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Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao
Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao
All Dissertations
In this dissertation, we address several research problems in statistical inference. We obtain results in the following four directions: linear model selection, minimax estimation of linear functionals, Bayes type estimators for the survival functions based on right censored data, and estimation of survival functions based on doubly censored data.
What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz
What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz
Dissertations
Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …
A Hyperbolic Two -Step Model Based Finite Difference Method For Studying Thermal Deformation In A Micro Thin Film Heated By Ultrashort -Pulsed Lasers, Tianchan Niu
Doctoral Dissertations
Heat transport through micro thin films plays a very important role in microtechnology applications. Many microelectronic devices have metal thin films as their key components. Microscale heat transfer is also important for the thermal processing of materials, including laser micromachining, laser patterning, laser synthesis and laser surface hardening. Hence, studying the thermal behavior of thin films is essential for predicting the performance of a microelectronic device or for obtaining the desired microstructure. Recently, it has become very popular to use ultrashort-pulsed lasers in thermal processing, which lasers have pulse durations of the order of subpicoseconds to femtoseconds, and these kinds …
Automorphic Decompositions Of Graphs, Robert Beeler
Automorphic Decompositions Of Graphs, Robert Beeler
All Dissertations
Let G and H be graphs. A G-decomposition D of a graph H is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. It is well known that a graceful labelling (or more generally a rho-valuation) of a graph G induces a cyclic G-decomposition of a complete graph. We will extend these notions to that of a general valuation in a cyclic group. Such valuations yield decompositions of circulant graphs. We will show that every graph has a valuation and hence is a …
Permutation Decoding Of Codes From Graphs And Designs, Padmapani Seneviratne
Permutation Decoding Of Codes From Graphs And Designs, Padmapani Seneviratne
All Dissertations
Permutation decoding is a technique, developed by Jessie McWilliams in 1960's. It involves finding a set of automorphisms of the code, called a PD-set. If such a set exists and if the generator matrix of the code is in standard form then a simple algorithm using this set can be followed to correct the maximum number of errors of which the code is capable. Primarily this method was used originally on cyclic codes and Golay codes.
In this dissertation we study binary codes formed from an adjacency matrix of some classes of graphs and apply the permutation decoding method to …
Planning, Scheduling, And Timetabling In A University Setting, Christine Kraft
Planning, Scheduling, And Timetabling In A University Setting, Christine Kraft
All Dissertations
Methods and procedures for modeling university student populations, predicting course enrollment, allocating course seats, and timetabling final examinations are studied and proposed. The university enrollment model presented uses a multi-dimensional state space based on student demographics and the Markov property, rather than longitudinal data to model student movement. The procedure for creating adaptive course prediction models uses student characteristics to identify groups of undergraduates whose specific course enrollment rates are significantly different than the rest of the university population. Historical enrollment rates and current semester information complete the model for predicting enrollment for the coming semester. The course prediction model …
Numerical Approximation Of Shear-Thinning And Johnson-Segalman Viscoelastic Fluid Flows, Jason Howell
Numerical Approximation Of Shear-Thinning And Johnson-Segalman Viscoelastic Fluid Flows, Jason Howell
All Dissertations
In this work computational approaches to the numerical simulation of steady-state viscoelastic fluid flow are investigated. In particular, two aspects of computing viscoelastic flows are of interest: 1) the stable computation of high Weissenberg number Johnson-Segalman fluids and 2) low-order approaches to simulating the flow of fluids obeying a power law constitutive model.
The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. For the nonlinear Johnson-Segalman constitutive model, defect-correction and continuation methods are examined …
Estimates Related To The Arithmetic Of Elliptic Curves, Bryan Faulkner
Estimates Related To The Arithmetic Of Elliptic Curves, Bryan Faulkner
All Dissertations
This dissertation presents results related to two problems in the arithmetic of elliptic curves.
