Mathematical modeling of a Ti:sapphire solid-state laser

The project initiated a study of a mathematical model of a tunable Ti:sapphire solid-state laser. A general mathematical model was developed for the purpose of identifying design parameters which will optimize the system, and serve as a useful predictor of the system's behavior

Note: On Summability and Positive Linear Operators

Quantitative estimates for approximation by positive linear operators are obtained with the use of a summability method which includes both convergence and almost convergence

Approximation by Discrete Operators

A discrete, positive, weighted algebraic polynomial operator which is based on Gaussian quadrature is constructed. The operator is shown to satisfy the Jackson estimate and an optimal version is obtained

On complementary extremum principles

AbstractImportant complementary extremum principles are generated without recourse to general variational theory. The results are illustrated by an application to a class of boundary value problems in Magnetohydrodynamics

Unbounded Functions and Positive Linear-Operators

The approximation of unbounded functions by positive linear operators under multiplier enlargement is investigated. It is shown that a very wide class of positive linear operators can be used to approximate functions with arbitrary growth on the real line. Estimates are given in terms of the usual quantities which appear in the Shisha-Mond theorem. Examples are provided

Overconvergence for a normal family of analytical functions

In the first part of this paper we provide some basic properties of power series and their analytic continuation which are essential in a study of function theory. Then, following E. Hille\u27s Analytic Function Theory, we develop the theory of holomorphy preserving operators. This theory is a useful tool in establishing the classical Hadamard Gap Theorem. Holomorphy preserving operators also prove to be useful in establishing several theorems giving sufficient conditions for overconvergence. We then state and prove several theorems concerning necessary conditions of overconvergence

Quantitative Estimates for Lp Approximation with Positive Linear Operators

Quantitative estimates for approximation with positive linear operators are derived. The results are in the same vein as recent results of Berens and DeVore. Two examples are provided

Local Lp-Saturation of Positive Linear Convolution Operators

Local Lp-saturation of positive linear convolution operators is investigated. Results are obtained for two important classes of operators previously studied by Bojanic, DeVore, Korovkin and the authors

Modeling Cr-to-Tm and Cr-to-Tm-to-Ho energy transfer in YAG crystals

A systematic analysis of energy transfer processes in crystals of YAG doped with varying concentrations of Cr and Tm is described. Both spectral measurements and measurements of the temporal response to pulsed excitation are used to give independent determinations of the microscopic interaction parameter for Cr to Tm transfer. The different factors in influencing the temperature dependence of the Cr to Tm transfer are discussed. The dependence of the Tm cross-relaxation rate on Tm concentration is determined

Construction of the Best Monotone Approximation on Lp [0, 1]

(First paragraph) For 1 ≤ p \u3c ∞, let Lp, denote the Banach space of pth power Lebesgue integrable functions on [0, l] ∥ƒ∥p = (∫¹₀∣ƒ∣ p)1/p Let Mp denote the set of nondecreasing functions in Lp. For l \u3c p \u3c ∞ , each ƒ∊Lp has a unique best approximation from Mp, while, for p = 1, existence of a best approximation from M1 follows from Proposition 4 of [6]