Applied Mathematics Commons^™

The Extended Picture Group, With Applications To Line Arrangement Complements, Charles Richard Egedy

LSU Doctoral Dissertations

We obtain the picture group as the quotient with a torsion subgroup, of an extended picture group, which is isomorphic to the kernel of a precrossed module homomorphism. In addition to expanding the notion of a picture group, the new formulation gives a natural way to construct homomorphisms between picture groups by describing deformations of one-vertex subpictures. The extended picture group thus provides a convenient way to describe generators for the second homotopy group of line arrangement complements as well as homomorphisms between these groups. In particular, we show that the homomorphisms relate to a lattice structure corresponding roughly to …

Function Spaces, Wavelets And Representation Theory, Jens Gerlach Christensen

LSU Doctoral Dissertations

This dissertation is concerned with the interplay between the theory of Banach spaces and representations of groups. The wavelet transform has proven to be a useful tool in characterizing and constructing Banach spaces, and we investigate a generalization of an already known technique due to H.G. Feichtinger and K. Gröchenig. This generalization is presented in Chapter 3, and in Chapters 4 and 5 we present examples of spaces which can be described using the theory. The first example clears up a question regarding a wavelet characterization of Bergman spaces related to a non-integrable representation. The second example is a wavelet …

Convolution Semigroups, Kevin W. Zito

LSU Doctoral Dissertations

In this dissertation we investigate, compute, and approximate convolution powers of functions (often probability densities) with compact support in the positive real numbers. Extending results of Ursula Westphal from 1974 concerning the characteristic function on the interval $[0,1]$, it is shown that positive, decreasing step functions with compact support can be embedded in a convolution semigroup in $L^1(0,infty)$ and that any decreasing, positive function $pin L^1(0,infty)$ can be embedded in a convolution semigroup of distributions. As an application to the study of evolution equations, we consider an evolutionary system that is described by a bounded, strongly continuous semigroup ${T(t)}_{tgeq0}$ in …

A Discrete Model Of Guided Modes And Anomalous Scattering In Periodic Structures, Natalia Grigoryevna Ptitsyna

LSU Doctoral Dissertations

We study a discrete prototype of anomalous scattering associated with the interaction of guided modes of a periodic scatterer and plane waves incident upon the scatterer. The transmission anomalies arise because of the non-robustness of a guided mode, a mode that exists only at a specific frequency and wave number pair. The simplicity of the discrete prototype allows one to make certain explicit calculations and proofs, and to examine details of important resonant phenomena of the open wave guides. The main results are (1) a formula for transmission anomalies near a non-robust guided mode with rigorous error estimates that extends …

Homological Width And Turaev Genus, Adam Lowrance

LSU Doctoral Dissertations

Khovanov homology and knot Floer homology are generalizations of the Jones polynomial and the Alexander polynomial respectively. They are bigraded Z-modules, and their underlying polynomials are recovered by taking the graded Euler characteristic. The two homologies share many characteristics, however their relationship has yet to be fully understood. In both Khovanov homology and knot Floer homology, the two gradings can be combined into a single diagonal grading. Homological width is a measure of the support of the homology with respect to the diagonal grading. In this thesis, we show that the homological width of Khovanov homology and knot Floer homology …

A Regularization Technique In Dynamic Optimization, Alvaro Guevara

LSU Doctoral Dissertations

In this dissertation we discuss certain aspects of a parametric regularization technique which is based on recent work by R. Goebel. For proper, lower semicontinuous, and convex functions, this regularization is self-dual with respect to convex conjugation, and a simple extension of this smoothing exhibits the same feature when applied to proper, closed, and saddle functions. In Chapter 1 we give a introduction to convex and saddle function theory, which includes new results on the convergence of saddle function values that were not previously available in the form presented. In Chapter 2, we define the regularization and extend some of …

Some Results On Cubic Graphs, Evan Morgan

LSU Doctoral Dissertations

Pursuing a question of Oxley, we investigate whether the edge set of a graph admits a bipartition so that the contraction of either partite set produces a series-parallel graph. While Oxley's question in general remains unanswered, our investigations led to two graph operations (Chapters 2 and 4) which are of independent interest. We present some partial results toward Oxley's question in Chapter 3. The central results of the dissertation involve an operation on cubic graphs called the switch; in the literature, a similar operation is known as the edge slide. In Chapter 2, the author proves that we can transform, …

