Effect of lattice deformation and phase transitions on the electronic spectra of TlGaS<Subscript>2</Subscript>, TlGaSe<Subscript>2</Subscript>, and TlInS<Subscript>2</Subscript> layered semiconductors

The effect of the lattice deformation on the electronic spectra of TlGaS₂, TlGaSe₂, and TlInS₂ layered semiconductor crystals is analyzed. It is shown that changes in the band gap of these semiconductors due to thermal expansion and a change in the composition under hydrostatic or uniaxial pressure can be described within a unified model of the deformation potential. The main feature of this model is the inclusion of deformation potentials with different signs, which is characteristic of other semiconductors with a layered structure. An analysis of the lattice deformation of the studied semiconductors in terms of the proposed model of the deformation potential has revealed that, in the immediate vicinity of the phase transitions, the crystal lattice under pressure undergo an unusual deformation.     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

Interior ballistics of a single-stage plasmatron and the general features of radiative heat exchange

A mathematical model of a single-stage ballistic plasmatron for producing radiating gas is proposed. Various operating conditions are analyzed and compared with experimental data. The general features of radiative heat exchange in the device are outlined.     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

Experience of Control over Process of Chemical-Informational Synthesis

Conditions under which various kinds of carbon nanoparticles are obtained by thermal oxidative conversion of methane in chlorine in the temperature range 20-500°C were studied. The influence exerted by conditions of synthesis of nanodispersed carbon on the properties of its samples was analyzed.     

Mean Busy Period of Infinite Multilinear Queues with a Doubly Stochastic Input Flow

The mean busy period of an infinite multilinear queue with a doubly stochastic flow of incoming queries having two intensities and exponential server is calculated.     

Correction to: On Webs of Maximum Rank (Geom. Dedicata 31 (1989), 19–35)

We correct an error in Example (3.4) in Geom. Dedicata 31 (1989), 19–35.     

An embedding domain approach for a class of 2-d shape optimization problems: mathematical analysis

This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains.     

The effect of high electric fields on the structure and dielectric properties of the B2 phase

Dielectric studies are presented of a banana-shaped compound that exhibits the antiferroelectric B₂ phase. Upon application and subsequent removal of strong electric fields the textures and dielectric properties of the phase drastically change. Most notable is the huge increase of the low frequency permittivity. This behaviour would suggest the induction of ferroelectricity by the electric field.