Feng and Xiong equate the nontriviality of the Selmer groups associated with congruent number curves to the presence of certain types of partitions of graphs associated with the prime factorization of n. The triviality of the Selmer groups associated to the congruent number curve implies that the curve has rank zero which in turn implies n is noncongruent. We extend the ideas of Feng and Xiong in order to compute the Selmer groups of congruent number curves.
We prove an average version of a generalization of …
Transmission Dynamics Of Avian Influenza Among Poultry With And Without Vaccination, Qiao Liang
Transmission Dynamics Of Avian Influenza Among Poultry With And Without Vaccination, Qiao Liang
Mathematics & Statistics ETDs
The continuing avian influenza (AI) out break that began in late 2003 and early 2004 has been disastrous for the poultry industry worldwide. It has resulted in severe socio-economic damage, and it has raised serious concerns for general public health. In this research, we use mathematics to analyze transmission dynamics of AI among poultry. We use a status-based approach to construct systems of differential equations to describe virus transmission dynamics. We develop theoretical means to eradicate the spread of the disease, and we calculate the size of healthy and infected populations during an AI outbreak, and the final population size …
The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui
The Fock Space And Related Bergman Type Integral Operators, Ovidiu Furdui
Dissertations
In this thesis we study the boundedness of a general class of integral operators induced by the kernel functions of Fock spaces. More precisely, for a, b, and c real parameters we study the action of [Special characters omitted.] and [Special characters omitted.] on Lp ([Special characters omitted.] ,dvs ), where dvs ( z ) = [Special characters omitted.] is the Gaussian probability measure on [Special characters omitted.] . We prove that, when p > 1, respectively p = 1, these operators are bounded if and only if p satisfies a quadratic, respectively a linear, inequality. The …
Measures Of Travers Ability In Graphs, Futaba Okamoto
Measures Of Travers Ability In Graphs, Futaba Okamoto
Dissertations
For a connected graph G of order n ≥ 3 and a cyclic ordering sc : v 1, v2,..., vn, v n+1 = v1 of vertices of G, the number d(sc) is defined by d(sc) = i=1n d(vi, vi +1), where d(vi, vi +1) is the distance between vi and vi+1 in G for 1 ≤ i ≤ n. The Hamiltonian number h(G) and upper Hamiltonian number h +(G) of G are defined as h(G) = min{d(sc)} and h+(G) = max{d(sc)}, respectively, where the minimum and maximum are taken over all cyclic orderings s c of vertices of G. For …
Equitable Efficiency In Multiple Criteria Optimization, Vijay Singh
Equitable Efficiency In Multiple Criteria Optimization, Vijay Singh
All Dissertations
Equitable efficiency in multiple criteria optimization was introduced mathematically in the middle of nineteen-nineties. The concept tends to strengthen the notion of Pareto efficiency by imposing additional conditions on the preference
structure defining the Pareto preference. It is especially designed to solve multiple criteria problems having commensurate criteria where different criteria values can be compared directly.
