Physical Sciences and Mathematics Commons^™

Laguerre Functions Associated To Euclidean Jordan Algebras, Michael Aristidou

LSU Doctoral Dissertations

Certain differential recursion relations for the Laguerre functions, defined on a symmetric cone Ω, can be derived from the representations of a specific Lie algebra on L²(Ω,dμ_v). This Lie algebra is the corresponding Lie algebra of the Lie group G that acts on the tube domain T(Ω)=Ω+iV, where V is the associated Euclidean Jordan algebra of Ω. The representations involved are the highest weight representations of G on L²(Ω,dμ_v). To obtain these representations, we start from the highest weight representations of G on H_v(T(Ω)), the Hilbert space of holomorphic functions …

Synthetic Development And Application Of Compounds With Biological Relevance, Jeffery Caleb Clark

LSU Doctoral Dissertations

Nature has provided a vast number of compounds that have medicinal application. The use of these compounds provided by nature however, is limited by the amount of a specific compound that nature provides. The synthesis of these molecules and their derivatives provides an even greater number of compounds for biological screening. Various pyrroles, the heterocyclic building blocks of porphyrins, can be prepared synthetically over several steps. The implementation of carboranes on pyrrole rings intrinsically provides substrates that can be converted into porphyrins bearing carborane substituents. The condensation of these carboranylpyrroles with carboranylaldehydes provides carboranylporphyrins bearing a higher order of carborane …

Boundary Effects On Non-Equilibrium Localized Structures In Spatially Extended Systems, Aniruddha Yadav

LSU Doctoral Dissertations

A study of the effects of system boundaries on bistable front propagation in nonequilibrium reaction-diffusion systems is presented. Two model partial differential equations displaying bistable fronts, with distinct experimental motivations and mathematical structure, are examined in detail utilizing simulations and perturbation techniques. We see that propagating fronts in both models bounce, trap, pin, or oscillate at the boundary, contingent on the imposed boundary condition, initial front speed and distance from the boundary. The similarities in front boundary interactions in these two models is traced to the fact that they display the same front instability (Ising-Bloch bifurcation) that controls the speed …

Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister

LSU Doctoral Dissertations

In this work we analyze error estimates for rational approximation methods, and their stabilizations, for strongly continuous semigroups. Chapter 1 consists of a brief survey of time discretization methods for semigroups. In Chapter 2, we demonstrate a new method for obtaining convergent approximations in the absence of stability for strongly continuous semigroups with arbitrary initial data. In Section 2.2, we state the stabilization result in more general form and show that this method can be used to improve known error estimates by a magnitude of up to one half for smooth initial data. In Section 2.3, we give concrete examples …

Macroinvertebrate Community Of Ecology Of Lowland, Subtropical Streams In Louisiana, Michael Douglas Kaller

LSU Doctoral Dissertations

Freshwater ecosystems, particularly streams and rivers, have been the subject of prodigious research. Unfortunately, in comparison to neighboring regions, the Gulf of Mexico coastal plain has not received as much attention. Therefore, I collected data on the macroinvertebrates of these streams to begin the understanding of the relationships between community structure and environmental characteristics. In contrast to the hypothesized ancestral streams of these macroinvertebrates, coastal plain streams are commonly devoid of rocks leaving only woody debris as usable hard substrates and are typically lower in dissolved oxygen. I examined habitat selection by colonization of woody debris with large and small …

Learning Discrete Hidden Markov Models From State Distribution Vectors, Luis G. Moscovich

LSU Doctoral Dissertations

Hidden Markov Models (HMMs) are probabilistic models that have been widely applied to a number of fields since their inception in the late 1960’s. Computational Biology, Image Processing, and Signal Processing, are but a few of the application areas of HMMs. In this dissertation, we develop several new efficient learning algorithms for learning HMM parameters. First, we propose a new polynomial-time algorithm for supervised learning of the parameters of a first order HMM from a state probability distribution (SD) oracle. The SD oracle provides the learner with the state distribution vector corresponding to a query string. We prove the correctness …

Characterization Of Aged Polymer Modified Asphalt Cements For Recycling Purposes, Codrin Daranga

LSU Doctoral Dissertations

Since polymer modified asphalt cement (PMAC) has been employed for a decade, the lifetime and wear on some of these pavements is reaching a stage where resurfacing is necessary. This research focuses on the characterization of aged polymer modified asphalt cements (PMAC) to evaluate their potential for recycling. A styrene-butadiene-styrene tri-block (SBS) polymer modified asphalt cement was selected and characterized using standard asphalt binder qualification techniques, i.e., the Superpave PG protocol. We developed a procedure to characterize the relative concentration of polymer in asphalt cements by gel permeation chromatography (GPC). Infrared spectrographic, thermogravimetric and rheological techniques were used to identify …

Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn

LSU Doctoral Dissertations

The theory of filaments on oriented chord diagrams can be used to detect some non-classical virtual knots. We extend existing filament techniques to virtual links with more than one component and give examples of virtual links that these techniques can detect as non-classical. Given a signed Gauss word underlying an oriented chord diagram, we describe how to construct a finite sequence of integers that encodes all of the filament information for the diagram. We also introduce a square array of integers called a MIN-square that summarizes the filament information about all of the signed Gauss words having a given Gauss …

Dynamical Systems With Time Delay, Norma Ortiz

LSU Doctoral Dissertations

In this dissertation, we study necessary conditions and weak invariance properties of dynamical systems with time delay. A number of results have been obtained recently that refine necessary conditions of optimal solutions for nonsmooth dynamical systems without time delay. In this dissertation, we examine the extension of some of these results to problems with time delay. In particular, we study the generalized problem of Bolza with the addition of delay in the state and velocity variables and refer to this problem as the Neutral Problem of Bolza. We consider the relationship between the generalized problem of Bolza with time delay …

Broadcast In Sparse Conversion Optical Networks Using Fewest Converters, Tong Yi

LSU Doctoral Dissertations

Wavelengths and converters are shared by communication requests in optical networks. When a message goes through a node without a converter, the outgoing wavelength must be the same as the incoming one. This constraint can be removed if the node uses a converter. Hence, the usage of converters increases the utilization of wavelengths and allows more communication requests to succeed. Since converters are expensive, we consider sparse conversion networks, where only some specified nodes have converters. Moreover, since the usage of converters induces delays, we should minimize the use of available converters. The Converters Usage Problem (CUP) is to use …

Dissipative Lipschitz Dynamics, Vinicio Rafael Rios

LSU Doctoral Dissertations

In this dissertation we study two related important issues in control theory: invariance of dynamical systems and Hamilton-Jacobi theory associated with optimal control theory. Given a control system modelled as a differential inclusion, we provide necessary and sufficient conditions for the strong invariance property of the system when the dynamic satisfies a dissipative Lipschitz condition. We show that when the dynamic is almost upper semicontinuous and satisfies the dissipative Lipschitz property, these conditions can be expressed in terms of approximate Hamilton-Jacobi inequalities, which subsumes the classic infinitesimal characterization of strongly invariant systems given under the Lipschitz assumtion. In the important …

Denitrification And Greenhouse Gas Emissions From Cultivated And Wetland Alluvial Soils, Sami Ullah

LSU Doctoral Dissertations

Agricultural development in the Mississippi River Basin has contributed to an 3-fold increase in NO3 loading of the river. Increased NO3 loading is a primary cause of eutrophication in the northern Gulf of Mexico. Identification of best management practices (BMPs) to reduce NO3 loss and wetlands restoration to remove NO3 through denitrification are critically needed. The objectives of this research were to determine factors controlling denitrification potential of different landscape units in an agricultural watershed and quantify the effects of BMPs and organic C amendments on denitrification rates of cultivated lands and restored forested wetlands. N2O, CH4 and CO2 emissions …

Population Dynamics Of Clausocalanus Furcatus (Copepoda, Calanoida) In The Northern Gulf Of Mexico, Hongsheng Bi

LSU Doctoral Dissertations

Copepods are important components of marine ecosystems. Understanding copepod population dynamics can help interpret variations in both primary producers and higher trophic levels. Egg production, stage duration, and stage-specific mortality rates are key parameters describing copepod population dynamics. Estimation of stage-specific mortality is complicated due to a complex life history, patchiness, and sampling biases. This study was undertaken to quantify the population dynamics of the copepod Clausocalanus furcatus in the northern Gulf of Mexico and to assess the utility of available mortality estimation methods in a highly advective environment. Zooplankton samples were taken every 12h from March 18-April 6, and …

Komatiites Of The Weltevreden Formation, Barberton Greenstone Belt, South Africa: Implications For The Chemistry And Temperature Of The Archean Mantle, Keena Kareem

LSU Doctoral Dissertations

The komatiites of the 3.29 Ga Weltevreden Formation, Barberton Greenstone Belt, South Africa represent extremely magnesian lavas derived from the Archean mantle. Three related papers are presented on aspects of the temperature and composition of the Archean mantle, and surface alteration processes. Petrographical and geochemical analyses confirm that olivines from the komatiites retain much of their original igneous character, containing fresh olivines, pyroxenes, and chromites. The olivines from the Weltevreden Formation are extremely magnesian, with Fo contents up to 95.6. Primitive mantle normalized Gd/Yb values near 1, and Al₂O₃/TiO₃ values of 26-33 for these rocks …

Quasicontinuous Derivatives And Viscosity Functions, Rodica Cazacu

LSU Doctoral Dissertations

In this work we demonstrate how the continuous domain theory can be applied to the theory of nonlinear optimization, particularly to the theory of viscosity solutions. We consider finding the viscosity solution for the Hamilton-Jacobi equation H(x, y) = g(x), with continuous hamiltonian, but with possibly discontinuous right-hand side. We begin by finding a new function space Q(X,L), the space of equivalence classes of quasicontinuous functions from a locally compact set X to a bicontinuous lattice L and we will define on Q(X,L) the qo-topology, which is a variant of classical order topology defined on complete lattices. On this …

Economic Valuation Of Natural Resource Management: A Case Study Of The Benuaq Dayak Tribe In Kalimantan, Indonesia, Indah D. Kusuma

LSU Doctoral Dissertations

The unavailability of total economic values of indigenous people in Indonesia, both in the short and long term, has created the rejection of their existences in the forest area. The purpose of this study is to estimate the total economic value of sustainable forest management conducted by indigenous tribes in Indonesia using total economic value concepts. The tribe’s total economic value is expressed by estimating the use value, indirect use value and non-use value. The study used benefit transfer and survey methods using questionnaires to estimate the tribe’s total economic value. The estimated total economic value of the Benuaq Dayak …

Carbonate Records Of Submarine Hydrocarbon Venting: Northern Gulf Of Mexico, Matthew S. Hackworth

LSU Doctoral Dissertations

Hydrocarbon seep sediments are examined from 3 sites in the Gulf of Mexico (Green Canyon Lease Blocks 232, 185, and 272) to relate the effects of gas hydrates and hydrocarbons on microbial process, pore fluid chemistry, and the processes of authigenic carbonate formation. Hydrocarbon-fueled microbial reactions result in pore fluids with lowered SO₄^2- (all consumed by –10 cm) and enrichments in H₂S, alkalinity, and DIC (up to 20 mmol, 30 meq/L, and 18 mmol/L, respectively) which promote carbonate formation. Pore fluid d¹³C_DIC (PDB) is influenced by thermogenic hydrocarbons and crude oil in GC …

Infrared And X-Ray Spectroscopic Studies Of The Copper(Ii) Oxide Mediated Reactions Of Chlorinated Aromatic Precursors To Pcdd/F, Steven L. Alderman

LSU Doctoral Dissertations

Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) are toxic compounds produced in combustion systems such as incinerators, and their emissions are an important environmental issue. Chlorinated phenols and benzenes form PCDD/F through heterogeneous reactions following adsorption onto fly-ash surfaces. Current research implicates transition metals in promoting formation of phenoxyl radicals that react to form PCDD/F, although this has not been studied extensively. This objective of this work is to better understand PCDD/F formation from chlorinated aromatic precursors. Using 2 chlorophenol as a model PCDD/F precursor and silica as a fly-ash surrogate, time-dependent chemisorption of 2 chlorophenol onto silica was studied in situ …

Spectroscopic And Synthetic Studies Relating To A Dirhodium Hydroformylation Catalyst, Petia Gueorguieva Gueorguieva

