Applied Mathematics Commons^™

Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang

Mathematics Faculty Publications

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.

A Critical Look At Self-Dual Codes, Judy L. Walker

Department of Mathematics: Faculty Publications

We investigate self-dual codes from a structural point of view. In particular, we study properties of critical indecomposable codes which appear in the spectrum of a self-dual code. As an application of the results we obtain, we revisit the study of self-dual codes of dimension at most 10.

In the late 1950’s, Slepian [4] became the first to take an abstract approach to the study of error-correcting codes. He introduced a structure theory for binary linear codes, developing in particular the idea of an indecomposable code; that is, a code which is not isomorphic to a nontrivial direct sum of …

Efficient Traitor Tracing Algorithms Using List Decoding, Alice Silverberg, Jessica Staddon, Judy L. Walker

Department of Mathematics: Faculty Publications

We use powerful new techniques for list decoding error-correcting codes to efficiently trace traitors. Although much work has focused on constructing traceability schemes, the complexity of the tracing algorithm has received little attention. Because the TA tracing algorithm has a runtime of O(N) in general, where N is the number of users, it is inefficient for large populations.We produce schemes for which the TA algorithm is very fast. The IPP tracing algorithm, though less efficient, can list all coalitions capable of constructing a given pirate. We give evidence that when using an algebraic structure, the ability to …

Investigation Of Optical Interference Effects In The Generalized Eikonal Formalism, Nyok Fah Thong

Student Works (2000-2009)

In recent studies, the generalized eikonal equation and the equation of continuity had been shown able to describe wave phenomena, which cannot be obtained by simple geometrical optics. The time dependent generalized eikonal equation, derived from the time dependent Maxwell wave equation, is able to describe dispersion and soliton effects. This method was exten4ed to include diffraction, self-trapping and self-focusing in linear and non-linear media for stationary waves. For cases that have no analytical solution, the generalized eikonal equation and the equation of continuity are solved numerically. The solutions are in good agreement with the solutions obtained from the Fresnel-Kirchhoff …

A New Compensating Element For A Femtosecond Photoelectron Gun, Bao-Liang Qian, Hani E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

Design and analysis of a new compensating element for improving the electron pulse front and compressing the pulse duration in a femtosecond photoelectron gun are described. The compensating element is a small metallic cylindrical cavity in which an external voltage is applied in such a way that a special electric field forms and interacts with the electron pulse. This electric field reduces the distances between the faster and slower electrons inside the cavity and efficiently compensates for electron pulse broadening caused by the photoelectron energy spread and space charge effects. Poisson's equation and the equation of motion are solved to …

Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi

LSU Doctoral Dissertations

This dissertation makes a contribution to the study of Witt rings of quadratic forms over number fields. To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. The situation is particularly nice when this number is 0; often it is not 0. Earlier investigations have established lower bounds for this number. In this dissertation an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered …