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Articles 1 - 30 of 38
Full-Text Articles in Physical Sciences and Mathematics
Navier-Stokes Equations In One And Two Dimensions, Jon Nerdal
Navier-Stokes Equations In One And Two Dimensions, Jon Nerdal
LSU Master's Theses
The Navier-Stokes equations are an important tool in understanding and describing fluid flow. We investigate different formulations of the incompressible Navier-Stokes equations in the one-dimensional case along an axis and in the two-dimensional case in a circular pipe without swirl. For the one-dimensional case we show that the velocity approximations are remarkably accurate and we suggest that understanding this simple axial behaviour is an important starting point for further exploration in higher dimensions. The complexity of the boundary is then increased with the two-dimensional case of fluid flow through the cross section of a circular pipe, where we investigate two …
Accelerated Gradient Descent Methods For The Uniaxially Constrained Landau-De Gennes Model, Edison E. Chukwuemeka
Accelerated Gradient Descent Methods For The Uniaxially Constrained Landau-De Gennes Model, Edison E. Chukwuemeka
LSU Master's Theses
Liquid crystal models with the capability of capturing defects has been one of the main focus in modeling the behavior of such phase mathematically. A uni-axially constrained Landau-de Gennes one-constant model, which has this capability was modeled using three minimization schemes - standard gradient descent, Nesterov accelerated gradient descent, and heavy-ball accelerated gradient descent. The uni-axially constrained Landau-de Gennes energy is discretized using finite element method and the performance of the minimization schemes are measured using the classical gradient descent scheme as the baseline. The numerical experiments conducted indicated that the accelerated gradient descent schemes improved the convergence rate and …
Maximizing And Modeling Malonyl-Coa Production In Escherichia Coli, Tatiana Thompson Silveira Mello
Maximizing And Modeling Malonyl-Coa Production In Escherichia Coli, Tatiana Thompson Silveira Mello
LSU Master's Theses
In E. coli, fatty acid synthesis is catalyzed by the enzyme acetyl-CoA carboxylase (ACC), which converts acetyl-CoA into malonyl-CoA. Malonyl-CoA is a major building block for numerous of bioproducts. Multiple parameters regulate the homeostatic cellular concentration of malonyl-CoA, keeping it at a very low level. Understanding how these parameters affect the bacterial production of malonyl-CoA is fundamental to maximizing it and its bioproducts. To this end, competing pathways consuming malonyl-CoA can be eliminated, and optimal nutritional and environmental conditions can be provided to the fermentation broth. Most previous studies utilized genetic modifications, expensive consumables, and high-cost quantification methods, making …
Fractal Shapes Generated By Iterated Function Systems, Mary Catherine Mckinley
Fractal Shapes Generated By Iterated Function Systems, Mary Catherine Mckinley
LSU Master's Theses
This thesis explores the construction of shapes and, in particular, fractal-type shapes as fixed points of contractive iterated function systems as discussed in Michael Barnsley's 1988 book ``Fractals Everywhere." The purpose of the thesis is to serve as a resource for an undergraduate-level introduction to the beauty and core ideas of fractal geometry, especially with regard to visualizations of basic concepts and algorithms.
Option Volatility & Arbitrage Opportunities, Mikael Boffetti
Option Volatility & Arbitrage Opportunities, Mikael Boffetti
LSU Master's Theses
This paper develops several methods to estimate a future volatility of a stock in order to correctly price corresponding stock options. The pricing model known as Black-Scholes-Merton is presented with a constant volatility parameter and compares it to stochastic volatility models. It mathematically describes the probability distribution of the underlying stock price changes implied by the models and the consequences. Arbitrage opportunities between stock options of various maturities or strike prices are explained from the volatility smile and volatility term structure.
Increasing Student Engagement In The Secondary Math Classroom, Chantell Holloway Walker
Increasing Student Engagement In The Secondary Math Classroom, Chantell Holloway Walker
LSU Master's Theses
This thesis reports on a professional development package developed by the author to help three teachers increase the level of student engagement in their math classrooms. There were three phases: 1) initial presentation of strategies and sample lessons, 2) classroom implementation, 3) reflection and evaluation. As a result of the professional development, the Louisiana Compass Teacher Evaluation Rubric scores of the teachers improved in the area of student engagement. This thesis can be used as a guide for principals or instructional specialists who wish to provide professional development for small groups of teachers, with a focus on increasing student engagement.