LSU Doctoral Dissertations

The main goal of this dissertation research was to further study and characterize our bimetallic hydroformylation catalyst, rac-[Rh₂(nbd)₂(et,ph-P4)](BF₄)₂, and to fully identify the catalytically inactive mono- and dirhodium complexes formed upon fragmentation of the catalyst under hydroformylation conditions. Various in situ NMR methods such as 1D ¹H and ³¹P, and 2D COSY, HMBC, and HMQC were employed and indicated the formation of the key catalyst, [rac-Rh₂H₂(μ-CO)₂(CO)₄(et,ph-P4)]²⁺, 4, and a number of other Rh-phosphine species on and off the catalytic cycle. …

Investigation Of Structure-Property Relationships Of Heavy-Fermion Materials, Robin Macaluso

LSU Doctoral Dissertations

This work focuses on how local structural features influence large effective masses, magnetism, and superconductivity that are yet to be understood in heavy-fermion materials. Three sets of structurally-related materials are discussed in light of dimensionality, layering effects, choice of transition metal, coordination, and structural distortions: LnnMIn3n+2 (Ln = La, Ce; n = 1, 2, ‡; M = Co, Rh, Ir), CePdGa6, and Ce2PdGa12, and CeNiSb3. The LnnMIn3n+2 (n = 1, 2, ‡; Ln = La, Ce; M = Rh, Ir) intergrowth homologous series presents a unique opportunity to study structure-property relationships. LnnMIn3n+2 (Ln = La, Ce; n = 1, 2; …

Attachment Of Oligonucleotide Probes To Polymer Biochips And Its Application For The Detection Of Point Mutations, Yun Wang

LSU Doctoral Dissertations

This dissertation is on the fabrication of polymer-based microfluidic arrays for the detection of genetic mutations. Poly(methyl methacrylate) was chosen as one of the polymer substrate materials due to its low background noise, low adsorption of biomolecules, and low assembly temperature. The surface modification of polymer substrates for covalent attachment of oligonucleotide probes, the construction of fluidic channels/arrays, and hybridization kinetics will be covered. As an example of the application, point mutation detection using immobilized arrays constructed in microfluidic devices will be demonstrated. The PMMA surface was derivatized with N-lithioethylenediamine solution to introduce amine groups, which were utilized for the …

A Distributed Quadtree Dictionary Approach To Multi-Resolution Visualization Of Scattered Neutron Data, Rion Dooley

LSU Doctoral Dissertations

Grid computing is described as dependable, seamless, pervasive access to resources and services, whereas mobile computing allows the movement of people from place to place while staying connected to resources at each location. Mobile grid computing is a new computing paradigm, which joins these two technologies by enabling access to the collection of resources within a user's virtual organization while still maintaining the freedom of mobile computing through a service paradigm. A major problem in virtual organization is needs mismatch, in which one resources requests a service from another resources it is unable to fulfill, since virtual organizations are necessarily …

Comparison Studies Of The Mechanistic Formation Of Polyhalogentaed Dibenzo-P-Dioxins And Furans From The Thermal Degradation Of 2-Bromophenol And 2-Chlorophenol, Catherine Spearing Evans

LSU Doctoral Dissertations

Emissions of polychlorinated dibenzo-p-dioxins and furans (PCDD/Fs) and polybrominated dibenzo-p-dioxins and furans (PBDD/Fs) from hazardous waste incinerators, and many other sources for combustion have been considered environmentally hazardous and a major health threat. Recently, a growing number of materials containing brominated hydrocarbons, commonly used flame retardants, have been disposed in municipal and hazardous waste incinerators. This results in the increased potential for formation of PBDD/Fs and other hazardous combustion by-products. In contrast to chlorinated hydrocarbons, the reactions of brominated hydrocarbons have been studied only minimally. In fact, studies have shown that brominated phenols form higher yields of PBDD/Fs than the …

Dynamics Of Complex Polymer Solutions: Putting Diffusion To Work And Exploring Rigid Rod Diffusion, Garrett John Doucet

