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Knots, Skein Theory And Q-Series, Mustafa Hajij

LSU Doctoral Dissertations

The tail of a sequence {P_n(q)} of formal power series in Z[q^{-1}][[q]], if it exists, is the formal power series whose first $n$ coefficients agree up to a common sign with the first n coefficients of P_n. The colored Jones polynomial is link invariant that associates to every link in S^3 a sequence of Laurent polynomials. In the first part of this work we study the tail of the unreduced colored Jones polynomial of alternating links using the colored Kauffman skein relation. This gives a natural extension of a result by Kauffman, Murasugi, and Thistlethwaite regarding the highest and lowest …

The Effectiveness Of Online Homework Tutorials As Compared To Pen And Paper Tutorials, Molly Shuman

LSU Master's Theses

The purpose of this study was to determine if students learn more from completing web based homework (WBHW) compared to completing homework by traditional means with pen and paper. Determining the efficacy of WBHW is important because many schools are being pressured to implement technology in the classroom. To determine the effectiveness of WBHW, student normalized learning gains were calculated from pre and post-test scores for 62 students. Learning gains were then compared when students completed WBHW, traditional homework, or did not complete homework at all, over four units in a high school chemistry class. No difference in learning gains …

Developing Co-Current And Counter-Current Spray Drying Computational Fluid Dynamics (Cfd) Simulation Studies To Predict The Quality Of Microencapsulated Fish Oil With Egg White Hydrolysates Powders, Kevin Estuardo Mis Solval

LSU Doctoral Dissertations

Eggs are an excellent source of high quality protein containing all essential amino acids (EAA) including leucine. Food-grade protein hydrolysates can enhance the growth of lactic acid bacteria (LAB). Thermal degradation of bioactives normally occurs during microencapsulation by spray drying. Spray drying modeling using computational tools is essential to engineer new food powders and to minimize and thermal degradation of bioactives. The first chapter of this work discusses the optimization of an enzymatic process in terms of reaction temperature, pH, enzyme:substrate ratio, and reaction time using a response surface methodology (RSM) to produce food-grade protein hydrolysates from egg whites (EWH). …

Applications Of Cfd Simulations On Fractal Fluid Distributor, Gongqiang He

LSU Master's Theses

Since its emergence in 1970s, process intensification has been attracting extensive research interests from both academic and industrial societies over the years. One good example of process intensification in chemical industry is the optimization of flow distributors. In many chemical processes, the uniformity of flow distributions plays the key role in determining the overall efficiency. Conventional distributors rely on high pressure drop to achieve acceptable flow distribution. With scaling symmetry from fractal, fractal distributors can handle fluid distribution much better than conventional distributors. With the rapid development of computation power and numerical simulation algorithms, Computer Fluid Dynamics (CFD) provides us …

Design And Validation Of A Prototype Collimation System With Reduced Applicator Weights For Elekta Electron Therapy Beams, Garrett Michael Pitcher

LSU Doctoral Dissertations

The objective of this study was to design an electron collimation system for Elekta Infinity accelerators with significantly reduced applicator weights, while maintaining acceptable in-field beam flatness and out-of-field leakage dose. The design was restricted to 6-20 MeV beams for 6x6 to 25x25 cm2 applicators at 100 cm SSD with the MLCi2 treatment head. In Aim1, measured off-axis profiles showed that the current Elekta collimation system met dose flatness (4%) and IEC leakage dose specifications in the patient plane for custom 7, 13, and 20 MeV beams at MBPCC. Also, Monte Carlo (MC) calculations based on MBPCC beam models sufficiently …

Topological Dynamics On Compact Phase Spaces, Lieth Abdalateef Majed

LSU Doctoral Dissertations

Our main focus will be to investigate the various facets of what are commonly called dynamical systems or flows, which are triples $(S,X,\pi)$, where $X$ is a compact Hausdorff space and $\pi:S \times X \longrightarrow X$ is a separately continuous action of a semigroup $S$ on $X$. Historically, as was introduced by R.Ellis 1960, the enveloping semigroup, which is a closure of the set of continuous functions on a compact space $X$, was discovered to be an important tool to study dynamical systems. Soon, a realization of the existence of a universal compactification of a phase semigroup with an extended …

