Mathematics Commons^™

Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems, Ibrahim Oumar Diakite

Mathematics Dissertations - Archive

To understand the effects of discrete time delays and of parameters variation on certain biological system models, we first consider a Delay Differential Equation model of human immunodeficiency virus (HIV). We investigate the effects of the discrete time on the virulence of the HIV strain, and present sufficient and necessary condition for the virulence of the pathogen to change as the time delay changes. We also consider the same delay differential model for HIV infection, and we investigate analytically and numerically the stability of the endemically infected equilibrium. Our analysis shows that certain key parameters, such as the rate of …

Haplotype-Based Statistical Inference For Case-Control Genetic Association Studies With Complex Sampling, Daoying Lin

Mathematics Dissertations - Archive

With the advances in human genome research, it is now believed that the risks of many complex diseases are triggered by the interplay of genetic susceptibilities and environmental exposures. The population-based case-control study (PBCCS) is widely used to investigate the role of genetic variants and environmental exposures in the etiology of complex diseases. There are numerous ways to implement the selection process of cases and controls. In its simplest form, a simple random sampling (SRS) design is used to choose cases and controls from diseased and disease-free population, respectively. Though SRS is easy to conduct and relevant statistical methodologies are …

The Polynomial Chaos Method With Applications To Random Differential Equations, Juan Antonio Licea Salazar

Mathematics Dissertations - Archive

The role of randomness in mathematical models is of paramount importance, with emphasis placed upon the accuracy and reliability of predictions a rational approach is the use of differential equations with random parameters to describe natural phenomena. Well known methods such as Monte Carlo methods and the method of moments have been implemented to approximate the solutions to random differential equations in the last few decades. In this work, analytic solutions to a particular Riccati type dierential equation and discrete delay dierential equation with random coefficients are derived, also, due to its spectral rate of convergence and simplicity, the polynomial …

Numerical Studies For M-Matrix Algebraic Riccati Equations, Weichao Wang

Mathematics Dissertations - Archive

A new doubling algorithm - Alternating-Directional Doubling Algorithm (ADDA) - is developed for computing the unique minimal nonnegative solution of an M-Matrix Algebraic Riccati Equation (MARE). It is argued by both theoretical analysis and numerical experiments that ADDA is always faster than two existing doubling algorithms - SDA of Guo, Lin, and Xu (Numer. Math., 103 (2006), pp. 393-412) and SDA-ss of Bini, Meini, and Poloni (Numer. Math., 116 (2010), pp. 553-578) for the same purpose. A deflation technique is then presented for an irreducible singular M-matrix Algebraic Riccati Equation (MARE). The technique improves the rateof convergence of a doubling …

Dns Study For The Origin Of The Chaos In Late Boundary Layer Transition Over A Flat Plate, Manoj Kumar Thapa

Mathematics Dissertations - Archive

This dissertation is devoted to the investigation of the origin and mechanism of chaos ( asymmetric or disorganized flow) in late boundary layer transition over a flat plate without pressure gradient. This kind of flow not only exists at the very late stage of transition but also is a crucial component for turbulence formation- still not well understood. According to existing theories, the formation of the chaos in late boundary layer transition was considered due to big background disturbances (noises) and use of non-periodic spanwise boundary condition during numerical simulations. It was further assumed that universal coherent structures (ring-like vortices) …

Toric Varieties And Cobordism, Andrew Wilfong

Theses and Dissertations--Mathematics

A long-standing problem in cobordism theory has been to find convenient manifolds to represent cobordism classes. For example, in the late 1950's, Hirzebruch asked which complex cobordism classes can be represented by smooth connected algebraic varieties. This question is still open. Progress can be made on this and related problems by studying certain convenient connected algebraic varieties, namely smooth projective toric varieties. The primary focus of this dissertation is to determine which complex cobordism classes can be represented by smooth projective toric varieties. A complete answer is given up to dimension six, and a partial answer is described in dimension …

Regularity And Uniqueness Of Some Geometric Heat Flows And It's Applications, Tao Huang

Theses and Dissertations--Mathematics

This manuscript demonstrates the regularity and uniqueness of some geometric heat flows with critical nonlinearity.

First, under the assumption of smallness of renormalized energy, several issues of the regularity and uniqueness of heat flow of harmonic maps into a unit sphere or a compact Riemannian homogeneous manifold without boundary are established.

For a class of heat flow of harmonic maps to any compact Riemannian manifold without boundary, satisfying the Serrin's condition,

the regularity and uniqueness is also established.

As an application, the hydrodynamic flow of nematic liquid crystals in Serrin's class is proved to be regular and unique.

The natural …

Relative Perturbation Theory For Diagonally Dominant Matrices, Megan Dailey

Theses and Dissertations--Mathematics

Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well conditioned L factor. We then establish relative perturbation bounds for the inverse that are entrywise and independent of the condition number. This allows us to also present relative perturbation bounds for the linear system Ax=b that are independent of the condition number. Lastly, we continue the work of Ye to provide relative perturbation bounds …

When Cp(X) Is Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

Let M be a metrizable group. Let G be a dense subgroup of M^X . If G is domain representable, then G = MX . The following corollaries answer open questions. If X is completely regular and C_p(X) is domain representable, then X is discrete. If X is zero-dimensional, T₂ , and C_p(X;D) is subcompact, then X is discrete.

