Estimation of multivariate binary density using orthogonal functions

In this paper, the authors studied certain properties of the estimate of Liang and Krishnaiah (1985, J. Multivariate Anal. 16, 162–172) for multivariate binary density. An alternative shrinkage estimate is also obtained. The above results are generalized to general orthonormal systems.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis     

Interfacial pattern formation far from equilibrium

Over the past few years diffusion-controlled systems have been shown to share a common set of interfacial morphologies. The singular nature of the microscopic dynamics of surface tension and kinetic growth far from equilibrium are critical to morphology selection, with special importance attributed to the anisotropy of these effects. The morphologies which develop can be organized via a morphology diagram according to the driving force and the effective anisotropy. We focus on the properties of the dense-branching morphology (DBM) which appears for sufficiently weak effective anisotropy, and the nature of morphology transitions between the DBM and dendritic growth stabilized by either surface tension or kinetic effects. The DBM is studied in the Hele-Shaw cell, and its structure analyzed by linear stability analysis. A comparison is made between the power spectrum of the structure and the stability analysis. We then provide a detailed account of the morphology diagram and morphology transitions in an anisotropic Hele-Shaw cell. Theoretically the question of morphology transitions is addressed within the boundary-layer model by computing selected velocities as a function of the undercooling for different values of the surface tension and the kinetic term. We argue that the fastest growing morphology is selected whether it is the DBM, surface tension dendrites, or kinetic dendrites. A comparison is made with our experimental results in electrochemical deposition for the correspondence between growth velocities and morphology transitions.     

Electric generators of singlet delta oxygen for an oxygen-iodine laser

Experimental and theoretical research into electric generators of singlet delta oxygen (SDO) for an oxygen-iodine laser made at the Lebedev Physics Institute and TRINITI is discussed. Breakdown and current-voltage characteristics of self-sustained electric discharge in SDO were studied both experimentally and theoretically, indicating that SDO and pure oxygen have quite different electric features. The electric properties and spectroscopy of an e-beam sustained discharge (EBSD) in oxygen and oxygen gas mixtures were experimentally studied. A comprehensive numerical model describing SDO kinetics in different kinds of discharge was developed. The pulsed EBSD in pure oxygen and its mixtures with noble gases was shown to be very unstable and characterized by low input energy. When adding small amounts of carbon monoxide or hydrogen, the electric stability of the EBSD increases, the specific input energy (SIE) per molecular component being more than order of magnitude higher and coming to 6.5 kJ/(l atm(O₂ + CO)) for the gas mixture O₂: Ar: CO = 1: 1: 0.1. Theoretical calculations demonstrated that, for an SIE of 6.5 kJ/(l atm), the SDO yield may reach ∼20%, exceeding its threshold value needed for oxygen-iodine laser operation at room temperature. The calibration of the optical scheme for measuring the SDO absolute concentration and yield using the detection of luminescence of the SDO going from a chemical SDO generator was performed. The measurement of the SDO yield demonstrated that it was ∼10.5% for an SIE of ∼3.0 kJ/(l atm(O2 + CO)), which is about 1.5 times less than the results of theoretical calculations for such an SIE. SDO production in RF slab discharge ignited in oxygen gas mixtures was experimentally studied, experimental SDO yield being about 10%. The choice of electrode material was demonstrated to be very important. Original Text ? Astro, Ltd., 2006.     

Gauge-Related Deformations of Ordinary Linear Differential Operators with Constant Coefficients

Relations between the coefficients of gauge-related deformations and the solutions of a certain system of ordinary nonlinear differential equations are studied. These coefficients are found in an explicit form. Bibliography: 14 titles. Dedicated to P. V. Krauklis on the occasion of his seventieth birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 235–251.     

Onset of crater formation during short pulse laser ablation

We report morphologic changes of metallic surfaces at the onset of ablation, starting from gentle ablation to the emergence of ablation craters. The evolution of both observed melting zones and of ablation craters therein are investigated in dependence of the ablation laser fluence for nanosecond ultraviolet laser pulses. Further, consequences of crater formation for cluster synthesis within the released atomic vapor are pointed out. PACS 52.38.Mf; 79.20.Ds; 65.40.De     

A warehouse-based design model for reverse logistics

In this paper, an MILP formulation is proposed for the design of a reverse logistics network based on a warehouse location–allocation model, which optimizes, simultaneously, the forward and reverse networks. A single product model with unlimited capacity is first defined. Subsequently, the model is extended to a multi-product capacitated recovery network model, where capacity limitations and a multi-product system can be considered. The proposed model is compared to published work in the field, where different model assumptions have been proposed. Two cases are described so as to gain a better insight into the model and allow a comparative analysis.     

Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems

The binding energies of a hydrogenic donor both in the parabolic and non-parabolic conduction band model within the effective mass approximation have been computed for the low-dimensional semiconducting systems (LDSS) like quantum well, quantum well wire and quantum dot taking GaAs/Al_xGa_1−xAs systems as an example. It is observed that the effect of non-parabolicity is not effective when the system goes to lower dimensionality. The diamagnetic susceptibility of a hydrogenic donor impurity has also been computed in these LDSS in the infinite barrier model. Since no theoretical or experimental works on the diamagnetic susceptibility of LDSS are available in the literature, as a realistic case the diamagnetic susceptibility has been computed in the finite barrier model (x=0.3) for a quantum well and the results are discussed in the light of semiconductor-metal transition.     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.