A Spatial Analysis Of Obesity And Its Associations With The Built And Natural Environment, Physical Inactivity, And Socioeconomic And Demographic Conditions In The United States Of America, Mustafa Erdem

LSU Doctoral Dissertations

Obesity has strong genetic determinants but the genetic composition of the population does not change rapidly. Thus in this study, the major changes in non-genetic factors such as the development of obesogenic environments and shifting socioeconomic status and lifestyle of individuals are hypothesized to increase the risk of obesity. As the prevalence of obesity continue to increase worldwide with substantial attention in the US, a clearer understanding of how spatial associations between obesity and confounding factors are interrelated is crucial to better tackle the issue of obesity. This study employs the ‘global’ and ‘local’ Exploratory Spatial Data Analysis (ESDA) methods …

Optimal Location Of Biomethane Gas Manufacturing Plants And Allocation Of Feedstock And Liquified Carbon Product, Bingqing Wu

LSU Doctoral Dissertations

Biomethane gas (BMG), known for its sustainability, low environmental impact, and high profitability, has received wide attention in recent years. To facilitate the process of making strategic plans for building a BMG production system, this dissertation leverages the mathematical modeling and optimization techniques to minimize the supply chain cost for such a system. Typical elements in a BMG production system consist of the local farms that produce the feedstock, the hubs that collect and store the feedstock produced by farms, the reactors that generate BMG from the feedstock transported from the hubs, the condensers that liquefy the BMG from the …

Classification In The Presence Of Ordered Classes And Weighted Evaluative Attributes, Forrest Justin Osterman

LSU Doctoral Dissertations

We are interested in an important family of problems in the interface of the Multi-Attribute Decision-Making and Data Mining fields. This is a special case of the general classification problem, in which records describing entities of interest have been expressed in terms of a number of evaluative attributes. These attributes are associated with weights of importance, and both the data and the classes are ordinal. Our goal is to use historical records and the corresponding decisions to best estimate the class values of new data points in a way consistent with prior classification decisions, without knowledge of the weights of …

Surface Structure/Property Relationship For (001) Surface Of Magnetite, Fangyang Liu

LSU Doctoral Dissertations

Magnetite (Fe3O4), a well-known magnetic material, is still attracting intense study because of its great application in catalyst and technology development. These useful properties are related to the coexistence and coupling of several degrees of freedom, including charge, lattice, orbital and spin. The interaction between Fe3O4 and hydrogen is one of the most important issues, which guides the development of catalytic efficiency and material practicality. In this work, natural single crystal Fe3O4 (001) surfaces are studied with a variety of techniques. It is discovered that the Fe3O4 (001) surface structure and properties are dependent on the surface preparation methods. Conventional …

A Model Of The Tonal-Chromatic System And Its Application To Selected Works Of Gustav Mahler, Andrew David Nicolette

LSU Doctoral Dissertations

During the latter half of the twentieth century there was a marked shift in the way that many scholars approached analysis of late-nineteenth-century tonality. This shift in approach was motivated by the behavior and interaction of harmonic and melodic entities encountered in the music of the great composers of the nineteenth century, such as Schubert, Schumann, Brahms, Mahler, Wagner, and Strauss. The question arose: did the diatonic system remain at the heart of tonality during the late nineteenth century, or—as some propose—did a new chromatic-based tonality emerge? The acceptance of this new chromatic-based tonality is at the heart of this …

Otoliths Then And Now: A Study Of Ancient And Modern Fish Populations In Louisiana's Coastal Waters, Marshall James Kormanec

LSU Master's Theses

Fish otoliths are composed of inorganic calcium carbonate that aid in gravity and auditory reception. Substances permanently accrete to otolith surfaces in distinct temporal patterns of alternating opaque and translucent rings; these rings are direct proxies for a fish’s age. The objective of my research is to demonstrate how otoliths can be used through time and space to estimate both age and growth of fish. I investigated the spatial differences in age distributions and growth models for red snapper, Lutjanus campechanus, at four natural shelf-edge reefs in the northwestern Gulf of Mexico. Red snapper cohorts ranged 1987-2010 cohorts, with the …

