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Computational Techniques For Optimal Control Of Quantum System, Gregory Von Winckel
Computational Techniques For Optimal Control Of Quantum System, Gregory Von Winckel
Mathematics & Statistics ETDs
The control of matter and energy at a fundamental level will be a cornerstone of new technologies for years to come. This idea is exemplified in a distilled form by controlling the dynamics of quantum mechanical systems via a time—dependent potential. The contributions detailed within this work focus on the computational aspects of formulating and solving quantum control problems efficiently. The accurate numerical computation of optimal controls of infinite—dimensional quantum control problems is a very difficult task that requires to take into account the features of the original infinite—dimensional problem. An important issue is the choice of the functional space …
Sasakian Geometry On Lens Space Bundles Over Riemann Surfaces, Candelario Castaneda
Sasakian Geometry On Lens Space Bundles Over Riemann Surfaces, Candelario Castaneda
Mathematics & Statistics ETDs
We compute the cohomology of the join of a 3 manifold with the sphere and we see the dependence of this cohomology on one of the parameters.
On Roots Of The Macdonald Function, Kaylee Tejeda
On Roots Of The Macdonald Function, Kaylee Tejeda
Mathematics & Statistics ETDs
An overview is given for the Dirichlet-to-Neumann map for outgoing solutions to the radial wave equation' in the context of nonreflecting radiation boundary conditions on a spherical domain. We then consider the Macdonald function K_l+1/2 (z) for l \u2208 Z \u22650 , a solution to the half-integer order modified Bessel equation. This function can be expressed as K_l+1/2 (z) = sqrt(\u03c0/2z)e^−z z^−l p_l (z), where p_l (z) is a degree-l monic polynomial with simple roots in the left-half plane. By exploiting radiation boundary conditions for the 'radial wave equation', we show that the root set of p_l (z) also obeys …
Arithmetic Differential Subgroups Of Gl_{N}, Alfonso E. Heras-Llanos
Arithmetic Differential Subgroups Of Gl_{N}, Alfonso E. Heras-Llanos
Mathematics & Statistics ETDs
A remarkable and special Galois Theory appears from the study of the arithmetic analogue of ordinary differential equations; where functions are replaced by integers, the derivative operator replaced by the Fermat quotient operator' and differential equations are replaced by arithmetic differential equations. The main result presented in the thesis will be the study of a very special class of arithmetic subgroups of GL_n. We also introduce a set of functions, that we call Leibniz systems. These functions 'generate' some examples of the differential subgroups of GL_n. As a by-product we found more analogies between the ordinary differential operator and the …
Changes In Student Proving Skills And Attitudes Following A Cooperative Learning Seminar, Martha Byrne
Changes In Student Proving Skills And Attitudes Following A Cooperative Learning Seminar, Martha Byrne
Mathematics & Statistics ETDs
This dissertation details research studies designed to explore undergraduate math students beliefs and attitudes about mathematical proof, ability to compose valid proofs, and ability to read and validate purported proofs written by other students. In two studies, a cohort of seminar participants were assessed twice on their attitudes and beliefs about mathematical proof, their ability to compose proofs, and their ability to validate arguments. Between assessments, these participants worked on carefully crafted problem sets in a Cooperative Learning environment. In each study, a cohort of comparison participants took both assessments but did not engage in structured, cooperative work in the …
Abc Theorems In The Functional Case, Cristina Toropu
Abc Theorems In The Functional Case, Cristina Toropu
Mathematics & Statistics ETDs
In this dissertation we will prove some ABC Theorems, namely for relatively prime by pairs p-adic entire functions in one variable, for p-adic meromorphic functions in several variables without common factors, under the hypothesis that no subsum vanishes, and also for pairwise relatively prime p-adic entire functions of several variables. In this thesis we will also prove a few generalizations of Buium's results that he used in order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem …
Star Operations And Numerical Semigroup Rings, Bryan White
Star Operations And Numerical Semigroup Rings, Bryan White
Mathematics & Statistics ETDs
We aim to classify the star and semistar operations on conductive numerical semigroup rings which are of the form $k + x^n k[[x]]$. By classifying the star and semistar operations on conductive numerical semigroup rings we obtain a better understanding of the set of star and semistar operations on general numerical semigroup rings. Here we classify all star and semistar operations on the ring $ k + x^4 k[[x]]$ as well as all semistar operations on $k+x^5k[[x]]$ that are not star. We investigate star operations on $k+x^5k[[x]]$ with Macaulay 2 and also present several results about general conductive numerical semigroup …
