Mathematics Commons^™

Strong Stationary Times And The Fundamental Matrix For Recurrent Markov Chains, P J Fitzsimmons

Communications on Stochastic Analysis

No abstract provided.

Bimodules And Hypergroups Associated With Actions Of A Pair Of Groups, Satoshi Kawakami, Tatsuya Tsurii, Shigeru Yamagami

Communications on Stochastic Analysis

No abstract provided.

A Study In Locally Compact Groups—Chabauty Space, Sylow Theory, The Schur-Zassenhaus Formalism, The Prime Graph For Near Abelian Groups, Wolfgang Herfort, Karl H Hofmann, Francesco G Russo

Communications on Stochastic Analysis

No abstract provided.

The Conjugacy Problem For Automorphism Groups Of Countable Homogeneous Structures, Samuel Coskey, Paul Ellis

Mathematics Faculty Publications and Presentations

We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.

The Decay Of Disease Association With Declining Linkage Disequilibrium: A Fine Mapping Theorem, Mehdi Maadooliat, Naveen K. Bansal, Jibal Upadhya, Manzur R. Farazi, Xiang Li, Max M. He, Scott J. Hebbring, Zhan Ye, Steven J. Schrodi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise …

Impact Of Myh6 Variants In Hypoplastic Left Heart Syndrome, Aoy Tomita-Mitchell, Karl D. Stamm, Donna K. Mahnke, Min-Su Kim, Pip M. Hidestrand, Huan-Ling Liang, Mary Goetsch, Pippa Simpson, Andrew N. Pelech, James S. Tweddell, D. Woodrow Benson, John Lough, Michael E. Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

Hypoplastic left heart syndrome (HLHS) is a clinically and anatomically severe form of congenital heart disease (CHD). Although prior studies suggest that HLHS has a complex genetic inheritance, its etiology remains largely unknown. The goal of this study was to characterize a risk gene in HLHS and its effect on HLHS etiology and outcome. We performed next-generation sequencing on a multigenerational family with a high prevalence of CHD/HLHS, identifying a rare variant in the α-myosin heavy chain (MYH6) gene. A case-control study of 190 unrelated HLHS subjects was then performed and compared with the 1000 Genomes Project. Damaging …

A Note On The Howson Property In Inverse Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

An algebra has the Howson property if the intersection of any two finitely generated subalgebras is again finitely generated. A simple necessary and sufficient condition is given for the Howson property to hold on an inverse semigroup with finitely many idempotents. In addition, it is shown that any monogenic inverse semigroup has the Howson property.

The Corona Problem For Kernel Multiplier Algebras, Eric T. Sawyer, Brett D. Wick

Mathematics Faculty Research

We prove an alternate Toeplitz corona theorem for the algebras of pointwise kernel multipliers of Besov-Sobolev spaces on the unit ball in C, and for the algebra of bounded analytic functions on certain strictly pseudoconvex domains and polydiscs in higher dimensions as well. This alternate Toeplitz corona theorem extends to more general Hilbert function spaces where it does not require the complete Pick property. Instead, the kernel functions kx (y) of certain Hilbert function spaces H are assumed to be invertible multipliers on H and then we continue a research thread begun by Agler and McCarthy in 1999, and continued …

Inequalities Of Hardy-Littlewood-Polya Type For Functions Of Operators And Their Applications, Vladyslav Babenko, Yuliya Babenko, Nadiia Kriachko

Faculty Articles

In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of a function of an operator on a class of elements defined with the help of another function of the operator. We then apply the results to solve the following problems: (i) the problem of approximating a function of an unbounded self-adjoint operator by bounded operators, (ii) the problem of best approximation of a certain class of elements from a Hilbert space by another class, and (iii) …

Integration Over Curves And Surfaces Defined By The Closest Point Mapping, Catherine Kublik, Richard Tsai

Mathematics Faculty Publications

We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is intended to be used in combination with level set techniques. However, contrary to the common practice with level set methods, the volume integrals derived from our formulation coincide exactly with the surface or line integrals that one wishes to compute. We study various aspects of this formulation and provide a geometric interpretation of this formulation in terms of the singular values of …

Pedagogical Moves As Characteristics Of One Instructor’S Instrumental Orchestrations With Tinkerplots And The Ti-73 Explorer: A Case Study, James L. Kratky

Dissertations

Those supporting contemporary reform efforts for mathematics education in the United States have called for increased use of technologies to support student-centered learning of mathematical concepts and skills. There is a need for more research and professional development to support teachers in transitioning their instruction to better meet the goals of such reform efforts.