Constructing Desirable Scalar Fields For Morse Analysis On Meshes, Mustafa Hajij

LSU Master's Theses

Morse theory is a powerful mathematical tool that uses the local differential properties of a manifold to make conclusions about global topological aspects of the manifold. Morse theory has been proven to be a very useful tool in computer graphics, geometric data processing and understanding. This work is divided into two parts. The first part is concerned with constructing geometry and symmetry aware scalar functions on a triangulated $2$-manifold. To effectively apply Morse theory to discrete manifolds, one needs to design scalar functions on them with certain properties such as respecting the symmetry and the geometry of the surface and …

Fish Assemblage Structure, Distribution, And Trophic Ecology At Northwestern Gulf Of Mexico Banks, Todd Langland

LSU Doctoral Dissertations

The northwest Gulf of Mexico (Gulf) shelf-edge banks both provide unique hard bottom habitat and support the northernmost coral reefs on the North American continental shelf in a region that is generally characterized by low relief, soft sediments. The habitat value of many of these banks has led to their designation as Habitat Areas of Particular Concern (HAPC) and the Flower Garden Banks National Marine Sanctuary (FGBNMS). However, little is known about the fisheries resources and dynamics of the banks outside the FGBNMS. This study had three main objectives: 1) define reef fish assemblages at northwestern Gulf shelf-edge banks and …

Musical Explorations In Creation And Performance: A School's Alternative Approach To Music Education, Laterence Edward Varnado

LSU Master's Theses

Students have various opportunities to participate in school music. The large ensemble model that follows the Western Classical music tradition is the most commonly used model for music education in secondary schools; however, many students in secondary schools do not participate in school music. Recently, alternative approaches (i.e. popular music, world music, guitar, etc.) have been proposed as valuable music experiences that may increase student participation in school music. The aim of this study was to examine the philosophical foundations and pedagogical practices used at a secondary school that has implemented alternative approaches. I also explored student experiences with these …

Examining The Effects Of Academic And Social Interventions On The Behavior Of Students With Or At-Risk For Emotional Or Behavioral Disorders, Lauren M. Lejeune

LSU Master's Theses

Certainly the educational issues of students with and at-risk for emotional and behavioral disorders (EBD) are complex and multi-faceted (Forness, Freeman, Paparella, Kauffman, & Walker, 2012; Lane, Walker, Crnobori, Oliver, Bruhn, & Oakes, 2013; Wagner, 2004; Wiley & Forness, 2011). While improvements have been made in interventions for challenging behavior through a developing technology of functional behavior assessment and multi-tiered models of support, there remains a need for the demonstration of more effective academic and behavioral interventions applied in schools and under the direction of school personnel. The current study examined two such interventions across multiple students in a variety …

A Study Of Mathematical Equivalence: The Importance Of The Equal Sign, Christy De'sha Duncan

LSU Master's Theses

The purpose of this study was to investigate students’ understanding and knowledge of the equal sign, so that instructional resources could be identified to improve student’s conceptual understanding about mathematical equivalence. A test, consisting of a combination of items taken from previous studies, as well as items developed by the researchers, was designed to gauge students’ understanding of the equality symbol. The test was administered to 54 seventh-graders in Spring 2015. The results of the test indicated a significant number of students in our district have a limited understanding of mathematical equivalence. This papers ends with some suggested activities recommended …

Wavelets, Coorbit Theory, And Projective Representations, Amer Hasan Darweesh

LSU Doctoral Dissertations

Banach spaces of functions, or more generally, of distributions are one of the main topics in analysis. In this thesis, we present an abstract framework for construction of invariant Banach function spaces from projective group representations. Coorbit theory gives a unified method to construct invariant Banach function spaces via representations of Lie groups. This theory was introduced by \Fch\, and \Gro\, in \cite{FG,FG1, FG2,FG3} and then extended in \cite{CO2}. We generalize this concept by constructing coorbit spaces using projective representation which is first studied by O. Christensen in \cite{O1}. This allows us to describe wider classes of function spaces as …

Application Of Computational Fluid Dynamics To Near-Wellbore Modeling Of A Gas Well, Oscar Mauricio Molina

