bicyclic compounds. The latter are formed when the initial salts contain a bromine atom to the sulfonyl group.For Communication 2, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 40–47, January, 1993.     

The classical ruin problem on a finite solvable group

For the classical ruin problem (a special case of a cyclic group), we use an explicit expression for the characteristic function of the time of first hitting an arbitrary subset of a finite solvable group by a random walk, from a fixed subset, to obtain a new proof of the well-known formula which allows one to estimate the characteristic function of the ruin probability (hitting the identity of a group) at theth- trial.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 361–366, March, 1993.     

On the localization and convergence of multiple Fourier integral by Bochner-Riesz means

In this paper we consider , in one case that f_{x 0} (t) is a ΛBMV function on [0, ∞], and in another case thatfεL ¹ _m-1(Rⁿ) and when |k|=m−1 and f(x)=0 when |x−x₀|<δ for some δ>0. Our theormes improve the results of Pan Wenjie ([1]).     

A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences

Summary With the help of an extension of Hoeffding's equality, we develop a way for estimating the covariance structures for empirical functions of associated sequences in terms of covariances of the original random variables. Based on these estimations, a Glivenko-Cantelli lemma for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, all under the conditions on covariances of the original random variables.This research has been supported partially by a scholarship from the Faculty of Graduate Studies and Research of Carleton University, Ottawa, and by an NSERC Canada grant of M. Csörg     

The stressed state of glass disks during strength testing

By applying the improved theory of plates, which makes it possible to determine all components of the stress tensor, we study the stressed state of glass disks under axisymmetric bending. We obtain a closed-form solution of the corresponding boundary-value problem for systems of singularly perturbed equations. It is shown that the size of the zone of pure bending-the domain with uniformly stretched surface-differs from those known in the literature. The results obtained make it possible to determine the optimal geometric parameters of the punch-glass disk-support system in strength testing of the glass by the method of axisymmetric bending.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 73–79.     

Designing a regression experiment in Hilbert space

Two forms of a priori information about unknown parameters in observing linear regression with noise in a Hilbert space are considered. In each section one gets best restricted linear unbiased estimates of the unknown parameters generalizing known results about the finite-dimensional case. Problems of choice of optimal designs are solved for bounded closed sets which are natural from the point of view of applications. The results are compared with those which hold without a priori information.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 23–28, 1988.