Shape Optimization For Drag Minimization Using The Navier-Stokes Equation, Chukwudi Paul Chukwudozie
Shape Optimization For Drag Minimization Using The Navier-Stokes Equation, Chukwudi Paul Chukwudozie
LSU Master's Theses
Fluid drag is a force that opposes relative motion between fluid layers or between solids and surrounding fluids. For a stationary solid in a moving fluid, it is the amount of force necessary to keep the object stationary in the moving fluid. In addition to fluid and flow conditions, pressure drag on a solid object is dependent on the size and shape of the object. The aim of this project is to compute the shape of a stationary 2D object of size 3.5 m2 that minimizes drag for different Reynolds numbers. We solve the problem in the context of shape …
A Study Of Mathematical Equivalence: The Importance Of The Equal Sign, Christy De'sha Duncan
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 …
Exploring Rational Numbers In Middle School, Robyn Jasmin Boudoin
Exploring Rational Numbers In Middle School, Robyn Jasmin Boudoin
LSU Master's Theses
The move by the state of Louisiana to fully implement the Common Core State Standards (CCSS) from 2013 -2014 school year on and to align all state mandated tests to the CCSS has caused teachers to change the way they teach and how they deliver content. The overall most crucial new part of the CCSS in Mathematics is the emphasis on the “Standards for Mathematical Practice”. In order to illustrate the meaning of the Mathematical Practice Standards, non routine problems must be used that allow students and teachers to “dig deeper” and practice their mathematical habits of mind. Rational numbers …
Developing Auxiliary Resource Materials To Support The Engageny Geometry Curriculum, Joanne Griffin
Developing Auxiliary Resource Materials To Support The Engageny Geometry Curriculum, Joanne Griffin
LSU Master's Theses
With the advent of current education reform, and the introduction of the Common Core State Standards for Mathematics, the present offerings of the geometry curriculum have become dated. One contribution to remedy this situation is a project by the state of New York called EngageNY. EngageNY is a common core aligned mathematics curriculum across all grades. The EngageNY Geometry Curriculum Module 1 is the basis from which this thesis was developed. It is the purpose of this thesis to present a supplement to the EngageNY Geometry Module 1 Curriculum and to describe why it is advantageous to have such a …
Effects Of Focused Instruction Process (Fip)On Student End-Of-Course Test (Predicting End-Of-Course Test Using Teacher-Made Test), Roland Damasco Dante
Effects Of Focused Instruction Process (Fip)On Student End-Of-Course Test (Predicting End-Of-Course Test Using Teacher-Made Test), Roland Damasco Dante
LSU Master's Theses
This study took place at a medium-sized suburban high school. It was designed to determine the usefulness of certain teacher-made tests in predicting students' end-of-course (EOC) tests. The teacher taught the students the skills in which their performance was weakest on the previous state test. The students were tested after each skill on a four-point quiz (teacher-made test). Students who scored 3—4 moved on to the next lesson or enrichment, while those who scored 0—2 were re-taught and re-tested. The procedure was repeated throughout the school year. At the end of the course, students took the state-mandated end-of-course test. The …
Damage Evolution In Pressurized Domain: A Gradient Based Variational Approach, Navid Mozaffari
Damage Evolution In Pressurized Domain: A Gradient Based Variational Approach, Navid Mozaffari
LSU Master's Theses
Construction of appropriate models through mathematical analysis for materials in order to find their main properties and ingredients and enhance the numerical simulations to predict their behavior under specific conditions is in interest even in mathematics departments rather than material science and engineering branches. Among these models, gradient damage models have reached to the specific stage because of their ability to bring the effects of micro cracks propagation into conventional continuum mechanics formulation and approximate brittle fracture as one of the most phenomena in the area of material behavior simulation. This thesis includes the application and extension of a previously …
Problem Solving Strategies And Metacognitive Skills For Gifted Students In Middle School, Lorena Aguelo Java
Problem Solving Strategies And Metacognitive Skills For Gifted Students In Middle School, Lorena Aguelo Java
LSU Master's Theses
This study is conducted to investigate if the designed four-step method strategy (GEAR strategy adapted from Polya, 1973) in solving math problems has improved students’ performance scores and enhanced the metacognitive skills of gifted students. The respondents of this study include middle school gifted students who took math eight course in the school year 2013-2014 at Westdale Middle School in East Baton Rouge Parish School System. There are four classes of math eight gifted students who participated in the study. The classes were chosen randomly for experimental and controlled group and were equalized on the basis of the pre-test results …
Uncertainty Quantification Of Film Cooling Effectiveness In Gas Turbines, Hessam Babaee
Uncertainty Quantification Of Film Cooling Effectiveness In Gas Turbines, Hessam Babaee
LSU Master's Theses
In this study the effect of uncertainty of velocity ratio on jet in crossflow and particual- rly film cooling performance is studied. Direct numerical simulations have been combined with a stochastic collocation approach where the parametric space is discretized using Multi-Element general Polynomial Chaos (ME-gPC) method. Velocity ratio serves as a bifurcation parameter in a jet in a crossflow and the dynamical system is shown to have several bifurcations. As a result of the bifurcations, the target functional is observed to have low-regularity with respect to the paramteric space. In that sense, ME-gPC is particularly effective in discretizing the parametric …