Local Behavior Of Distributions And Applications, Jasson Vindas

LSU Doctoral Dissertations

This dissertation studies local and asymptotic properties of distributions (generalized functions) in connection to several problems in harmonic analysis, approximation theory, classical real and complex function theory, tauberian theory, summability of divergent series and integrals, and number theory. In Chapter 2 we give two new proofs of the Prime Number Theory based on ideas from asymptotic analysis on spaces of distributions. Several inverse problems in Fourier analysis and summability theory are studied in detail. Chapter 3 provides a complete characterization of point values of tempered distributions and functions in terms of a generalized pointwise Fourier inversion formula. The relation of …

Impulsive Control Systems, Wei Cai

LSU Doctoral Dissertations

Impulsive control systems arose from classical control systems described by differential equations where the control functions could be unbounded. Passing to the limit of trajectories whose velocities are changing very rapidly leads to the state vector to "jump", or exhibit impulsive behavior. The mathematical model in this thesis uses a differential inclusion and a measure-driven control, and it becomes possible to deal with the discontinuity of movements happening over a small interval. We adopt the formulism of impulsive systems in which the velocities are decomposed by the slow and fast ones. The fast time velocity is expressed as the multiplication …

Biology In Mathematics At The University Of Richmond, Lester Caudill

Department of Math & Statistics Faculty Publications

In an effort to meet the needs of science students for modeling skills, three new courses have been created at the University of Richmond: Scientific Calculus I and II, and Mathematical Models in Biology and Medicine. The courses are described, and lessons learned and future directions are discussed.

Habitat Selection By Anolis Carolinensis (Green Anole) In Open Pine Forests In Eastern Texas, Richard R. Schaefer, Robert R. Fleet, D. Craig Rudolph, Nancy E. Koerth

Faculty Publications

We initiated a mark-recapture study to determine the effects of shrub density on Anolis carolinensis (Green Anole) populations. Green Anole perch site, shrub species, and shrub volume preferences were also examined. We established two study plots of different shrub densities in open pine forests on the Angelina National Forest in eastern Texas. In late spring, the Green Anole population at the higher shrub-density plot was estimated to be 16 times greater than the population at the lower shrub-density plot. Green Anoles most commonly perched on live shrubs, but exhibited very little preference or avoidance of any particular species of live …

The Analogue Of The Iterated Logarithm For Quantum Difference Equations, Karl Friedrich Ulrich

Masters Theses

"In this thesis, we consider oscillation and nonoscillation of q-difference equations, i.e., equations that arise while studying q-calculus. In particular, we prove an extension of Kneser’s theorem on q-calculus to cases in which no conclusion can be drawn by applying Kneser’s theorem. In order to accomplish this, we establish a change of variables which yields, when applied iteratively, a sequence of comparison functions. We use these comparison functions to establish our main result. Finally, we consider an analogue result for time scales which are unbounded from above"--Abstract, page iii.

Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Through this book, for the first time we represent every finite group in the form of a graph. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group …

When To Spray: A Time-Scale Calculus Approach To Controlling The Impact Of West Nile Virus, Diana Thomas, Marion Weedermann, Lora Billings, Joan Hoffacker, Robert Washington-Allen

Department of Mathematics Faculty Scholarship and Creative Works

West Nile Virus (WNV) made its initial appearance in the New York City (NYC) metropolitan area in 1999 and was implicated in cases of human encephalitis and the extensive mortality in crows (Corvus sp.) and other avian species. Mosquitoes were found to be the primary vectors and NYC’s current policy on control strategies involved an eradication program that depends on the synchronicity of the summer mosquito population’s increases with the occurrence of cases in humans. The purpose of this paper is to investigate whether this is the most effective control strategy because past mathematical models assumed discrete behavior that …

