Mathematics Commons^™

Integrable Equations With Non-Smooth Solitons, Xianqi Li

Theses and Dissertations - UTB/UTPA

In this thesis, we present a class of integrable equations with non-smooth soliton solutions. In particular, we derive the bi-Hamiltonian structure and Lax pair of the equation pt = bux + \[{u2 — u1)p]x,p = u — uxx, which guarantee its integrability. Another interesting integrable equation we study is (=Jff!i)t = 2uux, which is exactly the first member of the negative KdV hierarchy. Through traveling wave setting arid phase step analysis, we obtain non-smooth soliton solutions of these integrable equations under different boundary condition at infinities. These equations were shown to have peaked soliton (peakon), "W/M-shape" peakon or cusped soliton …

A Comparative Study Of Risk Factors Involved In Diabetes Between Texas And Other States, Andres Padilla Oviedo

Theses and Dissertations - UTB/UTPA

Diabetes is a serious concern in the United States and Texas is a state with high percentage of diabetes. The risk factors contributing to diabetes are current smoking, high blood cholesterol, hypertension, physical inactivity etc. In this thesis, we would like to identify the crucial risk factors for Texas. This motivates us to use the online data resources for a comparative study between Texas and other states. Looking at the data, we decide to use independent sample t-tests and independent sample non parametric tests [Wilcoxon Mann Whitney] for such comparative studies. This analysis has two parts – in the first …

On The Dynamics Of Quasi-Self-Matings Of Generalized Starlike Complex Quadratics And The Structure Of The Mated Julia Sets, Ross Flek

Dissertations, Theses, and Capstone Projects

It has been shown that, in many cases, Julia sets of complex polynomials can be "glued" together to obtain a new Julia set homeomorphic to a Julia set of a rational map; the dynamics of the two polynomials are reflected in the dynamics of the mated rational map. Here, I investigate the Julia sets of self-matings of generalized starlike quadratic polynomials, which enjoy relatively simple combinatorics. The points in the Julia sets of the mated rational maps are completely classified according to their topology. The presence and location of buried points in these Julia sets are addressed. The interconnections between …

Stochastic Modeling Of Retail Mortgage Loans Based On Past Due, Prepaid, And Default States, Chang Liu

Doctoral Dissertations

Stochastic models were developed that provide important measures related to retail mortgages and credit cards for the management of a bank. Based on Markov theory, two models were developed that predict mortgage portfolio size and expected duration of stay in each of the states, which are defined according to the criteria of Basel Accord II and the Federal Reserve Bank. Also, to facilitate comparisons among different types of credit products and different time periods, a model was developed to generate a health index for a retail mortgage. This model could be easily extended, using multivariate regression or multivariate time series …

A Numerical Method For Obtaining An Optimal Temperature Distribution In A Three-Dimensional Triple-Layered Skin Structure Embedded With Multi-Level Blood Vessels, Xingui Tang

Doctoral Dissertations

The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of …

Developing A B -Tagging Algorithm Using Soft Muons At Level-3 For The Dø Detector At Fermilab, Mayukh Das

Doctoral Dissertations

The current data-taking phase of the DØ detector at Fermilab, called Run II, is designed to aid the search for the Higgs Boson. The neutral Higgs is postulated to have a mass of 117 GeV. One of the channels promising the presence of this hypothetical particle is through the decay of b-quark into a muon. The process of identifying a b-quark in a jet using muon as a reference is b-tagging with a muon tag.

At the current data taking and analysis rate, it will take long to reach the process of identifying valid events. The triggering mechanism of the …

A Numerical Method For Obtaining An Optimal Temperature Distribution In A 3d Triple-Layered Cylindrical Skin Structure, Le Zhang

Doctoral Dissertations

In recent years, it has been interesting to research hyperthermia combined with radiation and cytotoxic drugs to enhance the killing of tumors. The crucial problem is that when heating the tumor tissues, one needs to keep the surrounding normal tissue below a temperature that will produce harm. Thus, it is important to obtain the temperature field of the entire treatment region. The objective of this dissertation is to develop a numerical model for obtaining an optimal temperature distribution in a 3D triple-layered cylindrical skin structure. To this end, we pre-specify the temperatures to be obtained at the center and perimeter …

Computational Approaches To The Design And Analysis Of Stability Of Polypeptide Multilayer Thin Films, Bin Zheng

Doctoral Dissertations

The focus of this research is the development of computational approaches to understanding the physical basis of layer-by-layer assembly (LBL), a key methodology of nanomanufacturing. The results provided detailed information on structure which cannot be obtained directly by experiments.