Adaptive Stochastic Conjugate Gradient Optimization For Temporal Medical Image Registration, Huanhuan Xu
Adaptive Stochastic Conjugate Gradient Optimization For Temporal Medical Image Registration, Huanhuan Xu
LSU Master's Theses
We propose an Adaptive Stochastic Conjugate Gradient (ASCG) optimization algorithm for temporal medical image registration. This method combines the advantages of Conjugate Gradient (CG) method and Adaptive Stochastic Gradient Descent (ASGD) method. The main idea is that the search direction of ASGD is replaced by stochastic approximations of the conjugate gradient of the cost function. In addition, the step size of ASCG is based on the approximation of the Lipschitz constant of the stochastic gradient function. Thus, this algorithm could maintain the good properties of the conjugate gradient method, meanwhile it uses less gradient computation time per iteration and adjusts …
Statistical Classification Problems In Assessment Of Teachers, Xuan Wang
Statistical Classification Problems In Assessment Of Teachers, Xuan Wang
LSU Master's Theses
Classification and regression trees form an important and indispensable tool in data analysis and classification problems. Class trees are described in detail with examples. The method is applied to a data set pertaining to evaluation of teachers. In addition, two other classification methods, bagging and AdaBoost are explained. These methods improve existing classifiers to nearly optimal classifiers.
Mathematical Models For Interest Rate Dynamics, Xiaoxue Shan
Mathematical Models For Interest Rate Dynamics, Xiaoxue Shan
LSU Master's Theses
We present a study of mathematical models of interest rate products. After an introduction to the mathematical framework, we study several basic one-factor models, and then explore multifactor models. We also discuss the Heath-Jarrow- Morton model and the LIBOR Market model. We conclude with a discussion of some modified models that involve stochastic volatility.
Improving Math Instruction In Schools That Serve The Poor, John, L. Jr. Sims
Improving Math Instruction In Schools That Serve The Poor, John, L. Jr. Sims
LSU Master's Theses
Public alarm concerning how well U.S. schools are performing in mathematics compared to other developed nations is increasing. Reports of inadequate teaching, poor curriculum design, and low performance on standardized test have been fueled by the media. These issues in American mathematics classrooms are far compounded in schools that serve the poorest in America. When comparing mathematical proficiency rates of U.S. schools with other countries, schools with less than 25% free and reduced lunch score competitively with counterparts in other countries. In contrast, schools with rates of free and reduced lunch higher than 50% score dismally in comparison. Conditions such …
Fraction Competency And Algebra Success, Coretta Thomas
Fraction Competency And Algebra Success, Coretta Thomas
LSU Master's Theses
Abstract In this thesis, I investigated the importance of fraction competence to success in algebra. I studied 107 of the students whom I teach. These students were all enrolled in Algebra I. A fraction pretest and an algebra pretest were given at the beginning of the 2009-2010 school year. A comparison was done to study the connection between the fraction pretest score and the semester grade as well as the algebra pretest score and the semester grade. The strongest correlation was between the fraction pretest and the semester grade. This supported the theory that fraction competence is a strong predictor …
A Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder
A Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder
LSU Master's Theses
This thesis focuses on graphs containing an edge whose removal results in an outer-planar graph. We present partial results towards the larger goal of describing the class of all such graphs in terms of a finite list of excluded graphs. Specifically, we give a complete description of those members of this list that are not 2-connected or do not contain a subdivision of a three-spoke wheel. We also show that no members of the list contain a five-spoke wheel.
Correlation Of Defaults In Complex Portfolios Using Copula Techniques, Adam Lodygowski
Correlation Of Defaults In Complex Portfolios Using Copula Techniques, Adam Lodygowski
LSU Master's Theses
This work, dealing with the correlation between subportfolios in more complex portfolios, begins with a brief survey of the necessary theoretical background. The basic statistical and probabilistic concepts are reviewed. The notion of copulas is introduced along with the fundamental theorem of Sklar. After this background a numerical procedure and code are developed for correlated defaults in multiple correlated portfolio. Further on, interesting results regarding the impact of changes in correlation on the portfolio performance are investigated in the simulations. The most valuable observations regarding the expected default ratios of two subportfolios considered jointly are presented and explained with particular …
Copula And Default Correlation, Dongxiang Yan
Copula And Default Correlation, Dongxiang Yan
LSU Master's Theses
This work presents a study of copulas, with special focus on the Gaussian copula model and its behavior under a certain conditioning process. Simulations are carried out to examine the behavior of the moments on conditional copula model, as measured by the behavior of Wick identities which hold for multivariate Gaussians.
