Physical Sciences and Mathematics Commons^™

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

Asymptotic Analysis Of Buffered Calcium Diffusion Near A Point Source, Arthur Sherman, Gregory D. Smith, Longxiang Dai, Robert M. Miura

Arts & Sciences Articles

The "domain" calcium (Ca2+) concentration near an open Ca2+ channel can be mod- eled as buffered diffusion from a point source. The concentration profiles can be well approximated by hemispherically symmetric steady-state solutions to a system of reaction-diffusion equations. After nondimensionalizing these equations and scaling space so that both reaction terms and the source amplitude are 0(1), we identify two dimensionless parameters, Cc and Eb, that correspond to the diffusion coefficients of dimensionless Ca2+ and buffer, respectively. Using perturbation methods, we derive approximations for the Ca2+ and buffer profiles in three asymptotic limits: (1) an "excess buffer approximation" (EBA), where …

The Range Of The Iterated Matrix Adjoint Operator, Tze-Jang Chen, Jenn-Tsann Lin, C. H. Cooke

Mathematics & Statistics Faculty Publications

The following inverse problem is considered: for a given n × n real matrix B, does there exist a real matrix A such that where the classical adjoint operation is intended? The rank of B and the number of applications of the adjoint operator determine the character of this general inverse problem for the iterated adjoint operator. Thus, for given B, the question of interest is whether or not B lies in the range of the iterated matrix adjoint operator. Maple V R5 is used as an aid to obtain results indicated here. (©) 2001 Elsevier Science Ltd. …

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 …

Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He

Tian-Xiao He

In this paper, we will discuss the construction of biorthogonal wavelets that possess the largest possible regularities and required vanishing moments. For the sake of applications, we also give a general Daubechies’ iteration method of constructing biorthogonal wavelets by using biorthogonal splines.

Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He

Tian-Xiao He

No abstract provided.

Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He

Tian-Xiao He

No abstract provided.

Commuting Self-Adjoint Extensions Of Symmetric Operators Defined From The Partial Derivatives, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(∂/∂x_j):j=1,...,d} with domain C^∞_c(Ω) where the self-adjointness is defined relative to L²(Ω), and Ω is a given open subset of R^d.

Normal Forms, Canonical Forms, And Invariants Of Single Input Nonlinear Systems Under Feedback, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analysing, step by step, the action of homogeneous transformations on the homogeneous part of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms coincide. We give an explicit construction of transformations bringing the system to its normal, dual normal, and canonical form.

The Expected Wet Period Of Finite Dam With Exponential Inputs, Eui Yong Lee, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

We use martingale methods to obtain an explicit formula for the expected wet period of the finite dam of capacity V, where the amounts of inputs are i.i.d exponential random variables and the output rate is one, when the reservoir is not empty. As a consequence, we obtain an explicit formula for the expected hitting time of either 0 or V and a new expression for the distribution of the number of overflows during the wet period, both without the use of complex analysis.

Alternative Principal Components Regression Procedures For Dendrohydrologic Reconstructions, Hugo G. Hidalgo, Thomas C. Piechota, John A. Dracup

Civil and Environmental Engineering and Construction Faculty Research

Streamflow reconstruction using tree ring information (dendrohydrology) has traditionally used principal components analysis (PCA) and stepwise regression to form a transfer function. However, PCA has several procedural choices that may result in very different reconstructions. This study assesses the different procedures in PCA-based regression and suggests alternative procedures for selection of variables and principal components. Cross-validation statistics are presented as an alternative for independently testing and identifying the optimal model. The objective is to use these statistics as a measure of the model's performance to find a conceptually acceptable model with a low prediction error and the fewest number of …

Stochastic Hybrid Control, A. Bensoussan, J. L. Menaldi

Mathematics Faculty Research Publications

The objective of this paper is to study the stochastic version of a previous paper of the authors, in which hybrid control for deterministic systems was considered. The modelling is quite similar to the deterministic case. We have a system whose state is composed of a continuous part and a discrete part. They are affected by a continuous type control and an impulse control. The dynamics is moreover perturbed by noise, also a continuous and a discrete noise process. The Markovian character of the state process is preserved. We develop the model and show how the dynamic programming approach leads …

A Nonlinear Parabolic Equation Modelling Surfactant Diffusion, Xinfu Chen, Chaocheng Huang, Jennifer Zhao

Mathematics and Statistics Faculty Publications

An initial-boundary value problem for nonlinear parabolic equations modelling surfactant diffusions is investigated. The boundary conditions are of nonlinear adsorptive types, and the initial value has a single point jump. We study the well-posedness of the problem, the convergence of a numerical scheme, and the regularity as well as quantitative behaviour of solutions.

