Mathematics Commons^™

Polynomial Solutions To The Diophantine Equation X² + Y³ = 6912z², Emel Demirel

Theses, Dissertations and Culminating Projects

In this paper, I investigate polynomial solutions to the Diophantine equa­ tion, X² +Y³ = 6912Z², where X = g(x,y), Y = h(x,y) and Z = f(x,y) are polynomials with integer coefficients. The focus is on the greatest common di­ visors for the integer values of these polynomials when the polynomials f (x, y), g(x, y) and h(x, y) are relatively prime in Q[x, y]. However, for a fixed integer pair xo, Yo, the integer values f(x0,y0), g(x0, y0) and h(x0,y0) are not necessarily relatively prime in Z. I investigate the greatest common divisors (GCDs) of these three polynomial values …

Row Reduction Of Macaulay Matrices, Lorrin Debenport

Honors Theses

A computer can use a matrix to represent a system of non-linear multivariate polynomial equations. The fastest known ways to transform this system into a form with desirable computational properties rely on transforming its matrix into upper-triangular form [8, 9]. The matrix for such a system will have mostly zero entries, which we call sparse [7]. We propose to analyze several methods of performing row-reduction, the process by which matrices are reduced into upper-triangular form [2].

What is special about row-reducing matrices in this context? When row-reducing a matrix, swapping rows or columns is typically acceptable. However, if the order …

Statistical Inference Of A Measure For Two Binomial Variates, Serena Petersen

UNLV Theses, Dissertations, Professional Papers, and Capstones

We study measures of a comparison for two independent binomial variates which frequently occur in real situations. An estimator for measure of reduction (MOR) is considered for two sample proportions based on a modified maximum likelihood estimation. We study the desirable properties of the estimator: the asymptotic behavior of its unbiasedness and the variance of the estimator. Since the measure ρ is approximately normally distributed when sample sizes are sufficiently large, one may establish approximate confidence intervals for the true value of the estimators. For numerical study, the Monte Carlo experiment is carried out for the various scenarios of two …

Modules Over Localized Group Rings For Groups Mapping Onto Free Groups, Nicholas Davidson

Boise State University Theses and Dissertations

In 1964, Paul Cohn showed that if F is a finitely-generated free group, and Q a field, then all ideals in the group ring Q[F] are free as Q[F]-modules. In particular, all finitely-generated submodules of free Q[F]-modules are free. In 1990, Cynthia Hog-Angeloni reproved this theorem using techniques from geometric group theory. Leaning on Hog-Angeloni's methods, we prove an analogous statement for crossed products D * F, with D a division ring.

With this result in hand, we prove that if G = H⋊F, the semi-direct product …

A Stochastic Model For Wind Turbine Power Quality Using A Levy Index Analysis Of Wind Velocity Data, Jonathan Blackledge, Eugene Coyle, Derek Kearney

Conference papers

The power quality of a wind turbine is determined by many factors but time-dependent variation in the wind velocity are arguably the most important. After a brief review of the statistics of typical wind speed data, a non- Gaussian model for the wind velocity is introduced that is based on a Levy distribution. It is shown how this distribution can be used to derive a stochastic fractional diusion equation for the wind velocity as a function of time whose solution is characterised by the Levy index. A Levy index numerical analysis is then performed on wind velocity data for both …

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …

Fraction-Free Methods For Determinants, Deanna Richelle Leggett

Master's Theses

Given a matrix of integers, we wish to compute the determinant using a method that does not introduce fractions. Fraction-Free Triangularization, Bareiss’ Algorithm (based on Sylvester’s Identity) and Dodgson’s Method (based on Jacobi’s Theorem) are three such methods. However, both Bareiss’ Algorithm and Dodgson’s Method encounter division by zero for some matrices. Although there is a well-known workaround for the Bareiss Algorithm that works for all matrices, the workarounds that have been developed for Dodgson’s method are somewhat difficult to apply and still fail to resolve the problem completely. After investigating new workarounds for Dodgson’s Method, we give a modified …