In this dissertation we study some theoretical and practical aspects of equitably efficient solutions. The literature on equitable efficiency is not very extensive and provides very limited number of ways of generating such solutions. After introducing
some relevant notations, we develop some scalarization based …
Random Vectors Over Finite Fields, Shannon Lockard
Random Vectors Over Finite Fields, Shannon Lockard
All Dissertations
The study of random objects is a useful one in many applications and areas of mathematics. The Probabilistic Method, introduced by Paul Erdos and his many collaborators, was first used to study the behavior of random graphs and later to study properties of random objects. It has developed as a powerful tool in combinatorics as well as finding applications in linear algebra, number theory, and many other areas. In this dissertation, we will consider random vectors, in particular, dependency among random vectors. We will randomly choose vectors according to a specified probability distribution. We wish to determine how many vectors …
Mathematical Methods In Composing Melodies, Thomas Brown
Mathematical Methods In Composing Melodies, Thomas Brown
Undergraduate Theses and Capstone Projects
This thesis, “Mathematical Methods in Composing Melodies,” explores the different ways in which mathematics can be used to create music. Some research has been done in this field already. Richard F. Voss and John Clarke used fractals and different frequencies of noise to create music. The Greek composer Iannis Xenakis used Markovian Stochastic trees to create some of his compositions. Explored in this thesis are seven different methods to compose melodies. After compiling the different melodies, they were categorized by different musical periods based on the musical characteristics found in the melody. This thesis differs from other research that deals …
Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba
Three Methods For Solving The Low Energy Neutron Boltzmann Equation, Tony Charles Slaba
Mathematics & Statistics Theses & Dissertations
The solution to the neutron Boltzmann equation is separated into a straightahead component dominating at high energies and an isotropic component dominating at low energies. The high-energy solution is calculated using HZETRN-05, and the low-energy isotropic component is modeled by two non-coupled integro-differential equations describing both forward and backward neutron propagation. Three different solution methods are then used to solve the equations. The collocation method employs linear I3-splines to transform each equation into a system of ODES; the resulting system is then solved exactly and evaluated using numerical integration techniques. Wilson's method uses a perturbational approach in which a fundamental …
A Multivariate Magnitude Robust Control Chart For Mean Shift Detection And Change Point Estimation, Ryan M. Harrell
A Multivariate Magnitude Robust Control Chart For Mean Shift Detection And Change Point Estimation, Ryan M. Harrell
Theses and Dissertations
Statistical control charts are often used to detect a change in an otherwise stable process. This process may contain several variables affecting process stability. The goal of any control chart is to detect an out-of-control state quickly and provide insight on when the process actually changed. This reduces the off-line time the quality engineer spends assigning causality. In this research, a multivariate magnitude robust chart (MMRC) was developed using a change point model and a likelihood-ratio approach. Here the process is considered in-control until one or more normally distributed process variables permanently and suddenly shifts to out-of-control, stable value. Using …
Spacecraft Proximity Operations Used To Estimate The Dynamical & Physical Properties Of A Resident Space Object, Abraham F. Brunner
Spacecraft Proximity Operations Used To Estimate The Dynamical & Physical Properties Of A Resident Space Object, Abraham F. Brunner
Theses and Dissertations
When conducting a space proximity operation, developing high-fidelity estimates of the dynamical and physical properties of a Resident Space Object (RSO) based on post-rendezvous observational data acquired, is imperative for the understanding of the RSO itself and the operating environment. This research investigates the estimation of relative motion dynamics, rotational dynamics, and the feasibility of estimating the moments of inertia of a RSO. Using the Hill-Clohessy-Wiltshire equations, rigid-body dynamics, and estimation theory, a nonlinear least squares estimation algorithm is implemented in the processing of range data from tracked observation points on the RSO body. Through simulation, it was determined that …
Surrogate Strategies For Computationally Expensive Optimization Problems With Cpu-Time Correlated Functions, Raymond Magallanez Jr.
Surrogate Strategies For Computationally Expensive Optimization Problems With Cpu-Time Correlated Functions, Raymond Magallanez Jr.
Theses and Dissertations
This research focuses on numerically solving a class of computationally expensive optimization problems that possesses a unique characteristic: as the optimal solution is approached, the computational time required to compute an objective function value decreases. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration and comparison process. The goal is to find the parameters of a predetermined image by comparing the flow dynamics from the numerical simulation and the predetermined image through the image comparison process. The generalized pattern search and mesh adaptive direct search methods …
Classifying Failing States, Nathan E. Nysether
Classifying Failing States, Nathan E. Nysether
Theses and Dissertations
The US is heavily involved in the first major war of the 21st Century -- The Global War on Terror (GWOT). As with any militant group, the foundation of the enemy's force is their people. There are two primary strategies for defeating the terrorists and achieving victory in the GWOT. First, we must root out terrorists where they live, train, plan, and recruit and attack them militarily. Second, we must suffocate them by cutting off the supply of new soldiers willing to choose aggression or even death over their current life. This thesis helps to achieve these objectives by applying …
Capstone Mathematics And Technology: A Collection Of Mathematical Technology Enhanced Activities For Students And Teachers, Heidi Eastman
Capstone Mathematics And Technology: A Collection Of Mathematical Technology Enhanced Activities For Students And Teachers, Heidi Eastman
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
The purpose of this project is to provide an introduction to how technology can be used in the mathematical classroom to enhance students' learning of mathematics, while at the same time leading students to a richer and deeper understanding of those mathematical concepts. The topics were selected based on their relevance to the Utah State Core Curriculum for middle and secondary mathematics courses. It was intended that each lesson plan would challenge a preservice mathematics educator to build relationships between different areas of mathematics and/or to create deeper understandings of specific mathematical concepts. At the same time many of the …
Comparison Of Kp And Bbm-Kp Models, Gideon Pyelshak Daspan
Comparison Of Kp And Bbm-Kp Models, Gideon Pyelshak Daspan
LSU Doctoral Dissertations
In this dissertation we show that the solution of the pure initial-value problems for the KP and regularize KP equations are the same, to within the order of accuracy attributable to either, on the time scale from zero to epsilon to negative three halves power, during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.