On The Effect Of Long-Wavelength Electron Plasma Waves On Large-Angle Stimulated Raman Scattering Of Short Laser Pulse In Plasmas, Nikolai E. Andreev, Serguei Y. Kalmykov

Serge Youri Kalmykov

Spectral features of a large-angle stimulated Raman scattering (LA SRS) of a short electromagnetic pulse in an underdense plasma, which are caused by the presence in a plasma of a given linear long-wavelength electron plasma wave (LW EPW), are investigated. It is shown that the LW EPW, whose phase velocity coincides with a group velocity of a pulse and a density perturbation normalized to a background electron density, \delta n_{LW} / n_0, exceeds the ratio of the electron plasma frequency to the laser frequency, \omega_{pe} / \omega_0, suppresses the well-known Stokes branch of the weakly coupled LA SRS. Under the …

An Efficient Method For Band Structure Calculations In 3d Photonic Crystals, David C. Dobson, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

A method for computing band structures for three-dimensional photonic crystals is described. The method combines a mixed finite element discretization on a uniform grid with a fast Fourier transform preconditioner and a preconditioned subspace iteration algorithm. Numerical examples illustrating the behavior of the method are presented.

Solvability Of A Parabolic Boundary Value Problem With Internal Jump Condition, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

We examine a model for the propagation of heat through a one-dimensional object with an interior ''flaw". The flaw is modeled as a nonlinear relationship between the flux and temperature jump at an interior point of the object. Under realistic hypotheses, the resulting nonlinear initial boundary value problem is shown to have a unique and suitably smooth solution.

The Structure Of Free Semigroup Algebras, Kenneth R. Davidson, Elias Katsoulis, David R. Pitts

Department of Mathematics: Faculty Publications

A free semigroup algebra is WOT-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting features. The first is that they provide useful information about unitary invariants of representations of the Cuntz-Toeplitz algebras. The second is that they form a class of nonself-adjoint operator algebras which are of interest in their own right. This class contains a distinguished representative, the "non-commutative Toeplitz algebra", which is generated by the left regular representation of the free semigroup on n letters and denoted . This paper provides a general …

Euclidean Weights Of Codes From Elliptic Curves Over Rings, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.

A code is a subset of Aⁿ, where A is a finite set (called the alphabet). Usually A is just the field of two elements and, in this case, one speaks of binary codes. Such codes are used in applications where one transmits information through noisy channels. By building redundancy into the code, transmitted …

Tiling As A Loop Parallelization Technique, Hoda Ahmed Khalil

Archived Theses and Dissertations

No abstract provided.

Time Domain Probabilistic Risk Assessment:, George H. Baker, Charles T. C. Mo

George H Baker

For critical facilities, survivability and reconstitution in stressful environments generated by electromagnetic transients, sabotage, terrorist activity, military conflict, or Murphy’s laws are issues of concern. Critical fixed facilities are likely to be functionally complex and their system-wide failure probabilities, modes, and consequences are often not obvious. To analyze and quantify survivability, existing probabilistic risk assessment tools usually provide a “snapshot” of failure modes at a single point of time for certain initiating conditions. Likewise, elaborate physics models developed to treat weapons effects on structures and individual functional components compute effects at a single time point.