LSU Master's Theses

Well completion plays a key role in the economically viable production of hydrocarbons from a reservoir. Therefore, it is of high importance for the production engineer to have as many tools available that aid in the successful design of a proper completion scheme, depending on the type of formation rock, reservoir fluid properties and forecasting of production rates. Because well completion jobs are expensive, most of the completed wells are usually expected to produce as much hydrocarbon and as fast as possible, in order to shorten the time of return of the investment. This research study focused on the evaluation …

Rare Earth Element Patterns In Conodont Apatite From The Upper Ordovician: Testing Enrichment Sources And Possible Oceanographic Changes, Cody Christian Schulte

LSU Master's Theses

The Mohawkian series of the Middle Late Ordovician was a time of great lithological and faunal changes that coincide with a positive ä13C excursion known as the Guttenberg Isotopic Carbon Excursion (GICE). Two prevailing hypotheses have been proposed to explain the cause of these changes. The “cold-water” hypothesis suggests that global cooling caused the tropical belt to shrink and cold water to invade the epicontinental sea while the “tectonic-forcing” hypothesis suggests that increased weathering rates led to basinal deepening, resulting in cooler oceanic waters invading the midcontinent sea. This study tests if regional tectonics caused by the Taconic Orogeny led …

Boron Functionalization Of Bodipy Dyes, And Their Evaluation As Bioimaging Agents, Alex Long Nguyen

LSU Doctoral Dissertations

BODIPY, also known as “porphyrin’s little sister,” belongs to a class of fluorescent dyes. It contains a dipyrromethene π-system with a disubstituted boron atom. The basic 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) is known for its numerous useful applications in the fields of biology and materials. Modification of this well-known fluorophore has been shown to change its photophysical and chemical properties. There has been great interest in the modification at the boron center in recent years for synthesizing new dyads and cascade-type dyes. This work focuses on functionalization at the boron center with carbon and oxygen nucleophiles for further investigation as bioimaging agents. Chapter …

Partial Cosine-Funk Transforms At Poles Of The Cosine-Λ Transform On Grassmann Manifolds, Christopher Adam Cross

LSU Doctoral Dissertations

The cosine-λ transform, denoted C^λ, is a family of integral transforms we can define on the sphere and on the Grassmannian manifolds of p-dimensional subspaces in Kⁿ where K is R, C or the skew field H of quaternions. We treat the Grassmannians as the symmetric spaces SO(n)/S(O(p) × O(q)), SU(n)/S(U(p) × U(q)) and Sp(n)/(Sp(p) × Sp(q)) and we work by analogy with the case of the cosine-λ transform on the sphere, which is also a symmetric space.

The family C^λ extends meromorphically in λ to the complex plane with poles at (among other values) λ …

Multiscale Modeling Of Smart Materials Under Static And Dynamic Thermo-Mechanical Loading, Soodabeh Sharafi

LSU Master's Theses

Engineering material systems with tailored capabilities are a topic trend in plethora of research. Polymer based Artificial Muscle, PAM, and Shape memory polymer fiber, SMPF, enable structural engineers to incorporate smartness functionality into their design through programming cycles. Smartness functionality leads to the production of artificial muscles with different load carrying capability. SMPF is another category of smart materials, which are capable of being micro-structurally engineered to isolate vibration at different temperature and frequency conditions. The smartness functionality offers the adjustment between inherent properties of these materials with their industrial applications through modeling techniques. Mixture of phenomenological, numerical, mathematical models …

Jean Cocteau: Orpheus Narcissus, Gordon Elliott Walker

LSU Master's Theses

Over the course of thirty years, the poet and filmmaker Jean Cocteau created a singular artistic project he called the Orphic trilogy: Le Sang d’un poète (1930), Orphée (1950), and Le Testament d’Orphée (1959). This trilogy is marked by an Orphic pattern of a poet’s journey into an underworld to confront death. I will show that Cocteau’s invention is to have Orpheus be in love with death, for death to be an attractive and irresistible force to the poet. Simultaneously, Cocteau avails himself of the Narcissus myth, the man in love with his own reflection. Orpheus and Narcissus converge in …

