Difference Equations and Discriminants for Discrete Orthogonal Polynomials

We prove that any set of polynomials orthogonal with respect to a discrete measure supported on equidistant points contained in a half line satisfy a second order difference equation. We also give a discrete analogue of the discriminant and give a general formula for the discrete discriminant of a discrete orthogonal polynomial. As an application we give explicit evaluations of the discrete discriminants of the Meixner and the Hahn polynomials. A difference analogue of the Bethe Ansatz equations is also mentioned.Research partially supported by NSF grant DMS 99-70865     

The Milne problem for partially plane-polarized light

An accurate numerical method has been devised to solve half-range problems for the scattering of azimuth-independent polarized radiation in stellar atmospheres. The use of the method is illustrated by solving the Milne problem for the radiation intensity at any optical depth, for the extrapolation distance, and for the law of darkening.     

Heterocyclic Synthesis with Enamines: Convenient Syntheses of Polyfunctionally Substituted Pyrazole,Pyridine, Pyrimidine and Pyrazolo[3,4-d]pyrimrdine Derivatives

Facile syntheses of pyrazole, pyridine, pyrimidine and pyrazolo[3,4-d]pyrimidine derivatives have been achieved by the reaction of β-enamino nitrile 2a with hydrazines, phenyl isothiocyanate, thiourea and active methylene reagents. The β-enamino ketone 2e with the same reagents affords 3,5-dimethyl heterocyclic ring systems.     

Multiband tight-binding theory of disordered A<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>1-</Subscript><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>C semiconductor quantum dots

Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a broad range of applications, as their spectrum and thus their excitation gap can be tailored by variation of their size. Additionally, nanocrystals of the type A _x B_{1- x} C can be realized by alloying of two pure compound semiconductor materials AC and BC, which allows for a continuous tuning of their absorption and emission spectrum with the concentration x. We use the single-particle energies and wave functions calculated from a multiband sp ³ empirical tight-binding model in combination with the configuration interaction scheme to calculate the optical properties of Cd _x Zn_{1- x} Se nanocrystals with a spherical shape. In contrast to common mean-field approaches like the virtual crystal approximation (VCA), we treat the disorder on a microscopic level by taking into account a finite number of realizations for each size and concentration. We then compare the results for the optical properties with recent experimental data and calculate the optical bowing coefficient for further sizes.     

Thermoluminescence characterization of traps involved in the photodarkening of ytterbium-doped silica fibers

The photodarkening (PD) mechanisms of ytterbium-doped silica optical fibers have still not been elucidated, although hardening routes have been proposed. Most basic questions are still under debate about the assignment of the darkening excitation bands into the UV range, the nature of absorbing centers (photoionized centers or trapped carriers?), or of traps accepting photo-released carriers (electron or hole traps?). We used thermoluminescence measurements to characterize traps populated by different radiation types. It is notably demonstrated that photodarkening involves silica hole traps. The popular idea that color centers are formed upon carrier trapping is not consistent with our observations.     

Approximate controllability of fractional neutral stochastic evolution equations in Hilbert spaces with fractional Brownian motion

In this paper, the approximate controllability for Sobolev-type fractional neutral stochastic evolution equations with fractional stochastic nonlocal conditions and fractional Brownian motion in a Hilbert space are studied. The results are obtained by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem, and methods adopted directly from deterministic control problems for the main results. Finally, an example is given to illustrate the application of our result.     

Reconstruction of cracks of different types from far‐field measurements

In this paper, we deal with the acoustic inverse scattering problem for reconstructing cracks of possibly different types from the far‐field map. The scattering problem models the diffraction of waves by thin two‐sided cylindrical screens. The cracks are characterized by their shapes, the type of boundary conditions and the boundary coefficients (surface impedance). We give explicit formulas of the indicator function of the probe method, which can be used to reconstruct the shape of the cracks, distinguish their types of boundary conditions, the two faces of each of them and reconstruct the possible material coefficients on them by using the far‐field map. To test the validity of these formulas, we present some numerical implementations for a single crack, which show the efficiency of the proposed method for suitably distributed surface impedances. The difficulties for numerically recovering the properties of the crack in the concave side as well as near the tips are presented and some explanations are given. Copyright © 2009 John Wiley & Sons, Ltd.     

Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients

One of the basic inverse problems in an anisotropic media is the determination of coefficients in a bounded domain with a single measurement. We consider the problem of finding the coefficient of the second derivatives in a second-order hyperbolic equation with variable coefficients.

Under a weak regularity assumption and a geometrical condition on the metric, we prove the uniqueness in a multidimensional hyperbolic inverse problem with a single measurement. Moreover we show that our uniqueness results yield the Lipschitz stability estimate in L ² space for solution to the inverse problem under consideration.     

First principle calculation of the electronic and magnetic properties of Mn-doped 6H-SiC

The electronic and magnetic properties of 6H-SiC with Mn impurities have been calculated using GGA formalism. Various configurations of Mn sites were considered. It was found that 6H-SiC doped with Mn atoms possess a moment for both types of substitution. The Mn atom at Si site possesses larger magnetic moment than Mn atom at C site. The energy levels appearing in the band gap due to vacancies and due to Mn impurities are determined and the calculated densities of states (DOSs) are used to analyse the different value of the magnetic moments for different types of substitution. A model that explains the magnetic moment at Mn site is proposed.     

DABCOnium: An Efficient and High‐Voltage Stable Singlet Oxygen Quencher for Metal–O2 Cells

Singlet oxygen (¹O₂) causes a major fraction of the parasitic chemistry during the cycling of non‐aqueous alkali metal‐O₂ batteries and also contributes to interfacial reactivity of transition‐metal oxide intercalation compounds. We introduce DABCOnium, the mono alkylated form of 1,4‐diazabicyclo[2.2.2]octane (DABCO), as an efficient ¹O₂ quencher with an unusually high oxidative stability of ca. 4.2 V vs. Li/Li⁺. Previous quenchers are strongly Lewis basic amines with too low oxidative stability. DABCOnium is an ionic liquid, non‐volatile, highly soluble in the electrolyte, stable against superoxide and peroxide, and compatible with lithium metal. The electrochemical stability covers the required range for metal–O₂ batteries and greatly reduces ¹O₂ related parasitic chemistry as demonstrated for the Li–O₂ cell.