Mathematics Commons^™

Quantitative Estimates For Lp Approximation With Positive Linear Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

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.

On The First Passage Time Distribution For A Class Of Markov Chains, Mark Brown, Narasinga Rao Chaganty

Mathematics & Statistics Faculty Publications

Consider a stochastically monotone chain with monotone paths on a partially ordered countable set S. Let C be an increasing subset of S with finite complement. Then the first passage-time from i ∈ S to C is shown to be IFRA (increasing failure rate on the,av;rage). Several applications are presented including coherent systems, shock models, and convolutions of IFRA distributions.

Smallest Cubic And Quartic Graphs With A Given Number Of Cutpoints And Bridges, Gary Chartrand, Farrokh Saba, John K. Cooper Jr., Frank Harary, Curtiss E. Wall

Mathematics & Statistics Faculty Publications

For positive integers b and c, with c even, satisfying the inequalities b+1≤c≤2b, the minimum order of a connected cubic graph with b bridges and c cutpoints is computed. Furthermore, the structure of all such smallest cubic graphs is determined. For each positive integer c, the minimum order of a quartic graph with c cutpoints is calculated. Moreover, the structure and number of all such smallest quartic graphs are determined.

Local Lp-Saturation Of Positive Linear Convolution Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

Local L_p-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.

Unbounded Functions And Positive Linear-Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

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.

A Method Of Modeling Multirate Two-Dimensional Recursive Digital Filters Author, Albert P. Gerheim

Electrical & Computer Engineering Theses & Dissertations

This dissertation presents a method of modeling two dimensional sampled data systems with two sampling rates in each dimension. This methodology is applied to the problem of synthesizing two dimensional velocity filters using one dimensional prototypes and multirate concepts.

The modeling method includes the replacement of scalar z-transforms of signals by vectors of polynomials, and the replacement of scalar z-transforms of impulse responses by matrices of polynomials.

The synthesis of velocity filters is accomplished through the use of coordinate transformations in the z-transform domain which skew the ω₁ -ω₂ axes on the unit bidisc. The filters synthesized using …

Feasibility Of Quasi-Random Band Model In Evaluating Atmospheric Radiance, Navin Mirakhur

Mechanical & Aerospace Engineering Theses & Dissertations

The use of the quasi-random band model in evaluating the upwelling atmospheric radiation is investigated. The spectral transmittance and total band absorptance are evaluated for selected molecular bands by using the line-by-line model, quasi-random band model, exponential sum fit method, and empirical correlations, and these are compared with the available experimental results. The atmospheric transmittance and up­ welling radiance have been calculated by using the line-by-line and quasi-random models and are compared with the results of an existing program called LOWTRAN. The results obtained by the exponential sum fit and empirical relations are not in good agreement with experimental results …

A Note On The Degree Of Approximation With An Optimal, Discrete Polynomial, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

A saturation theorem and an asymptotic theorem are proved for an optimal, discrete, positive algebraic polynomial operator. The operator is based on the Gauss-Legendre quadrature formula.

Note: On Summability And Positive Linear Operators, J. J. Swetits

Mathematics & Statistics Faculty Publications

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, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

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.

Complementary Extremum Principles, J. Swetits, C. Rogers

Mathematics & Statistics Faculty Publications

Important 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.