Sourcing And Framing Analysis Of Source Messages In The Coverage Of Armed Conflicts By American And British Foreign Reporters, Ellada Gamreklidze

LSU Doctoral Dissertations

This dissertation contributes to closing several gaps in mass communication scholarship as well as indicates new avenues for further research in the area of sourcing and framing. This study explored whether reliance on official sources in foreign reporting of international crises is as heavy as the hypothesis predicts, and, by studying messages delivered by official sources in this coverage, revealed how those messages were framed. The results showed that officials were dominant sources of information in all the three media outlets studied. The results also supported the argument that the same indexing mechanisms are at force in foreign reporting and …

Holocene Palynology Of The Gulf Of Papua, Papua New Guinea: Using Modern Palynomorph Distribution To Better Constrain Paleoenvironmental Changes, Marie Louise Thomas

LSU Doctoral Dissertations

Multiple NSF (National Science Foundation)-funded MARGINS Source-to-Sink cruises were conducted in the Gulf of Papua (GoP), Papua New Guinea (PNG), from 2003 through 2005 to better understand how sediment is created, transported, and deposited. Although much work has been done on the data collected during these cruises, palynological analysis has never been conducted on the hundreds of available cores. The first phase of this project (Chapters 2 and 3) examines the connection between modern depositional regimes in the GoP and species assemblages recovered. Statistical analysis of palynomaceral assemblages (Chapter 2) indicates a correlation between their distribution and bathymetry, sedimentation rate, …

Effects Of Inbreeding On Endangered Red Wolves (Canis Rufus), Kristin E. Brzeski

LSU Doctoral Dissertations

Inbreeding depression, the reduction in offspring fitness caused by mating among close relatives, is widespread in small populations and a major concern in conservation biology because it can affect population persistence. The negative effects of inbreeding results in the evolution of inbreeding avoidance behaviors; within small populations, such behaviors may encourage individuals to select mates outside of their respective species. Mate choice may also be facilitated by variation at major histocompatibility complex (MHC) genes, a gene group critical for immune response and disease resistance. Given broad impacts of inbreeding and MHC variation on fitness and behavior, evaluating their effects is …

Post-Treatment Assessment Of Hydraulic Fracturing With Integrated Modeling Of Natural Fracture Distribution, Ping Puyang

LSU Master's Theses

Hydraulic fracturing has been serving as the principal reservoir stimulation technique for decades to improve production capacities of low permeability formations. On the other hand, through core and outcrop studies, advanced logging tools, microseismic fracture mapping and well testing analysis, it has been further revealed that many of the shale gas formations are naturally fractured. The presence of natural fractures and their interactions with hydraulic fractures must be taken into consideration while designing fracturing treatment. Although most natural fractures are cemented by precipitations during diagenesis, they may be reactivated during hydraulic fracturing and serve as weak paths for fluid flow …

A Spatial Dynamic Model Of Population Changes In A Vulnerable Coastal Environment, Kenan Li

LSU Doctoral Dissertations

Achieving coastal sustainability in low-lying coastal areas is a great challenge. This study developed a spatial dynamic model to study the coupled natural-human responses in the form of population changes in the Lower Mississippi River Basin region. The goal was to identify the key social-economic factors (utility) and selected environmental factors (such as hazards damage, elevation, and subsidence rate) that affect population changes, as well as how population changes affect the local utility and the local environment reciprocally. The study area was partitioned into the “north’ and the “south” by a hypothetical boundary to test the differences of the emergence. …

Mathematical Model Of The Split Firefly Luciferase Assay, Renee Dale

LSU Master's Theses

The firefly luciferase complementation assay is widely used as a bioluminescent reporter technology to detect protein-protein interactions in vitro and in vivo. Firefly luciferase oxidates its substrate, luciferin, resulting in the emission of light. A previous study suggests that the firefly luciferase complementation assay has different luminescence kinetics from full length luciferase. The mechanism behind this is still unknown. Although half of the previously published studies utilizing the firefly luciferase complementation assay consider it quantitative. To understand how the molecular reactions and the changes in the affinity of the protein pair affect experimental results, a mathematical model was constructed. This …