Instrumental approaches to conceptualizing technology use in mathematics education, arising out of the theoretical and empirical work in France and other European nations, show promise for use to frame studies on school mathematics in the United States. Instrumental genesis is used to describe the bidirectional and …

Latin Squares And Their Applications To Cryptography, Nathan O. Schmidt

Boise State University Theses and Dissertations

A latin square of order-n is an n x n array over a set of n symbols such that every symbol appears exactly once in each row and exactly once in each column. Latin squares encode features of algebraic structures. When an algebraic structure passes certain "latin square tests", it is a candidate for use in the construction of cryptographic systems. A transversal of a latin square is a list of n distinct symbols, one from each row and each column. The question regarding the existence of transversals in latin squares that encode the Cayley tables of finite groups …

Error Analysis Of An Hdg Method For A Distributed Optimal, Huiqing Zhu, Fatih Celiker

Faculty Publications

In this paper, we present a priori error analysis of a hybridizable discontinuous Galerkin (HDG) method for a distributed optimal control problem governed by diffusion equations. The error estimates are established based on the projection-based approach recently used to analyze these methods for the diffusion equation. We proved that for approximations of degree k on conforming meshes, the orders of convergence of the approximation to fluxes and scalar variables are k+1 when the local stabilization parameter is suitably chosen.

Bezout Inequality For Mixed Volumes, Ivan Soprunov, Artem Zvavitch

Mathematics and Statistics Faculty Publications

In this paper we consider the following analog of Bezout inequality for mixed volumes: V(P1,…,Pr,Δn−r)Vn(Δ)r−1≤∏i=1rV(Pi,Δn−1) for 2≤r≤n. We show that the above inequality is true when Δ is an n-dimensional simplex and P1,…,Pr are convex bodies in Rn. We conjecture that if the above inequality is true for all convex bodies P1,…,Pr, then Δ must be an n-dimensional simplex. We prove that if the above inequality is true for all convex bodies P1,…,Pr, then Δ must be indecomposable (i.e. cannot be written as the Minkowski sum of two convex bodies which are not homothetic to Δ), which confirms the conjecture …

Matching Transversal Edge Domination In Graphs, Anwar Alwardi

Applications and Applied Mathematics: An International Journal (AAM)

Let G =(V,E) be a graph. A subset X of E is called an edge dominating set of G if every edge in E - X is adjacent to some edge in X . An edge dominating set which intersects every maximum matching inG is called matching transversal edge dominating set. The minimum cardinality of a matching transversal edge dominating set is called the matching transversal edge domination number of G and is denoted by γ_mt(G). In this paper, we begin an investigation of this parameter.

Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4- free projective-planar graphs which we call M¨obius hyperladders. Furthermore, every simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a minor of a M¨obius hyperladder. As applications of these structures we determine the page number of patch graphs and of M¨obius hyperladders.

Common Core In Tennessee: An Analysis Of Eighth Grade Mathematics Standards, Hayley Little

Honors Theses

Since their introduction in 2010, the Common Core State Standards (CCSS) have been a highly controversial topic in educational reform. Though the standards are not a product of the federal government and are not federally mandated, they do represent a push towards national academic standards in America. For states such as Tennessee, educational policies of the past pushed them to lower their academic standards in order to create the illusion of success. Those states are now some of the places that have seen the most change with the adoption of the CCSS. It still remains somewhat unclear, however, which changes …

A Scalable Preconditioner For A Primal Dpg Method, Andrew T. Barker, Veselin A. Dobrev, Jay Gopalakrishnan, Tzanio Kolev

Portland Institute for Computational Science Publications

We show how a scalable preconditioner for the primal discontinuous Petrov-Galerkin (DPG) method can be developed using existing algebraic multigrid (AMG) preconditioning techniques. The stability of the DPG method gives a norm equivalence which allows us to exploit existing AMG algorithms and software. We show how these algebraic preconditioners can be applied directly to a Schur complement system arising from the DPG method. One of our intermediate results shows that a generic stable decomposition implies a stable decomposition for the Schur complement. This justifies the application of algebraic solvers directly to the interface degrees of freedom. Combining such results, we …

Computational Methods For Asynchronous Basins, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

For a Boolean network we consider asynchronous updates and define the exclusive asynchronous basin of attraction for any steady state or cyclic attractor. An algorithm based on commutative algebra is presented to compute the exclusive basin. Finally its use for targeting desirable attractors by selective intervention on network nodes is illustrated with two examples, one cell signalling network and one sensor network measuring human mobility.

Planar Graphs, Biplanar Graphs And Graph Thickness, Sean M. Hearon

Electronic Theses, Projects, and Dissertations

A graph is planar if it can be drawn on a piece of paper such that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this thesis, we determine the smallest complete and complete bipartite graphs that are not biplanar.