We have developed a tool …

Finite Element Model Updating Using Antiresonant Frequencies, Keith W. Jones

Theses and Dissertations

The applications of antiresonant frequencies to finite element (FE) model updating are few and usually limited to numerical examples. This work uses antiresonant frequencies in the model updating of an experimental structure and analyzes the physical correctness of the updated model by using it to detect damage. Antiresonant frequencies were used in the FE model updating of a six-meter aluminum truss. The model used rigid links to model welded and bolted joints. Rigid link dimensions were used as parameters in an iterative update based on eigenvalue and antiresonance sensitivities. The first update used 11 natural frequencies and 21 antiresonant frequencies …

Singular Solutions To A Nonlinear Elliptic Boundary Value Problem Originating From Corrosion Modeling, Kurt M. Bryan, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We consider a nonlinear elliptic boundary value problem on a planar domain. The exponential type nonlinearity in the boundary condition is one that frequently appears in the modeling of electrochemical systems. For the case of a disk we construct a family of exact solutions that exhibit limiting logarithmic singularities at certain points on the boundary. Based on these solutions we develop two criteria that we believe predict the possible locations of the boundary singularities on quite general domains.

Tight Bounds On The Algebraic Connectivity Of A Balanced Binary Tree, Jason J. Molitierno, Michael Neumann, Bryan L. Shader

Mathematics Faculty Publications

In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2^k - 1 vertices. This is accomplished by considering the inverse of a matrix of order k - 1 readily obtained from the Laplacian matrix. It is shown that the algebraic connectivity is 1/(2^k - 2k + 3) + 0(1/2^2k).

Codes And Curves, Judy L. Walker

Department of Mathematics: Faculty Publications

When information is transmitted, errors are likely to occur. Coding theory examines effi cient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed- Solomon codes, one can see how to defi ne new codes based on divisors on algebraic curves. For instance, using modular curves over fi nite fi elds, Tsfasman, Vladut, and Zink showed that one can defi ne a sequence of …

Behavior Of Grain Boundary Resistivity In Metals Predicted By A Two-Dimensional Model, Rand Dannenberg, Alexander H. King

Alexander H. King

The behavior of a model for the specific grain boundary resistivity in metallic bamboo conductor lines is developed and compared to other theoretical treatments, and to experiment. The grain boundary is modeled as an array of scatterers on a plane. The scatterers are called “vacancy-ion” complexes, in which the vacancy represents the boundary free volume, and the ion is an atom adjacent to the vacancy. Three cases are investigated, that of noninterfering scatterers, a continuum of interfering scatterers, and discrete interfering scatterers. The approximations used lead to a specific grain boundary resistivity ∼10−16 Ω m2 for aluminum, in agreement with …

Two-Frequency Forced Faraday Waves: Weakly Damped Modes And Pattern Selection, Mary Silber, Chad M. Topaz, Anne Skeldon

Chad M. Topaz

Recent experiments [A. Kudrolli, B. Pier, J.P. Gollub, Physica D 123 (1998) 99–111] on two-frequency parametrically excited surface waves produce an intriguing "superlattice" wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves onset simultaneously, but with different spatial wavenumbers. The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small-scale triangular structure. Similar patterns have been shown to exist as primary solution branches of a generic 12-dimensional ${\rm D}_6\dot{+}{\rm T}^2$-equivariant bifurcation problem, and may be stable if the nonlinear coefficients of the bifurcation problem satisfy certain inequalities [M. Silber, …

Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng

Yi Li

In this paper, we study the following elliptic problem[formula]where K(x) is a given function in C^α(ⁿ\0) for some fixed α∈(0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.

Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

In this paper, we study the following elliptic problem[formula]where K(x) is a given function in C^α(ⁿ\0) for some fixed α∈(0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Mathematics Faculty Publications

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.

Two-Groups With Few Conjugacy Classes, Nigel Boston, Judy L. Walker

Department of Mathematics: Faculty Publications

An old question of Brauer asking how fast numbers of conjugacy classes grow is investigated by considering the least number c_n of conjugacy classes in a group of order 2ⁿ. The numbers c_n are computed for n ≤ 14 and a lower bound is given for c₁₅. It is observed that c_n grows very slowly except for occasional large jumps corresponding to an increase in coclass of the minimal groups G_n. Restricting to groups that are 2-generated or have coclass at most 3 allows us to extend these computations.