The star chromatic number of a graph

We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. © 1993 John Wiley & Sons, Inc.     

Estimate of the concentration function for a class of additive functions

We show how methods for estimating the concentration function of the sum of independent random variables can be used to obtain estimates of the concentration function for the values of additive functions under suitable conditions. Previously obtained estimates of the concentration function are consequences of the estimate obtained in the present paper for functions from of the class under consideration.     

Microstructural evolution of decagonal quasicrystal in the undercooled Al72Ni12Co16 alloy melts

The microstructure evolution of decagonal quasicrystals in Al₇₂Ni₁₂Co₁₆ alloy was investigated by the electromagnetic melting and cyclic superheating method. Single-phase decagonal quasicrystals have been obtained when the undercoolings were larger than 60 K. The decagonal quasicrystals formed at various undercoolings show different microstructural morphologies. Furthermore, grain refinement was found near the undercooling of 120 K. Based on current thermodynamic and dendrite growth theories, a dimensionless superheating parameter was adopted to explain the effect of processing conditions on the microstructure of Al₇₂Ni₁₂Co₁₆ alloy. The result indicate that the fine equiaxied microstructure of decagonal quasicrystal (D-phase) formed near on undercooling of 120 K originates from the break-up of dendrites.     

Pressure effects in a plastic columnar discotic triphenylene

The effect of hydrostatic pressure on the structure of a plastic columnar discotic triphenylene has been investigated. The goal was to determine whether pressure can be used to modify electronic properties via changes in structural properties of columnar discotics to any significant extent. The findings are that (i) the intra- and inter-columnar distances are reduced in a nearly isotropic fashion, (ii) that the crystal sizes are reduced and (iii) that a transition takes place from a more highly ordered plastic columnar to a less ordered hexagonal columnar state with increasing pressure. The induced decrease of the molecular distances, amounting to 6% for pressures up to 17 kbar, are clearly too small to induce an appreciable modification of the electronic structure and thus opto-electronic properties.     

Andreev-Fano Effect in a Hybrid Normal-Metal/Superconductor Interferometer

We report on a new type of Fano effect, named as Andreev-Fano effect, in a hybrid normal-metal/supeeconductor (N/S) interferometer embedded with a quantum dot. Compared with the conventional Fano effect, AndreevFano effect has some new features related to the characteristics of Andreev reflection. In the Iinear response regime, the line shape is the square of the conventional Fano shape, while in the nonlinear transport, a sharp resonant structure is superposed on an expanded interference pattern, which is qualitatively different from the conventional Fano effect. The phase dependence of the hybrid N/S interferometer is also distinguished from those of all-N or all-S interferometers.     

A Second-Order Theory for Electron Plasma Solitary Waves in a Cylindrical Waveguide

To describe the long time asymptotic behaviour of weakly nonlinear plasma waves propagating in a strongly magnetized plasmafilled cylindrical waveguide the usual KDV equation which is first order in wave amplitude is extended to second order including the effects of finite temperature, mobile ions and giving a proper treatment to the radial co-ordinate for all possible modes of propagation. The second-order effects on the first-order solitary wave profile, phase speed and first order correction to the wavelength are all determined and discussed.     

Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.     

Asymptotic integration of a problem of convection

Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 69–75, July–August, 1989.