LSU Doctoral Dissertations

This dissertation is concerned with random coil and rodlike polymer diffusion in complex solutions. The development of fluorescence photobleaching recovery, FPR, as a technique to determine polymer molecular weight distributions by measuring the diffusion distribution and converting it to a molecular weight distribution using a calibration curve is first covered. Fluorescently tagged probes were individually dissolved in polymer solutions at negligible amounts and measured with FPR to construct the calibration curve of self-diffusion vs. molecular weight. Once calibration curves were constructed, bimodal distributions were separated using the matrices corresponding to the calibration curves. The diffusion of the probes and separation …

Asymptotic Laplace Transforms, Claudiu Mihai

LSU Doctoral Dissertations

In this work we discuss certain aspects of the classical Laplace theory that are relevant for an entirely analytic approach to justify Heaviside's operational calculus methods. The approach explored here suggests an interpretation of the Heaviside operator ${cdot}$ based on the "Asymptotic Laplace Transform." The asymptotic approach presented here is based on recent work by G. Lumer and F. Neubrander on the subject. In particular, we investigate the two competing definitions of the asymptotic Laplace transform used in their works, and add a third one which we suggest is more natural and convenient than the earlier ones given. We compute …

Electronic Structural Investigations Of Bi- And Polymetallic Complexes Using Quantum Mechanical Methods, Zakiya Sheni Wilson

LSU Doctoral Dissertations

Understanding the dynamics influencing chemical reactivity is essential for properly exploiting matter into more useful purposes. In that manner, computational chemistry is a tool frequently used to study chemical properties at the most intimate level, i.e. the single molecule.

With this work, we probe the chemistry governing a variety of multi-faceted bi- and polymetallic compounds. To date our research consists of four major projects: bimetallic rhodium-catalyzed hydroformylation and aldehyde-water shift hydrocarboxylation catalysis; a novel linear M-H-M interaction in a bridged bis(dialkylphosphino)methane complex of nickel; and CeBe₁₃, a heavy fermion conductor. Computational investigations on these systems allow us to …

Pattern-Based Model Transformation: A Metamodel-Based Approach To Model Evolution, Sheena Judson Miller

LSU Doctoral Dissertations

Software systems continue to grow in complexity at a rapid pace, creating systems that are complex to build and evolve. The problems that accompany changes in requirements, system upgrades, and error correction produce a desire for software evolution methods that increase the efficiency and effectiveness of adapting complex software to changes. As software systems evolve, design models must be modified to accommodate the required changes. Techniques that control the changes to models in a systematic manner are a key to model evolution. A process that improves the ability to effectively modify a design, thereby enhancing design qualities, supports the need …

The Syntheses Of Novel Indicators And Materials For Chiral Separation, Rolanda Johnson

LSU Doctoral Dissertations

The colorimetric properties of resorcinarene solutions had not been fully investigated since von Baeyer's initial synthesis. We find that the solutions containing resorcinarene macrocycles develop color upon heating or standing. In the presence of saccharides, these solutions exhibit significant color changes which are readily observable by visual inspection. We determined that the solution color is due to macrocycle ring opening and oxidation. The optical responses to saccharides are due to complexation of the sugar with the acyclic chromophores. We have applied these mechanistic insights towards the challenging problems of the visual detection of saccharides and other important biologically analytes. In …

Applications Of The Titanium Catalyzed Cyclocarbonylation Towards Natural Product Syntheses, Jongtae Yang

LSU Doctoral Dissertations

Recently an efficient methodology, a hetero Pauson-Khand reaction, based on titanium-catalyzed cyclocarbonylation of tethered enals for the general preparation of ¥ã-butyrolactone rings, which are typically embedded in polycyclic systems of many natural products was reported. To demonstrate this new strategy, the total syntheses of the natural products asteriscanolide and ginkgolide were investigated. The first part of this work is dedicated to synthetic efforts toward the total synthesis of asteriscanolide. Approaches highlighted by the [2,3]-Wittig rearrangement, the thermal silyloxy-Cope rearrangement, and a titanium-catalyzed cyclocarbonylation, which is the pivotal step to afford the ¥ã-butyrolactone ring. This study firmly established the utility of …

Class Groups And Norms Of Units, Costel Ionita

LSU Doctoral Dissertations

Our object of study is relative quadratic extensions of algebraic number fields. In 'Class Number Parity', the authors P.E. Conner and J. Hurrelbrink study in detail the cases of real and CM-extensions. In this paper we generalize some of the results without any assumption on the type of the relative quadratic extension.