An Introduction To Boolean Algebras, Amy Schardijn

Electronic Theses, Projects, and Dissertations

This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and proved many properties involving Boolean algebras and related structures.

We …

Regular Round Matroids, Svetlana Borissova

Electronic Theses, Projects, and Dissertations

A matroid M is a finite set E, called the ground set of M, together with a notion of what it means for subsets of E to be independent. Some matroids, called regular matroids, have the property that all elements in their ground set can be represented by vectors over any field. A matroid is called round if its dual has no two disjoint minimal dependent sets. Roundness is an important property that was very useful in the recent proof of Rota's conjecture, which remained an unsolved problem for 40 years in matroid theory. In this thesis, we …

Bio-Mathematics: Introduction To The Mathematical Model Of The Hepatitis C Virus, Lucille J. Durfee

Electronic Theses, Projects, and Dissertations

In this thesis, we will study bio-mathematics. We will introduce differential equations, biological applications, and simulations with emphasis in molecular events. One of the first courses of action is to introduce and construct a mathematical model of our biological element. The biological element of study is the Hepatitis C virus. The idea in creating a mathematical model is to approach the biological element in small steps. We will first introduce a block (schematic) diagram of the element, create differential equations that define the diagram, convert the dimensional equations to non-dimensional equations, reduce the number of parameters, identify the important parameters, …

Some Spectral Properties Of A Quantum Field Theoretic Hamiltonian, Devin Burnell Mcghie

Theses and Dissertations

We derive the ground-state eigenvalues and eigenvectors for a simplified version of the 1-D QED single electron-photon model that Glasgow et al recently developed [2]. This model still allows for meaningful interaction between electrons and photons while keeping only the minimum needed to do so. We investigate the interesting spectral properties of this model. We determine that the eigenvectors are orthogonal as one would expect and normalize them.

Privacy Protection And Aggregate Health Data: A Review Of Tabular Cell Suppression Methods (Not) Employed In Public Health Data Systems, Gregory J. Matthews, Ofer Harel, Robert H. Aseltine Jr.

Mathematics and Statistics: Faculty Publications and Other Works

Public health research often relies on individuals’ confidential medical data. Therefore, data collecting entities, such as states, seek to disseminate this medical data as widely as possible while still maintaining the privacy of the individual for legal and ethical reasons. One common way in which this medical data is released is through the use of Web-based Data Query Systems (WDQS). In this article, we examined WDQS listed in the National Association for Public Health Statistics and Information Systems (NAPHSIS) specifically reviewing them for how they prevent statistical disclosure in queries that produce a tabular response. One of the most common …

Managing The Spread Of Alfalfa Stem Nematodes (Ditylenchus Dipsaci): The Relationship Between Crop Rotation Periods And Pest Re-Emergence, S. Jordan, Claudia Nischwitz, R. Ramirez, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against alfalfa stem nematodes and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties of alfalfa. In this paper we present a basic host-parasite model that describes the spread of the …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

Discrete And Continuous Operational Calculus In Stochastic Games, Kenneth Ibe Iwezulu

Theses and Dissertations

First, we consider a class of antagonistic stochastic games between two players A and B. The game is specified in terms of two "hostile" stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. This game is observed upon random epochs of time and the outcome of the game is not known in real time. The game ends at the time when the underlying fixed threshold of either player is crossed (referred to as the first passage time). The first passage time is then shifted to an epoch, i.e. upon one of the observation instants of time. …

Numerical Simulations Of Shock Waves Reflection And Interaction, Ligang Sun

Theses and Dissertations

The main objective of this dissertation is to detect and study the phenomena of reflection of one shock wave and interaction of two shock waves using numerical methods. In theory, solutions of non-linear Euler equations of compressive inviscid gas dynamics in two dimensions can display various features including shock waves and rarefaction waves. To capture the shock waves properly, highly accurate numerical schemes are designed according to second order Lax-Wendroff method. In this thesis, three numerical experiments were designed to show the reflection and interaction phenomena. Firstly, one shock was formed due to the encounter of two high speed gas …

Toral And Spherical Aluthge Transforms Of 2-Variable Weighted Shifts, Raul E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We introduce two natural notions of Aluthge transforms (toral and spherical) for 2-variable weighted shifts and study their basic properties. Next, we study the class of spherically quasinormal 2-variable weighted shifts, which are the fixed points for the spherical Aluthge transform. Finally, we briefly discuss the relation between spherically quasinormal and spherically isometric 2-variable weighted shifts.