Unoccupied electronic states of epitaxial iron layers on Cu(100)

Inverse photoemission spectra were taken for thin epitaxial iron films on Cu(100). For a film thickness of eight monolayers the observed electronic states are characteristic for a fcc(100) surface. Thed-bands of iron show a ferromagnetic exchange splitting of 1.1 eV, considerably smaller than the bulk value of 1.8 eV, which we observe for film thicknesses above 18 monolayers.     

Phase diagram of multilayer magnetic structures

Multilayer ferromagnet-layered antiferromagnet (Fe/Cr) structures frustrated because of roughness of interlayer boundaries were studied by mathematical modeling methods. The phase diagram of a three-layer system (plotted as film thickness versus the degree of roughness of the interfaces) was obtained, and the order parameter distributions in each phase were determined. The character of phase transitions in this system was studied. The applicability range of the Slonczewski magnetic proximity model was determined.     

Influence of layer and anisotropic fluctuations of the refractive index on the beyond-the-horizon SHF propagation in the troposphere over the sea when there is an evaporation duct

On the basis of the invariant imbedding method the disturbance theory for complex constants of propagation is proposed. This approach allows us to consider the influence of layer and anisotropic fluctuations of refractive index on the beyond-the-horizon propagation in the adiabatic approximation with the existence of an evaporation duct. Finally, the authors consider some examples of the calculations and investigate stochastic effects connected with the interaction between fluctuating and regular waveguides.     

Nonparametric decision-making models for large samples

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 79–83, September, 1995.     

Positive solutions and dynamics of a finite difference reaction–diffusion system

We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction–diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.     

Fredholm property of elliptic boundary value problems for partial differential and differential- operator equations

In this paper we find conditions on boundary value problems for elliptic differential-operator equations of the 4-th order in an interval to be fredholm. Apparently, this is the first publication for elliptic differential-operator equations of the 4-th order, when the principal part of the equation has the form u′?n(t) + Au″(t) + Bu(t), where AB^-1/2 is a bounded operator and is not compact. As an application we find some algebraic conditions on boundary value problems for elliptic partial equations of the 4-th order in cylindrical domains to be fredholm. Note that a new method has actually been suggested here for investigation of boundary value problems for elliptic partial equations of the 4-th order.     

Invariant interpolation formulas for higher-order derivatives of functions of a vector argument

Interpolation formulas for higher-order derivatives which guarantee the invariance of the results under changes of coordinates are obtained for functions of a vector argument.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 22–25, 1987.     

General-relativistic cosmology with expansion and rotation

A model of an expanding and rotating universe is constructed in the framework of general relativity. The parameters of the model are compared with the fundamental observables and shown to be in good agreement.Kaluzhsk Branch, N. É. Bauman Moscow State Technical University (MGTU). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1993.