Mathematics Commons^™

Spatial Models With Specific Error Structures, Nathaniel Adu

Electronic Theses and Dissertations

The purpose of this dissertation is to study the first order autoregressive model in the spatial context with specific error structures. We begin by supposing that the error structure has a long memory in both the i and the j components. Whenever the model parameters alpha and beta equal one, the limiting distribution of the sequence of normalized Fourier coefficients of the spatial process is shown to be a function of a two parameter fractional Brownian sheet. This result is used to find the limiting distribution of the periodogram ordinate of the spatial process under the null hypothesis that alpha …

An Invitation To Linear Algebra, David N. Pham, Jonathon Funk, Wenjian Liu

Open Educational Resources

This is an OER textbook on linear algebra.

Numerical Approaches To A Thermoelastic Kirchhoff-Love Plate System, Zeyu Zhou

Wayne State University Dissertations

In this work, theory background of the sobolev spaces and finite element spaces are

reviewed first. Then the details of how the thermoelastic Kirchhoff-Love(KL) plates numerically established are presented. Later we approaches to the thermoelastic KL system numerically with mixed element method, H^1−Galerkin method and interior penalty discontinuous galerkin method(IP-DG).

What is more, the SIP-DG also applied to solve this KL system numerically. The well-posedness, existence, uniqueness and convergence properties are theoretical analyzed. The gain of the convergence rate is also O(h^k), that is 1 less than the observed convergence rate.

When discussing the H1-Galerkin method, the main advantages over …

Spectral Methods For Hamiltonian Systems And Their Applications, Lewei Zhao

Wayne State University Dissertations

Hamiltonian systems typically arise as models of conservative physical systems and have many applications. Our main emphasis is using spectral methods to preserve both symplectic structure and energy up to machine error in long time. An engery error estimation is given for a type of Hamiltonian systems with polynomial nonlinear part, which is numerical verified by solving a Henon-Heiles systems. Three interesting applications are presented : the first one is the N-body problems. The second one is approximation for Weyl's Law and the third one is simulating quantum cooling in an optomechanical system to study the dissipative dynamics. Moreover, nonsmooth …

Rigid Equilibriums Of A Rotating String, Teddrick Schaffer

Electronic Theses and Dissertations

This paper describes some possible equilibrium configurations of a string rotating in a certain class of force fields, which have properties motivated by the inverse square gravitational force. Specifically it is shown that for a given number n, there exists a sufficient rotational rate such that any equilibrium configuration with no more than n zeros is guaranteed to exist for any force field in the class considered.

A Study Of Several Applications Of Parallel Computing In The Sciences Using Petsc, Nicholas Stegmeier

Electronic Theses and Dissertations

The importance of computing in the natural sciences continues to grow as scientists strive to analyze complex phenomena. The dynamics of turbulence, astrophysics simulations, and climate change are just a few examples where computing is critical. These problems are computationally intractable on all computing platforms except supercomputers, necessitating the continued development of efficient algorithms and methodologies in parallel computing. This thesis investigates the use of parallel computing and mathematical modeling in the natural sciences through several applications, namely computational fluid dynamics for impinging jets in mechanical engineering, simulation of biofilms in an aqueous environment in mathematical biology, and the solution …

Mental Imagery Practice As A Therapy For Naming Impairments: A Preliminary Study, Subhash Bhatnagar, Bridget Patek, Yasmeen Khan-Ansari, Naveen K. Bansal, Hugh Buckingham, Lotfi Hacein-Bey

Speech Pathology and Audiology Faculty Research and Publications

Background

Anomia remains one of the most recalcitrant linguistic disruptions in aphasia to treat. Developing successful interventions to address the word-finding deficits are complicated by the post-stroke symptom variability and inconsistent recovery patterns associated with anomia. Most of the current treatment methods, with a focus on specific compensating techniques and the repetitive practice of a limited set of items, have had variable success in naming treatment. However, it has not been possible to predict the gains in generalizing the learning beyond the stimuli used in practice or the controlled clinical setting. In this preliminary case study, we explore the value …

A (Co)Algebraic Approach To Hennessy-Milner Theorems For Weakly Expressive Logics, Zeinab Bakhtiari, Helle Hvid Hansen, Alexander Kurz

Engineering Faculty Articles and Research

"Coalgebraic modal logic, as in [9, 6], is a framework in which modal logics for specifying coalgebras can be developed parametric in the signature of the modal language and the coalgebra type functor T. Given a base logic (usually classical propositional logic), modalities are interpreted via so-called predicate liftings for the functor T. These are natural transformations that turn a predicate over the state space X into a predicate over TX. Given that T-coalgebras come with general notions of T-bisimilarity [11] and behavioral equivalence [7], coalgebraic modal logics are designed to respect those. In particular, if two states are behaviourally …

Practical Design Approaches For Assessing Parallelism In Dose Response Modelling, Timothy O'Brien, Jack Silcox

Mathematics and Statistics: Faculty Publications and Other Works

No abstract provided.