The model systems chosen for study are polypeptide chains. Reasons for this are that polypeptides are no less polyelectrolytes than the more usual polyions, and one can control the primary structure of a polypeptide on a residue-by-residue basis using modern synthetic methods. Moreover, as peptides constitute one of the four major classes of biological macromolecules, research in this direction is expected …

A High -Order Finite Difference Method For Solving Bioheat Transfer Equations In Three-Dimensional Triple -Layered Skin Structure, Haofeng Yu

Doctoral Dissertations

Investigations on instantaneous skin burns are useful for an accurate assessment of burn-evaluation and for establishing thermal protections for various purposes. Meanwhile, hyperthermia with radiation is important in the treatment of cancer, and it is essential for developers and users of hyperthermia systems to predict, and interpret correctly the biomass thermal and vascular response to heating. In this dissertation, we employ the well-known Pennes' bioheat transfer equation to predict the degree of skin burn and the temperature distribution in hyperthermia cancer treatment.

A fourth-order compact finite difference scheme is developed to solve Pennes' bioheat transfer equation in a three-dimensional single …

Modeling Of The Inverse Heat -Conduction Problem With Application To Laser Chemical Vapor Deposition And Bioheat Transfer, Peng Zhen

Doctoral Dissertations

This dissertation consists of two parts. Part one deals with three-dimensional laser induced chemical vapor deposition (3D-LCVD), whereas part two deals with a Pennes model of a 3D skin structure. LCVD is an important technique in manufacturing complex micro-structures with high aspect ratio. In part one, a numerical model was developed for simulating kinetically-limited growth of an axisymmetric cylindrical rod by pre-specifying the surface temperature distribution required for growing the rod and then by obtaining optimized laser power that gives rise to the pre-specified temperature distribution. The temperature distribution at the surface of the rod was assumed to be at …

Pattern Recognition For Electric Power System Protection, Yong Sheng

Doctoral Dissertations

The objective of this research is to demonstrate pattern recognition tools such as decision trees (DTs) and neural networks that will improve and automate the design of relay protection functions in electric power systems. Protection functions that will benefit from the research include relay algorithms for high voltage transformer protection (TP) and for high impedance fault (HIF) detection. A methodology, which uses DTs and wavelet analysis to distinguish transformer internal faults from other conditions that are easily mistaken for internal faults, has been developed. Also, a DT based solution is proposed to discriminate HIFs from normal operations that may confuse …

Fuzzy Product -Limit Estimators: Soft Computing In The Presence Of Very Small And Highly Censored Data Sets, Kian Lawrence Pokorny

Doctoral Dissertations

When very few data are available and a high proportion of the data is censored, accurate estimates of reliability are problematic. Standard statistical methods require a more complete data set, and with any fewer data, expert knowledge or heuristic methods are required. In the current research a computational system is developed that obtains a survival curve, point estimate, and confidence interval about the point estimate.

The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The “fuzzy” data are then used to estimate a survival curve, and the mean survival …

Modeling And Experimental Verification Of Growth Of An Axisymmetric Cylindrical Rod By Three-Dimensional Laser-Induced Chemical Vapor Deposition, Qing Chen

Doctoral Dissertations

Three-dimensional laser-induced chemical vapor deposition (3D-LCVD) is a recently developed micro-manufacturing process that holds great potential for the production of complex microstructures with high aspect ratio. A laser beam is focused through a vacuum chamber window onto a movable substrate. The heat from the laser at or near the focal spot on the substrate induces the decomposition reaction of precursor gas in the chamber. As a result, solid-phase reaction products are deposited on the substrate to form the microstructure. In this dissertation, a numerical model is developed for simulating kinetically-limited growth of an axisymmetric cylindrical rod by pre-specifying the surface …

A Multigrid Method For Elliptic Grid Generation Using Compact Schemes, Balaji S. Iyangar

Doctoral Dissertations

Traditional iterative methods are stalling numerical processes, in which the error has relatively small changes from one iteration to the next. Multigrid methods overcome the limitations of iterative methods and are computationally efficient. Convergence of iterative methods for elliptic partial differential equations is extremely slow. In particular, the convergence of the non-linear elliptic Poisson grid generation equations used for elliptic grid generation is very slow. Multigrid methods are fast converging methods when applied to elliptic partial differential equations. In this dissertation, a non-linear multigrid algorithm is used to accelerate the convergence of the non-linear elliptic Poisson grid generation method. The …

Orbit Structure Of Finite And Reductive Monoids, Zhuo Li

Digitized Theses

A reductive monoid is an algebraic monoid with a reductive unit group. We introduce a new class of reductive monoids, $({\cal T}, \sigma)$-irreducible monoids. Generally, we have the question of finding the orbits of the unit group of a reductive monoid acting on both sides of the monoid. Putcha and Renner give a recipe to determine the orbits for ${\cal T}$-irreducible monoids. Motivated by their construction of finite reductive monoids, the concept of (${\cal T}, \sigma)$-irreducible monoid arises naturally.

We obtain that the ${\cal T}$-irreducible monoids turn out to be a special class of the $({\cal T}, \sigma)$-irreducible monoids. We …