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.     

Chlorokomplexe von Cu2+ und Ni2+ in Dimethylformamid

Zusammenfassung Durch spektrophotometrische Messungen in Dimethylformamid (DMF) werden die Koordinationsformen [CuCl]⁺ und [CuCl₃]^– sowie [NiCl]⁺, [NiCl₃]^– und [NiCl₄]^2– nachgewiesen. Bei Nickel(II)-chlorid und Kupfer(II)-chlorid wird Autokomplexbildung diskutiert. Die Solvate [Cu(DMF)₄] (ClO₄)₂ und [Ni(DMF)₆] (ClO₄)₂ werden isoliert.Im Zuge der Untersuchungen über Chlorokomplexe von Ionen der Übergangsmetalle^{1, 2} in nichtwäßrigen Lösungsmitteln wurden die Spektren der Lösungen von Kupfer(II)- und Nikkel(II)-perchlorat inDMF in Gegenwart verschiedener Mengen Tetraäthylammoniumchlorid aufgenommen.Mit 5 Abbildungen     

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.     

Threshold anomaly in doubletn-d scattering

The behaviour of the doubletn-d scattering phase shift ₂(k) at energies close to the three-particle threshold is studied analytically and numerically. The scattering parameters possess an anomaly associated with the low energy of the singletN-N virtual state. The anomaly manifests itself both as a bend in the energy dependence of the functionk cot(Re ₂) in the range around 0.5 MeV and in the nonstandard behaviour of the break-up cross section near the threshold.     

Bound on the Higgs boson mass with no zero-charge behaviour in a magnetic field

The upper boundm<280 GeV/c² on the Higgs boson mass is obtained by considering the requirement that the electroweak theory must be consistent in a magnetic fieldH. The restriction emerges naturally by studying the effective potential in a magnetic field as a function of mass, and the values ofm when there is no zero-charge, in the fieldsH～H ₀=M _w ² /e are obtained.     

Meta-Hamiltonian groups with elementary commutant of rank 2

This paper is concerned with the structure of periodic meta-Hamiltonian groups with elementary commutant of rank 2 that have complemented Miller Moreno subgroups. It is proved that there exist four types of such groups.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 168–175, February, 1990.The proof of this assertion will be given in another paper of the authors.     

A variational problem in the theory of green potential. I

For a condenser E in an open set D R ^p , p 3, the problem of the minimum of the Green energy in a class of charges, associated with E, is solved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 494–500, April, 1990.     

Asymptotics of solutions of a linear singularity perturbed system with degeneracy

Asymptotic expansions with respect to a small parameter e are constructed for a fundamental system of solutions of a linear singularity perturbed system of equations of the form