Basis Reduction In Lattice Cryptography, Raj Kane

Honors Theses

We develop an understanding of lattices and their use in cryptography. We examine how reducing lattice bases can yield solutions to the Shortest Vector Problem and the Closest Vector Problem.

Primes In Arithmetical Progression, Edward C. Wessel

Honors Theses

This thesis will tackle Dirichlet’s Theorem on Primes in Arithmetical Progressions. The majority of information that follows below will stem from Tom M. Apostol’s Introduction to Analytical Number Theory. This is the main source of all definitions, theorems, and method. However, I would like to assure the reader that prior knowledge of neither the text nor analytical number theory in general is needed to understand the result. A rough background in Abstract Algebra and a moderate grasp on Complex and Real Analysis are more than sufficient. In fact, my project’s intent is to introduce Dirichlet’s ideas to the mathematics student …

Pressure Versus Impulse Graph For Blast-Induced Traumatic Brain Injury And Correlation To Observable Blast Injuries, Barbara Rutter

Doctoral Dissertations

"With the increased use of explosive devices in combat, blast induced traumatic brain injury (bTBI) has become one of the signature wounds in current conflicts. Animal studies have been conducted to understand the mechanisms in the brain and a pressure versus time graph has been produced. However, the role of impulse in bTBIs has not been thoroughly investigated for animals or human beings.

This research proposes a new method of presenting bTBI data by using a pressure versus impulse (P-I) graph. P-I graphs have been found useful in presenting lung lethality regions and building damage thresholds. To present the animal …

Dendrites Or Lambda-Dendroids As Generalized Inverse Limits, Faruq Abdullah Mena

Doctoral Dissertations

"This research centers on the study of generalized inverse limits. We show that all members of an infinite family of inverse limit spaces are homeomorphics to one particularly complicated inverse limit space known as "The Monster". Further, properties of factor spaces and graphs of bonding functions which are preserved in generalized inverse limit spaces with upper semi-continuous bonding functions with appropriate restrictions are investigated. Some of the properties are locally connectedness, hereditary decomposability, hereditary indecomposability, hereditary unicoherence, arc-likeness, and tree-likeness. The theorems are illustrated by several examples"--Abstract, page iv.

Decoupling Methods For The Time-Dependent Navier-Stokes-Darcy Interface Model, Changxin Qiu

Doctoral Dissertations

"In this research, several decoupling methods are developed and analyzed for approximating the solution of time-dependent Navier-Stokes-Darcy (NS-Darcy) interface problems. This research on decoupling methods is motivated to efficiently solve the complex Stokes-Darcy or NS-Darcy type models, which arise from many interesting real world problems involved with or even dominated by the coupled porous media flow and free flow. We first discuss a semi-implicit, multi-step non-iterative domain decomposition (NIDDM) to solve a coupled unsteady NS-Darcy system with Beavers-Joseph-Saffman-Jones (BJSJ) interface condition and obtain optimal error estimates. Second, a parallel NIDDM is developed to solve unsteady NS-Darcy model with Beavers-Joseph (BJ) …

Modeling Of Hiv, Sir And Sis Epidemics On Time Scales And Oscillation Theory, Gülşah Yeni

Doctoral Dissertations

"We study higher dimensional systems of first order dynamic equations on time scales together with their applications. In particular, we focus on epidemic models such as HIV (Human Immunodeficiency Virus), SIS (Susceptible-Infected-Susceptible) and SIR (Susceptible-Infected-Recovered).

First, we generalize the early studied continuous three dimensional linear model of drug therapy for HIV-1 decline on time scales in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. We compare these models to explore the impact of the theory of time scales. After fitting the models to the data collected at a clinical …

Gelfand-Naimark Duality For Non-Commutative C*-Algebras, Natee Pitiwan

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we prove a duality between a class of non-commutative C*-algebras and projective C*-categories. After developing ideas from infinite matrices and bounded operators on Hilbert spaces, we define projective C*-categories and then define functors between the category of matrix C*-algebras and the category of projective C*-categories. Then from these functors we derive a duality between the two categories that generalizes Gelfand-Naimark duality for commutative C*-algebras. In the last chapter we discuss possibility of combining the result in this dissertation with already known results regarding sectional representations of C*-algebras to obtain a duality for a broader class of C*-algebras.