Conceptual Circuit Models Of Neurons, Bo Deng

Department of Mathematics: Faculty Publications

A systematic circuit approach tomodel neurons with ion pump is presented here by which the voltage-gated current channels are modeled as conductors, the diffusion-induced current channels are modeled as negative resistors, and the one-way ion pumps are modeled as one-way inductors. The newly synthesized models are different from the type of models based on Hodgkin-Huxley (HH) approach which aggregates the electro, the diffusive, and the pump channels of each ion into one conductance channel. We show that our new models not only recover many known properties of the HH type models but also exhibit some new that cannot be extracted …

Connections Between Computation Trees And Graph Covers, Deanna Dreher, Judy L. Walker

Department of Mathematics: Faculty Publications

Connections between graph cover pseudocodewords and computation tree pseudocodewords are investigated with the aim of bridging the gap between the theoretically attractive analysis of graph covers and the more intractable analysis of iterative message-passing algorithms that are intuitively linked to graph covers. Both theoretical results and numerous examples are presented.

Analysis Of Connections Between Pseudocodewords, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker

Department of Mathematics: Faculty Publications

The role of pseudocodewords in causing noncodeword outputs in linear programming (LP) decoding, graph cover decoding, and iterative message-passing decoding is investigated. The three main types of pseudocodewords in the literature — linear programming pseudocodewords, graph cover pseudocodewords, and computation tree pseudocodewords — are reviewed and connections between them are explored. Some discrepancies in the literature on minimal and irreducible pseudocodewords are highlighted and clarified, and a value for the minimal degree cover necessary to realize an LP pseudocodeword is found. Additionally, some conditions for the existence of connected realizations of graph cover pseudocodewords are given. This allows for further …

An H-Adaptive Finite-Element Technique For Constructing 3d Wind Fields, Darrell Pepper, Xiuling Wang

Mechanical Engineering Faculty Research

An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions …

Singular Superposition/Boundary Element Method For Reconstruction Of Multi-Dimensional Heat Flux Distributions With Application To Film Cooling Holes, Mahmood Silieti, Eduardo Divo, Alain J. Kassab

Publications

A hybrid singularity superposition/boundary element-based inverse problem method for the reconstruction of multi-dimensional heat flux distributions is developed. Cauchy conditions are imposed at exposed surfaces that are readily reached for measurements while convective boundary conditions are unknown at surfaces that are not amenable to measurements such as the walls of the cooling holes. The purpose of the inverse analysis is to determine the heat flux distribution along cooling hole surfaces. This is accomplished in an iterative process by distributing a set of singularities (sinks) inside the physical boundaries of the cooling hole (usually along cooling hole centerline) with a given …

Bifurcation Analysis Of A Kaldor-Kalecki Model Of Business Cycle With Time Delay, Liancheng Wang, Xiaoqin P. Wu

Faculty Articles

In this paper, we investigate a Kaldor-Kalecki model of business cycle with delay in both the gross product and the capital stock. Stability analysis for the equilibrium point is carried out. We show that Hopf bifurcation occurs and periodic solutions emerge as the delay crosses some critical values. By deriving the normal forms for the system, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Examples are presented to confirm our results.

A Covert Encryption Method For Applications In Electronic Data Interchange, Jonathan Blackledge, Dmitry Dubovitskiy

Articles

A principal weakness of all encryption systems is that the output data can be ‘seen’ to be encrypted. In other words, encrypted data provides a ‘flag’ on the potential value of the information that has been encrypted. In this paper, we provide a new approach to ‘hiding’ encrypted data in a digital image.

In conventional (symmetric) encryption, the plaintext is usually represented as a binary stream and encrypted using an XOR type operation with a binary cipher. The algorithm used is ideally designed to: (i) generate a maximum entropy cipher so that there is no bias with regard to any …

On Nonlinear Generalizations Of The Kdv And Bbm Equations From Long Range Water Wave Theory, Timothy A. Smith

Publications

A generalization of the famous KdV and BBM equation are considered with a new nonlinear term. Sufficient conditions of solvability, existence and uniqueness are established.

Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such extensions are a fundamental ingredient of high order finite element analysis.