Bayesian Partially Ordered Probit And Logit Models With An Application To Course Redesign, Xueqi Wang
Bayesian Partially Ordered Probit And Logit Models With An Application To Course Redesign, Xueqi Wang
Mathematics & Statistics ETDs
Large entry-level courses are commonplace at public 2- and 4-year institutions of higher education (IHEs) across the United States. Low pass rates in these entry-level courses, coupled with tight budgets, have put pressure on IHEs to look for ways to teach more students more effectively at a lower cost. Efforts to improve student outcomes in such courses are often called ``course redesigns.' The difficulty arises in trying to determine the impact of a particular course redesign; true random-controlled trials are expensive and time-consuming, and few IHEs have the resources or patience to implement them. As a result, almost all evaluations …
Quantification Of Stability In Systems Of Nonlinear Ordinary Differential Equations, Jason Terry
Quantification Of Stability In Systems Of Nonlinear Ordinary Differential Equations, Jason Terry
Mathematics & Statistics ETDs
A common process in ODE theory is to linearize an ODE system about an equilibrium point to determine the local stability properties of its orbits. Less common are results that quantify the domain of stability in the original system. We study a class of ODE systems where the domain of nonlinear stability is significantly small given the parameters of the problem. The aim of this paper is to attempt to quantify this region of stability.
Social Network Analysis Of Peer Influence On Adolescent Smoking, Gregory Lambert
Social Network Analysis Of Peer Influence On Adolescent Smoking, Gregory Lambert
Mathematics & Statistics ETDs
Adolescent cigarette smoking behavior is affected by peer relationships, but how these peer relationships influence the behavior of other adolescent smokers is not well understood. Mixing among cigarette smokers in adolescent friendship networks could indicate peer influence or a homophilous association among likeminded individuals. The goal of this thesis will be to examine a set of adolescent friendship networks to determine if different cigarette smoking behaviors can be predictive of friendship nominations in the network. Examining the structure of social networks requires among other things, inspection of the presence (or absence) of relational ties. Tie formations in social networks are …
Using Bayesian Statistics To Model The Reliability Of Complex Weapon Systems, Rebecca Lilley
Using Bayesian Statistics To Model The Reliability Of Complex Weapon Systems, Rebecca Lilley
Mathematics & Statistics ETDs
This work describes a Bayesian model for assessing the reliability of complex systems using component tests, full system tests, and covariate information. Development of the model focused on understanding the relationship between component reliability and system reliability; and defining this relationship using mathematical expressions. The method in this thesis uses pass/fail data coupled with different levels of prior information about system reliability and covariate information to derive posterior distributions that model component and system reliability. This work provides insights on how the number of components, amount of prior information used, inclusion of covariates and spread of failures across components affects …
Modeling The Mechanical Response Of Polycrystalline Thin Films, Pedro Joaquin Madrid
Modeling The Mechanical Response Of Polycrystalline Thin Films, Pedro Joaquin Madrid
Mathematics & Statistics ETDs
Microelectromechanical systems (MEMS) are part of every modern technological advance. Electrodeposited thin nickel (Ni) polycrystalline films in MEMS often show fiber texture resulting in transverse isotropic elastic properties. It is of interest to determine these elastic properties, in particular the in-plane Young's modulus, since it plays a fundamental role in device performance. The fabrication process of MEMS films introduces uncertainties in the microstructure geometry, crystallographic texture, the crystal elastic constants, the physical film dimensions and other parameters. In this thesis the numerical value of the in-plane Young's modulus of thin Ni polycrystalline films is predicted. The predicted values lie between …
A Survey Of Lack-Of-Fit Tests Based On Sums Of Ordered Residuals, Mohammad Hattab
A Survey Of Lack-Of-Fit Tests Based On Sums Of Ordered Residuals, Mohammad Hattab
Mathematics & Statistics ETDs
Christensen and Lin (2014), henceforth C-L, suggested two lack-of-fit tests to assess the adequacy of a linear model based on partial sums of residuals. In particular, their tests evaluated the adequacy of the mean function. Their tests relied on asymptotic results without requiring small sample normality. We extend this research by proposing additional tests based on partial sums of residuals. The asymptotic distribution for each test statistic is found so that the $P$ value can be efficiently approximated. To assess their strengths and weaknesses, the C-L tests and the new tests are compared in different scenarios by simulation. We propose …