Integral operators determined by quasielliptic equations. I

Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 52–67, November–December, 1993.     

Fence facets from non-regular graphs for the linear ordering polytope

We present a new class of facet defining inequalities for the linear ordering polytope. The underlying graphs of these new inequalities are non-regular (have vertices of different degrees); the other known classes of fence inequalities are induced by regular graphs.     

Asymptotic Behavior at Infinity of Solutions to the Nonhomogeneous Sobolev Equation

Under study is the asymptotic behavior at infinity of solutions to the Cauchy problem to the nonhomogeneous Sobolev equation. We obtain the form of the limit function and the convergence rate.     

On Stability of the Inverted Pendulum Motion with a Vibrating Suspension Point

Under study is the stability of the inverted pendulum motion whose suspension point vibrates according to a sinusoidal law along a straight line having a small angle with the vertical. Formulating and using the contracting mapping principle and the criterion of asymptotic stability in terms of solvability of a special boundary value problem for the Lyapunov differential equation, we prove that the pendulum performs stable periodic movements under sufficiently small amplitude of oscillations of the suspension point and sufficiently high frequency of oscillations.     

Role of electronic structure in the formation of the properties and characteristics of interatomic interaction in alloys of iron with chromium and vanadium

In this work, the electronic structure and the magnetic state of Fe-Cr, Fe-V, and Fe-Cr-V alloys are investigated by the method of coherent potential in the approximation of Hartree-Fock. The effective fields on the nuclei of Fe of the ternary alloys are calculated using the results that have been obtained. The effective fields on Fe nuclei in Fe-Cr-V alloys have been experimentally measured. Comparison with the experimental results shows that the electronic and magnetic states of both the binary and ternary alloys are reasonably described by the coherent potential method. Analysis of the available results allows one to explain the differences existing in the phase diagrams of binary alloys as well as to reach conclusions about the shape of the equilibrium phase diagram of the ternary alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 77–83, December, 1988.     

Orientation-dependent tunneling of electrons between planar cyclic molecules

We have investigated the dependence of the efficiency of electron tunneling between planar cyclic molecules on their mutual orientation. An expression has been obtained for the dependence on orientation of the tunneling probability in terms of the cyclic polyene model. The magnitude of the orientation effect has been estimated for a change in the orientation of the molecules from the face-to-face to the edge-to-edge position.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 2, pp. 222–225, March, 1989.