New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.     

Flicker noise in degenerately doped Si single crystals near the metal-insulator transition

In this paper we report some of the important results of experimental investigations of the flicker noise near the metal-insulator (MI) transition in doped silicon single crystals. This is the first comprehensive work to study low-frequency noise in heavily doped Si over an extensive temperature range (2 K<T<500 K). The measurements of conductance fluctuations (flicker noise) were carried out in the frequency range 10⁻²<f<4 × 10¹ Hz in single crystalline Si across the MI transition by doping with phosphorous and boron. The magnitude of noise in heavily doped Si is much larger than that seen in lightly doped Si over the whole temperature range. The extensive temperature range covered allowed us to detect two distinct noise mechanisms. At low temperatures (T<100 K) universal conductance fluctuations (UCF) dominate and the spectral dependence of the noise is determined by dephasing the electron from defects with two-levels (TLS). At higher temperatures (T>200 K) the noise arises from activated defect dynamics. As the MI transition is approached, the 1/f spectral power, typical of the metallic regime, gets modified by the presence of discrete Lorentzians which arise from generation-recombination process which is the characteristic of a semiconductor.     

Interface-induced states with an incommensurate spin-density wave in Fe/Cr-type multilayers

A model is proposed for magnetic ordering in Fe/Cr-type multilayers substantially above the Néel temperature of bulk chromium. Redistribution of the charge (and, hence, spin) density near the Fe/Cr interfaces gives rise to the formation of an essentially inhomogeneous spin-density-wave (SDW) state in the chromium spacer. The spatial structure of the antiferromagnetic order parameter in thick spacers is described. The SDW contribution to the effective exchange coupling between the moments in adjacent iron layers is calculated. The data obtained are used in the interpretation of experimental data on the tunneling spectroscopy of trilayers and neutron diffraction from Fe/Cr superlattices.     

Equitable Total Coloring of Graphs with Maximum Degree 3

 The equitable total chromatic number χr d q u o; _e (G) of a graph G is the smallest integer k for which G has a total k-coloring such that the number of vertices and edges in any two color classes differ by at most one. We prove in this paper that χr d q u o; _e (G)≤5 if G is a multigraph with maximum degree at most 3. Received: February 24, 2000 Final version received: February 2, 2001 Acknowledgments. The author would like to thank the referee for valuable suggestions to improve this work.     

Anomalous states of the crystal structure of (Rb0.1(NH4)0.9)2SO4 solid solutions in the temperature range 4.2–300 K

Crystals of (Rb_0.1(NH₄)_0.9)₂SO₄ solid solutions are studied using x-ray diffractometry. It is revealed that the temperature dependence of the lattice parameter a exhibits an anomalous behavior, namely, the “invar effect” at temperatures above the ferroelectric phase transition point T _c and an anomalous increase in the temperature range from T _c to the liquid-helium temperature. An anomalous increase in the lattice parameter a and an increase in the intensity of Bragg reflections with a decrease in the temperature are interpreted within the model of the coexistence of two sublattices hypothetically responsible for the ferroelectric phase transition. A series of superstructure reflections observed along the basis axes corresponds to a sublattice formed in the matrix of the host structure. Analysis of the ratio between the lattice parameters of these structures allows the inference that, in the temperature range 4.2–300 K, the structure of the crystal under investigation can be considered an incommensurate single-crystal composite.     

Conductivity and field and current distributions in a two-component system composed of regular triangles

The problem of the effective conductivity and the distributions of a field and currents is analyzed in a regular two-component system composed of regular triangles. An efficient solution method is developed that admits a generalization to multicomponent systems.     

Secondary anti-stokes emission from the bulk of gallium phosphide at 4.2 K

Secondary radiation (photoluminescence and Raman scattering) emitted by gallium phosphide single crystals at helium temperatures is investigated. It is established for the first time that, in the case when the secondary emission spectra are excited by a cw low-power He-Ne laser, whose linewidth lies in the transparency region of GaP, anti-Stokes photoluminescence from the bulk of the sample occurs due to interband and impurity recombination. The results obtained make it possible to carry out a qualitative and quantitative analysis of impurities which are present in the bulk of a semiconductor by recording the bulk anti-Stokes photoluminescence spectra at low temperatures.     

An optimal repeat inspection plan with several classifications

Multicharacteristic critical components exist in many systems. Such components could be a part of an aircraft, space shuttle or a gas ignition system. A component is critical if it causes disaster or a very high cost upon failure. In this paper, a new inspection plan for critical multicharacteristic components is presented. A mathematical model that depicts the plan is developed. An algorithm is proposed for finding the optimal number of repeat inspections and the sequence of characteristics for inspection that minimizes expected total cost per accepted component. The expected cost consists of the cost of inspection and the cost of misclassifications. The inspection plan and the model developed generalize existing models in the literature and provide a more realistic formulation. An example is given to demonstrate the plan and the model.     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.