On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Isomorphisms of Certain Locally Nilpotent Finitary Groups and Associated Rings

For any chain Γ the ring NT(Γ,K) of all finitary Γ-matrices ‖a _ij ‖ _i,jεΓ over an associative ring K with zeros on and above the main diagonal is locally nilpotent and hence radical. If R′=NT(Γ′,K′),R=NT(Γ,K) and either |Γ|<∞ or K is a ring with no zero-divisors, then isomorphisms between rings R and R′, their adjoint groups and associated Lie rings are described.     

Large N phase transition in the heat kernel on the U (N) group

The large N phase transition point is investigated in the heat kernel on the U(N) group with respect to arbitrary boundary conditions. A simple functional relation is found relating the density of eigenvalues of the boundary field to the saddle point shape of the typical Young tableaux in the large N limit of the character expansion of the heat kernel. Both strong coupling and weak coupling phases are investigated for some particular cases of the boundary holonomy.     

Quantification problems in depth profiling of pwr steels using Ar+ ion sputtering and XPS analysis.

The oxide scales of AISI 304 formed in boric acid solutions at 300 degrees C and pH = 4.5 have been studied using X-ray photoelectron spectroscopy (XPS) depth profiling. The present focus is depth profile quantification both in depth and chemical composition on a molecular level. The roughness of the samples is studied by atomic force microscopy before and after sputtering, and the erosion rate is determined by measuring the crater depth with a surface profilometer and vertical scanning interferometry. The resulting roughness (20-30 nm), being an order of magnitude lower than the crater depth (0.2-0.5 microm), allows layer-by-layer profiling, although the ion-induced effects result in an uncertainty of the depth calibration of a factor of 2. The XPS spectrum deconvolution and data evaluation applying target factor analysis allows chemical speciation on a molecular level. The elemental distribution as a function of the sputtering time is obtained, and the formation of two layers is observed-one hydroxide (mainly iron-nickel based) on top and a second one deeper, mainly consisting of iron-chromium oxides.     

On the coherent inelastic processes in collisions of elementary particles with nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a → b, which may take place in the interaction of hadrons and γ quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. Analytical formulas for the effective cross-section σ_coh(a→b) are obtained.     

Comparative analysis of the frequency noise in two distributed circuits of semiconductor self-excited oscillators

Kuibyshev State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 2, pp. 242–245, February, 1989.     

An asymptotic theory of higher-order operator differential equations with nonsmooth nonlinearities

We develop an asymptotic theory of nonlinear operator differential equations of an arbitrary order in Banach spaces. The nonlinear part of the equation is written in a divergent form. It is shown that the main term in an asymptotic representation of solutions at infinity satisfies a finite-dimensional dynamical system perturbed by a small nonlocal operator.     

Energy spectrum of <Emphasis Type="Italic">p</Emphasis> electrons in a plane crystal lattice and in a strong magnetic field

Harper equations are derived for a _px, _py electronic system. Analysis is carried out for extreme points of the quasi-continuous spectrum in the cases when the number of magnetic flux quanta through a unit cell is a rational number and calculations are made for square and triangular lattices as well as for a honeycomb lattice with two nonequivalent atoms. The possibility of application of the results for explaining the fractional Hall effect is considered.