Stability Of Linear Flocks On A Ring Road, J. J. P. Veerman, Carlos Martins Da Fonseca

Mathematics and Statistics Faculty Publications and Presentations

We discuss some stability problems when each agent of a linear flock on the line interacts with its two nearest neighbors (one on either side).

Automated Traffic And The Finite Size Resonance, J. J. P. Veerman, Borko D. Stošić, F. M. Tangerman

Mathematics and Statistics Faculty Publications and Presentations

We investigate in detail what one might call the canonical (automated) traffic problem: A long string of N+1 cars (numbered from 0 to N) moves along a one-lane road “in formation” at a constant velocity and with a unit distance between successive cars. Each car monitors the relative velocity and position of only its neighboring cars. This information is then fed back to its own engine which decelerates (brakes) or accelerates according to the information it receives. The question is: What happens when due to an external influence—a traffic light turning green—the ‘zero’th’ car (the “leader”) accelerates?

As …

Cedar Rapids Flood Of 2008: Manmade Or Statistical Anomaly?, Beth Kolsrud

Honors Program Theses

One of the main research questions for this thesis is what factors caused the flooding last summer and why was it so extreme? This is an important question to answer because it is vital to understand what causes a flood of this magnitude so communities can take steps to avoid or minimize damage that may result from floods in the future. The second question is what impact does this flood have on flood insurance? Flood insurance is one tool used to protect property owners from substantial loss due to flooding and plays a vital role in recovery after a flood, …

A Two-Population Insurgency In Colombia: Quasi-Predator-Prey Models - A Trend Towards Simplicity, John A. Adam, John A. Sokolowski, Catherine M. Banks

Mathematics & Statistics Faculty Publications

A sequence of analytic mathematical models has been developed in the context of the "low-level insurgency" in Colombia, from 1993 to the present. They are based on generalizations of the two-population "predator-prey" model commonly applied in ecological modeling, and interestingly, the less sophisticated models yield more insight into the problem than the more complicated ones, but the formalism is available to adapt the model "upwards" in the event that more data becomes available, or as the situation increases in complexity. Specifically, so-called "forcing terms" were included initially in the coupled differential equations to represent the effects of government policies towards …

Integrated Remote Sensing And Gis Techniques For Groundwater Exploration In Semi-Arid Region: A Case Of Karamoja Region – Uganda, Lubang Nobert

Tanzania Journal of Engineering and Technology (TJET)

Groundwater is a precious resource that covers wide geographical extent. Proper evaluation is required in order to ensure prudent use of groundwater resources. The current groundwater assessment in Karamoja region, as in many parts of the world, uses Apparent Resistivity and Vertical Electrical Sounding, which has limited coverage to some localized usually predetermined areas. Comprehensive groundwater development program needs a wide area coverage and large volume of multidisciplinary data. In the present study, an integrated remote sensing and GIS based methodology is developed and tested for the evaluation of groundwater resources of Karamoja Sub Region, Northeastern Uganda. The components of …

Analytical Modeling Of A Large Local Area Network - Part I: Internet Traffic Characterization, Mathew Luhanga

Tanzania Journal of Engineering and Technology (TJET)

The goal of both IP network operators and the end users is to get the highest performance from the system for a given cost. This makes Performance a key criterion in the design, procurement, and use of computer and communication systems. In order to address problems associated with performance degradation of operational communications systems, over the last decade, traffic engineering techniques have emerged in an attempt to optimize communication systems’ performance and ensure more efficient use of their resources. One of these techniques is analytical modeling. Analytic performance models are an excellent tool for quickly evaluating the performance of operational …

Identification Of Unbalanced Forces And Foundation Parameters Of Rotating Machines From Vibration Measurements, Nalitolela G

Tanzania Journal of Engineering and Technology (TJET)

A technique is described to use measured vibration data of a rotating machine and its foundation to identify unbalanced forces, stiffness and damping parameters of the mountings, and the parameters of the foundation. It is based on an idealisation treating the rotor, the machine structure and the foundation as rigid masses supported by springs and dampers. Operational vibration data of the machine and its foundation before and after the rotating unbalanced forces are perturbed by adding unbalanced mass to the rotor are used in the identification procedure. Once the parameters are identified, dynamic forces transmitted to the foundation can be …