Applying Support Vector Machine With Connectivity Of Primitive Biochemical Compound Structure To Identify Target Characteristics Of Molecules, Peemapat Wongsriphisant

Chulalongkorn University Theses and Dissertations (Chula ETD)

Graph-structured data are widely used in many fields of study. For example, in cheminformatics, the data of biochemical compounds can be encoded as a compound graph where atoms are represented by vertices and chemical bonds between pairs of atoms are represented by edges. By this setting, we can predict the molecular characteristics of an unseen biochemical compound by considering the similarity between two compound graphs. This problem is called a graph classification. This study, proposes an algorithm for compound graph classification by finding primitive substructures of the compounds and encode them in a new graph form. Then, their similarities are …

Hidden Symmetries In Classical Mechanics And Related Number Theory Dynamical System, Mohsin Md Abdul Karim

Masters Theses

Classical Mechanics consists of three parts: Newtonian, Lagrangian and Hamiltonian Mechanics, where each part is a special extension of the previous part. Each part has explicit symmetries (the explicit Laws of Motion), which, in turn, generate implicit or hidden symmetries (like the Law of Conservation of Energy, etc). In this Master's Thesis, different types of hidden symmetries are considered; they are reflected in the Noether Theorem and the Poincare Recurrence Theorem applied to Lagrangian and Hamiltonian Systems respectively.

The Poincare Recurrence Theorem is also applicable to some number theory problems, which can be considered as dynamical systems. In …

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method For A Transient Stokes Interface Problem With Jump Coefficients, Andrew Lundberg, Pengtao Sun, Cheng Wang, Chen-Song Zhang

Mathematical Sciences Faculty Research

The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated.

Volume 11, Jacob Carney, Ryan White, Joseph Hyman, Jenny Raven, Megan Garrett, Ibrahim Kante, Summer Meinhard, Lauren Johnson, William "Editha" Dean Howells, Laura Gottschalk, Christopher Siefke, Pink Powell, Natasha Woodmancy, Katharine Colley, Abbey Mays, Charlotte Potts

Incite: The Journal of Undergraduate Scholarship

Table of Contents:

Introduction, Dr. Roger A. Byrne, Dean

From the Editor, Dr. Larissa "Kat" Tracy

From the Designers, Rachel English, Rachel Hanson

Synthesis of 3,5-substituted Parabens and their Antimicrobial Properties, Jacob Coarney, Ryan White

Chernobyl: Putting "Perestroika" and "Glasnot" to the Test, Joseph Hyman

Art by Jenny Raven

Watering Down Accessibility: The Issue with Public Access to Alaska's Federal Waterways, Meagan Garrett

Why Has the Democratic Republic of the Congo outsourced its Responsibility to Educate its Citizens? Ibrahim Kante

Art by Summer Meinhard

A Computational Study of Single Molecule Diodes, Lauren Johnson

Satire of …

Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski

Communications on Stochastic Analysis

No abstract provided.

Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar

Communications on Stochastic Analysis

No abstract provided.

Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan

Communications on Stochastic Analysis

No abstract provided.

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas

Communications on Stochastic Analysis

No abstract provided.

Using Social Network Analysis To Examine The Connections Within A Noyce Community’S Facebook Group, Amanda Jensen

Electronic Theses and Dissertations

One of the successes of the Rural Enhancement of Mathematics And Science Teachers (REMAST) Scholarship Program at South Dakota State University is the community we have built. This community has been built through a summer conference and a closed Facebook group. As we near the end of our Phase II Noyce funding, we are using social network analysis to examine the connections within the REMAST Facebook group. What we learn in this research project will be useful to other Noyce projects as it is a model for developing a strong professional learning community. In order to determine information about the …

Development Of A Data-Driven Patient Engagement Score Using Finite Mixture Models, Eric Bae

Electronic Theses and Dissertations

Patient activation measure (PAM) is widely adopted by health care providers to access individual's knowledge, skill, and confidence for managing one's health and healthcare. Patient activation measure (PAM), licensed by Insignia Health, is widely adopted by health care providers to access individual's knowledge, skill, and confidence for managing one's health and healthcare. Multiple studies corroborate the effectiveness of activation measure in predicting most health behaviors, including preventive behaviors, healthy behaviors, self-management behaviors, and health information seeking. However, PAM is heavily dependent on subjective patient-reported data, which are often incomplete. The purpose of this study is to develop an objective statistical …

Ua66/15/2 Ogden College Of Science & Engineering Mathematics & Computer Science Publications, Wku Archives

WKU Archives Collection Inventories

Publications created by and about Mathematics & Computer Science.

Quasilinearization And Boundary Value Problems At Resonance For Caputo Fractional Differential Equations, Saleh S. Almuthaybiri, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The quasilinearization method is applied to a boundary value problem at resonance for a Caputo fractional differential equation. The method of upper and lower solutions is first employed to obtain the uniqueness of solutions of the boundary value problem at resonance. The shift argument is applied to show the existence of solutions. The quasilinearization algorithm is then developed and sequences of approximate solutions are constructed that converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two applications are provided to illustrate the main results.

Some Transitivity-Like Concepts In Abelian Groups, Gabor Braun, Brendan Goldsmith, Ketao Gong, Lutz Strungmann

Articles

The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.