An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai

Mathematics Faculty Publications

We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.

An Example Employing Convexity In Functional Fixed Point Arguments, Richard I. Avery, Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

This paper illustrates a convexity technique to be employed with functional fixed point theorems in proving the existence of solutions to boundary value problems.

Hjb Equation And Statistical Arbitrage Applied To High Frequency Trading, Yonggi Park

Electronic Theses and Dissertations

In this thesis we investigate some properties of market making and statistical arbitrage applied to High Frequency Trading (HFT). Using the Hamilton-Jacobi-Bellman(HJB) model developed by Guilbaud, Fabien and Pham, Huyen in 2012, we studied how market making works to obtain optimal strategy during limit order and market order. Also we develop the best investment strategy through Moving Average, Exponential Moving Average, Relative Strength Index, Sharpe Ratio.

More On Intuitionistic Neutrosophic Soft Sets, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Intuitionistic Neutrosophic Soft Set theory proposed by S. Broumi and F. Samarandache [28], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper new operations on intuitionistic neutrosophic soft sets have been introduced . Some results relating to the properties of these operations have been established. Moreover ,we illustrate their interconnections between each other.

(P,\\Lambda)-Koszul Algebras And Modules, Ii, Jiafeng Lu

Turkish Journal of Mathematics

This paper is a continuous work of [14], where the notions of (p,\lambda)-Koszul algebra and (p,\lambda)-Koszul module were first introduced. More precisely, some new criteria for a positively graded algebra to be (p,\lambda)-Koszul are provided. We also generalize (p,\lambda)-Koszul objects to the nongraded case and define the so-called quasi-(p,\lambda)-Koszul objects. Further, the relationships between (quasi-) (p,\lambda)-Koszul modules and minimal Horseshoe Lemma are established.

On Some Results On Ip-Graphs, Roghayeh Hafezieh, Moohammadali Iranmanesh

Turkish Journal of Mathematics

The IP-graph of a naturally valenced association scheme and some of its properties have been studied recently. In this paper we introduce the bipartite version of this graph for a naturally valenced association scheme (X,S), denoted by BIP(S). We also investigate some of its properties.

On The Centroid Of Prime Semirings, Hasret Yazarli, Mehmet Ali̇ Öztürk

Turkish Journal of Mathematics

We define and study the extended centroid of a prime semiring. We show that the extended centroid is a semifield and give some properties of the centroid of a right multiplicatively cancellable prime semiring.

Math Department Newsletter, 2012-2013 (Year In Review), Mathematics Department

Mathematics Newsletter

No abstract provided.

Horizon Content Knowledge In The Work Of Teaching: A Focus On Planning, Nick Wasserman, Julianna Connelly Stockton

Mathematics Faculty Publications

Horizon content knowledge, one component of Ball et al.’s mathematical knowledge for teaching framework (e.g., Ball, Thames, & Phelps, 2008), has yet to reach adequate clarity and consensus in the field. Recently, various scholars have worked to further conceptualize and describe the mathematical horizon (e.g., Jakobsen, Thames & Ribeiro, 2013; Figueiras et al., 2011; Zazkis & Mamolo, 2011). In this communication, we identify some limitations in the ways such knowledge has thus far been described and offer an additional form of potential impact of horizon content knowledge on the work of teaching.

Eigenfunction Expansions Associated With The One-Dimensional Schrödinger Operator, Daphne Gilbert

Articles

We consider the form of eigenfunction expansions associated with the time-independent Schrödinger operator on the line, under the assumption that the limit point case holds at both of the infinite endpoints. It is well known that in this situation the multiplicity of the operator may be one or two, depending on properties of the potential function. Moreover, for values of the spectral parameter in the upper half complex plane, there exist Weyl solutions associated with the restrictions of the operator to the negative and positive half-lines respectively, together with corresponding Titchmarsh-Weyl functions.

Structure Theorems For Rings Under Certain Coactions Of A Hopf Algebra, Gaetana Restuccia, Rosanna Utano

Turkish Journal of Mathematics

Let \{D_1,..., D_n\} be a system of derivations of a k-algebra A, k a field of characteristic p > 0, defined by a coaction \delta of the Hopf algebra H_c = k[X_1,..., X_n]/(X_1^p,..., X_n^p), c \in \{0,1\}, the Lie Hopf algebra of the additive group and the multiplicative group on A, respectively. If there exist x_1, \dots, x_n \in A, with the Jacobian matrix (D_i(x_j)) invertible, [D_i,D_j] = 0, D_i^p = cD_i, c \in \{0, 1\}, 1 \leq i, j \leq n, we obtain elements y_1,..., y_n \in A, such that D_i(y_j) = \delta_{ij}(1 + cy_i), using properties of H_c-Galois extensions. …