Index Future Pricing Under Imperfect Market And Stochastic Volatility, Wei-Hsien Li
Index Future Pricing Under Imperfect Market And Stochastic Volatility, Wei-Hsien Li
LSU Master's Theses
Financial markets in emerging countries are volatile and imperfect, so pricing model under traditional perfect-market frameset may not give reliable price of financial derivatives. The most famous pricing model for stock index future is the cost of carry model. The mis-pricing of cost of carry model inspires lots of following researches. Even transaction costs, dividends, stochastic interest rate, stochastic volatility, market imperfection, and other factors are considered, we still do not obtain a model price consistently better than cost of carry model. But these researches offer important insights, for example, the market needs time to mature and the more complex …
Optimal Binary Trees With Height Restrictions On Left And Right Branches, Song Ding
Optimal Binary Trees With Height Restrictions On Left And Right Branches, Song Ding
LSU Master's Theses
We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth's famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n2), while previous algorithms had been O(n3) (n = size of input). We present the known generalization of Knuth's algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and …
Using Elimination To Describe Maxwell Curves, Lucas P. Beverlin
Using Elimination To Describe Maxwell Curves, Lucas P. Beverlin
LSU Master's Theses
Cartesian ovals are curves in the plane that have been studied for hundreds of years. A Cartesian oval is the set of points whose distances from two fixed points called foci satisfy the property that a linear combination of these distances is a fixed constant. These ovals are a special case of what we call Maxwell curves. A Maxwell curve is the set of points with the property that a specific weighted sum of the distances to n foci is constant. We shall describe these curves geometrically. We will then examine Maxwell curves with two foci and a special case …
Characterization Of The Dependency Across Foreign Exchange Markets Using Copulas, Ryan Coelho
Characterization Of The Dependency Across Foreign Exchange Markets Using Copulas, Ryan Coelho
LSU Master's Theses
Though Pearson's correlation coefficient provides a convenient approach to measuring the dependency between two variables, in the last few years, there has been a significant amount of literature cautioning against the use of Pearson's correlation coefficient, as it does not remain invariant under monotone transformations of the underlying distribution functions. Since we are interested in examining the dependency pattern observed by the return on the Sterling Pound with that of the Japanese Yen, we will use the notion of a copula to approximate the joint density function between the daily returns on the Sterling Pound and the Japanese Yen. In …
The Asymptotic Z-Transform, Scott Jude Champagne
The Asymptotic Z-Transform, Scott Jude Champagne
LSU Master's Theses
Sequences of numbers and transformations from sequences to functions have been studied extensively, including the multiplication of two sequences through convolution and the equivalent multiplication of functions. The focal points of this thesis are the convolution field of causal sequences and their Z-transforms. Classically, the treatment of the Z-transform has been limited to those causal sequences for which the power series has a nontrivial radius of convergence. In this thesis it is shown that the Z-transform can be extended to all causal sequences without compromising any of the operational properties of the classical Z-transform.
Modern Interpretation Of Euclid's Theory Of Ratio And Proportion, Mark Robert Stecher
Modern Interpretation Of Euclid's Theory Of Ratio And Proportion, Mark Robert Stecher
LSU Master's Theses
Euclid’s Elements is the foundation for geometry. Book V of Euclid’s Elements, which is independent from the earlier books, focuses on multiples, ratios, and proportions. This paper presents a model of the conceptual content of Book V, but using carefully selected modern notation to represent Euclid’s ideas without changing them drastically. All of the propositions and proofs from Euclid have been restated using just enough modern language to make clear for a modern reader. We also present a modern theory that bears analogy, proposition by proposition, to Euclid’s theory, but uses rigorous modern methods of proof.
Stability Of Stochastic Pricing Models Under Volatility Fluctuations, Krassimir Zhivkov Nikolov
Stability Of Stochastic Pricing Models Under Volatility Fluctuations, Krassimir Zhivkov Nikolov
LSU Master's Theses
The standard theory of the stochastic models used to value financial derivatives contracts involves models whose input parameters are deterministic functions and often constants. Because of the random nature of the changes in the market prices of the financial instruments, the coefficients of these models are inevitably susceptible to random perturbation from their initial estimates. In this paper we will investigate the behavior of some of the most widely used models when small changes are applied to their volatility component. Starting with the Black-Scholes model for the price of a European call option, we will continue our analysis of the …
Cox Regression Model, Lindsay Sarah Smith
Cox Regression Model, Lindsay Sarah Smith
LSU Master's Theses
Cox, in 1972, came up with the Cox Regression Model to deal handle failure time data. This work presents background information leading up to the Cox's regression model for censored survival data. The marginal and partial likelihood approaches to estimate the parameters in this model are presented in detail. The estimation techniques of the hazard and survivor functions are explained. All of these ideas are illustrated using data from the Veteran’s Administration lung cancer study.