Browsing PhD Dissertations - DO NOT EDIT by Issue Date
Now showing items 41-60 of 154
-
Numerical Integration Of Matrix Riccati Differential Equations With Solution Singularities
(Mathematics, 2013-07-22)A matrix Riccati differential equation (MRDE) is a quadratic ODE of the form X' = A₂₁ + A₂₂X - XA₁₁ - XA₁₂X ; where X is a function of t with X : R Rnxm and the Aij's are constant or functions of t with matrix sizes ... -
Optimal Stopping For Markov Modulated Ito-diffusion With Applications To Finance
(Mathematics, 2013-07-22)Despite the outstanding success of the Black-Scholes model, it relies on the assumption that drift and volatility of the underlying equity remain constant throughout time. This inaccuracy has motivated a number of interesting ... -
Numerical Studies For M-Matrix Algebraic Riccati Equations
(Mathematics, 2013-10-22)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 ... -
The Polynomial Chaos Method With Applications To Random Differential Equations
(Mathematics, 2013-10-22)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 ... -
Effects Of Discrete Time Delays And Parameters Variation On Dynamical Systems
(Mathematics, 2013-10-23)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 ... -
Mathematical Models Of Nutrient Recycling And Toxin Production In A Gradostat
(Mathematics, 2013-10-23)We discuss several gradostat models in which a microbial population excretes a biochemical that can get recycled back into the system as a nutrient source. Each mathematical model consists of six ordinary differential ... -
DNS Study For The Origin Of The Chaos In Late Boundary Layer Transition Over A Flat Plate
(Mathematics, 2014-03-12)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 ... -
High Order Numerical Schemes For PDEs And Applications To CFD
(Mathematics, 2014-03-12)In the past two decades, many efforts have been made in developing high-order schemes with high resolution, such as compact scheme, essentially non-oscillatory scheme (ENO), weighted essentially non-oscillatory scheme ... -
A Generalized Approach To Darboux Transformations For Differential Equations
(Mathematics, 2014-07-14)A Darboux transformation is a mathematical procedure to produce a solution to a differential equation when the solution to a related differential equation is known. The basic idea behind a Darboux transformation is to ... -
Haplotype-based Statistical Inference For Case-control Genetic Association Studies With Complex Sampling
(Mathematics, 2014-09-17)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 ... -
A Method For Exact Solutions To Integrable Evolution Equations In 2+1 Dimensions
(Mathematics, 2014-09-17)A systematic method is developed to obtain solution formulas for certain explicit solutions to integrable nonlinear partial differential equations in two spatial variables and one time variable. The method utilizes an ... -
Applications Of Cubical Arrays In The Study Of Finite Semifields
(Mathematics, 2014-09-17)It is well known that any finite semifield, S, can be viewed as an n-dimensional vector space over a finite field or prime order, Fp, and that the multiplication in S defines and can be defined by an n x n x n cubical ... -
Representation Theory Of Totally Reflexive Modules Over non-Gorenstein Rings
(Mathematics, 2014-09-17)In the late 1960's Auslander and Bridger published Stable Module Theory, in whichthe idea of totally reflexive modules first appeared. These modules have been studiedby many. However, a bulk of the information known about ... -
Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity
(Mathematics, 2014-09-17)A preliminary test estimator of variance in the bivariate normal distribution is proposed after Pitman-Morgan test of homogeneity of two variances. We propose one estimator of variance after preliminary test of two tails ... -
Properties Of The Pinched Tensor Product
(Mathematics, 2014-12)For complexes of modules we study a new construction, called the pinched tensor product, which was introduced by Lars Winther Christensen and David A. Jorgensen to study Tate homology. We explore properties of the pinched ... -
Numerical LES For MVG Controlled Supersonic Ramp Flow
(Mathematics, 2014-12)An implicitly implemented large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with micro-ramp vortex generators (MVG) at Mach 2.5 and Re=5760. ... -
Stochastic Reliability Models for a General Server and Related Networks
(2016-04-22)There are many types of systems which can be dubbed servers, i.e. a retail checkout counter, a shipping company, a web server, or a customer service hotline. All of these systems have common general behavior: requests or ... -
A Bisection Method for the Banded Hyperbolic Quadratic Eigenvalue Problem
(2016-05-10)It is well-known that the eigenvalues of a Hermitian matrix in a given interval can be approximated within a predefined error tolerance using the bisection method as a direct application of the Sylvester's Law of Inertia. ... -
On the Quantum Spaces of Some Quadratic Regular Algebras of Global Dimension Four
(2016-05-10)A quantum $\mathbb{P}^3$ is a noncommutative analogue of a polynomial ring on four variables, and, herein, it is taken to be a regular algebra of global dimension four. It is well known that if a generic quadratic quantum ... -
Representations of the Extended Poincare Superalgebras in Four Dimensions
(2016-05-13)Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner’s students spent considerable amount of time translating ...