Sign Ambiguities Of Gaussian Sums, Heon Kim
Sign Ambiguities Of Gaussian Sums, Heon Kim
LSU Doctoral Dissertations
In 1934, two kinds of multiplicative relations, extit{norm and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample disproving the conjecture when Gaussian sums are considered as numbers. This counterexample was a new type of multiplicative relation, called a {it sign ambiguity} (see Definition ef{defi:of_sign_ambi}), involving a $pm$ sign not connected to elementary properties of Gauss sums. In Chapter $5$, we provide an explicit product formula giving an infinite class …
Subrepresentation Semirings And An Analogue Of 6j-Symbols, Nam Hee Kwon
Subrepresentation Semirings And An Analogue Of 6j-Symbols, Nam Hee Kwon
LSU Doctoral Dissertations
Let G be a quasi simply reducible group, and let V be a representation of G over the complex numbers $mathbb{C}$. In this thesis, we introduce the twisted 6j-symbols over G which have their origin to Wigner's 6j-symbols over the group SU(2) to study the structure constants of the subrepresentation semiring S_{G}(End(V)), and we study the representation theory of a quasi simply reducible group G laying emphasis on our new G-module objects. We also investigate properties of our twisted 6j-symbols by establishing the link between the twisted 6j-symbols and Wigner's 3j-symbols over the group G.
Backward Stochastic Navier-Stokes Equations In Two Dimensions, Hong Yin
Backward Stochastic Navier-Stokes Equations In Two Dimensions, Hong Yin
LSU Doctoral Dissertations
There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained …
Multiplicative Renormalization Method For Orthogonal Polynomials, Suat Namli
Multiplicative Renormalization Method For Orthogonal Polynomials, Suat Namli
LSU Doctoral Dissertations
To study the orthogonal polynomials, Asai, Kubo and Kuo recently have developed the multiplicative renormalization method. Motivated by infinite dimensional white noise analysis, it is an alternative to the computational part of the classical Gram-Schmidt process to find the orthogonal polynomials for a given measure. Instead of finding the orthogonal polynomials recursively as described in the Gram-Schmidt process, one analyzes different types of generating functions systematically in order to obtain polynomials after power series expansion. This work also produces the Jacobi-Szego parameters easily and paves the way for the study of one-mode interacting Fock spaces related to these parameters. They …
First Passage Time Problem For Multivariate Jump-Diffusion Processes: Models, Computation, And Applications In Finance, Di Zhang
Theses and Dissertations (Comprehensive)
The first passage time (FPT) problems are ubiquitous in many applications, from physics to finance. Mathematically, such problems are often reduced to the evaluation of the probability density of the time for a process to cross a certain level, a boundary, or to enter a certain region. While in other areas of applications the FPT problems can often be solved analytically, in finance we usually have to resort to the application of numerical procedures, in particular when we deal with jump-diffusion stochastic processes (JDP). The application of the conventional Monte-Carlo procedure is possible for the solution of the resulting model, …