Conditional distributions of record values and characterizations of distributions

We consider some regression relations for record values X(n), n > 0, generated by a sequence of independent random variables X₁, X₂, X₃,... with a common continuous cumulative distribution function F(x). New characterizations of distributions based on regression properties of record values are obtained. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 5–14.     

The solution existence of general variational inclusion problems

We propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous. Sufficient conditions for the solution existence are established. As applications we derive consequences for several special cases of variational inclusion problems, quasioptimization problems, equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

On a certain nonlocal problem for a hyperbolic equation

The author proves the existence and uniqueness of a generalized solution of a nonlocal problem with an integral condition for a hyperbolic equation with n spatial variables. This work is a continuation of the studies started in [3–5], where the solvability problem of nonlocal problems with an integral condition was studied for hyperbolic equations on the plane. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.     

Correlation between energy positions of deep intrinsic point-defect levels and a limiting fermi level in irradiated III–V semiconductors

The energy levels of neutral anion (V_A) and cation (V_C) vacancies and antisite defects are calculated for the anion C_A and cation A_C sublattices of III–V semiconductors. An averaged energy level position for these defects is estimated to be E_av ^abs = 4.9 eV. The position coincides with the local charge electroneutrality level. It is shown that the case, where the total energies of formation of V_A, V_C and antisite C_A, A_C defects in the sublattices of binary semiconductors are similar, corresponds to the point-defect equilibrium condition and stabilization of the Fermi level in the proximity of the local charge electroneutrality level. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 17–22, May, 2007.     

Electronic spectrum and ballistic transport in a helical nanotube

A model of a helical nanotube permitting analytical calculation of the spectrum and wave functions is proposed and studied. It is shown that the specific character of the symmetry of the Hamiltonian results in an electronic spectrum having no band structure despite the periodicity of the potential along the system axis. A two-dimensional ribbon rolled into a helix and a quasi-one-dimensional helix in a magnetic field are considered as limiting cases of the model. It is shown that the presence of additional local minima in the subbands of the electronic spectrum leads to a nonmonotonic dependence of the ballistic conductance of the system on the chemical potential.     

Variation of the temperature factor of models on a ballistic range

A technique for variation of the temperature factor of free-flight models by varying their initial temperature is described. An experiment on a ballistic range is carried out with a free-flying supersonic blunt cone with a half-angle of 15° at a Mach number of 2.3. The flow at the cone base is studied in the transition range (from the laminar to turbulent flow) of Reynolds numbers. The base flow pattern is determined from the shadowgraphs of the flow about the models. The drag coefficient of the blunt cone at a zero angle of attack is found by processing trajectory data. It is found that the near wake geometries and the drag coefficients of the models tested at the laboratory temperature and a temperature of 120 K differ. Explanations of this effect are given.     

Relaxation contribution to shear moduli of the low-temperature phase of solid C60

The relaxation contribution of the molecular reorientation in an elastic field of an acoustic wave to the effective shear moduli is calculated in the framework of the phenomenological two-level model of orientational states in the low-temperature phase of solid C₆₀. The polarity of the rotation axis of C₆₀ molecules and the possible existence of orientational domains in the structure of the low-temperature phase are taken into consideration. The estimates obtained are compared with the available experimental data.