Euler E271 : A Link Between Mathematics Of Yesterday, Today, And Tomorrow, Sarah Ann Nelson

Honors Theses

The major focus of this departmental thesis was to complete t he first English translation of E271 Arithmetic Theorems Proven by a New Method, a mathematical treatise published by Leonhard Euler in Latin in 1761. Most importantly, E271 contains Euler's generalization of Fermat's Litt le Theorem and an exploration of the properties of (n). Altogether, this paper includes an Abstract, Introduction, Note to the Readers, Translation of Arithmetic Theorems Proven by a New Method, Epilogue, and References. More specifically, the Introduction is about the historical background of the mathematics and applications leading up to E271 and the key corresponding mathematicians. …

Groups And Semigroups Generated By Automata, David Mccune

Department of Mathematics: Dissertations, Theses, and Student Research

In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups ``expanding automaton semigroups''. We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups …

Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer

Department of Mathematics: Dissertations, Theses, and Student Research

This work is primarily concerned with the study of artinian modules over commutative noetherian rings.

We start by showing that many of the properties of noetherian modules that make homological methods work seamlessly have analogous properties for artinian modules. We prove many of these properties using Matlis duality and a recent characterization of Matlis reflexive modules. Since Matlis reflexive modules are extensions of noetherian and artinian modules many of the properties that hold for artinian and noetherian modules naturally follow for Matlis reflexive modules and more generally for mini-max modules.

In the last chapter we prove that if the Betti …

Hilbert–Samuel And Hilbert–Kunz Functions Of Zero-Dimensional Ideals, Lori A. Mcdonnell

Department of Mathematics: Dissertations, Theses, and Student Research

The Hilbert-Samuel function measures the length of powers of a zero-dimensional ideal in a local ring. Samuel showed that over a local ring these lengths agree with a polynomial, called the Hilbert-Samuel polynomial, for sufficiently large powers of the ideal. We examine the coefficients of this polynomial in the case the ideal is generated by a system of parameters, focusing much of our attention on the second Hilbert coefficient. We also consider the Hilbert-Kunz function, which measures the length of Frobenius powers of an ideal in a ring of positive characteristic. In particular, we examine a conjecture of Watanabe and …

On Morrey Spaces In The Calculus Of Variations, Kyle Fey

Department of Mathematics: Dissertations, Theses, and Student Research

We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫_Ω f(x, u, ∇u)dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(|·|)^α(x), where h is an N-function.

Following this, we provide a characterization of the class of Young measures that can be generated by a sequence …

On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate the structure and properties of a variety of generalized Wiener spaces. Our main focus is on Wiener-type measures on spaces of continuous functions; our generalizations include an extension to multiple parameters, and a method of adjusting the distribution and covariance structure of the measure on the underlying function space.

In the second chapter, we consider single-parameter function spaces and extend a fundamental integration formula of Paley, Wiener, and Zygmund for an important class of functionals on this space. In the third chapter, we discuss measures on very general function spaces and introduce the specific example of a generalized …

Comparison Study Between Mapreduce (Mr) And Parallel Data Management Systems (Dbms) In Large Scale Data Analysis, Miriam Lawrence Mchome

Mathematics, Statistics, and Computer Science Honors Projects

As the quantity of structured and unstructured data increases, data processing
experts have turned to systems that analyze data using many computers in parallel.
This study looks at two systems designed for these needs: MapReduce and parallel
databases. In the MapReduce programming model, users express their problem in
terms of a map function and a reduce function. Parallel databases organize data as a
system of tables representing entities and relationships between them. Previous
comparison studies have focused on performance, concluding that these two
systems are complimentary. Parallel databases scored high on performance and
MapReduce scored high on flexibility in handling …

Soliton Solutions Of Ultradiscrete Integrable Systems, Wei Yin

Theses and Dissertations - UTB/UTPA

In recent years, ultradiscrete integrable systems, in which both independent and dependent variables are discretized, have attracted much attention. In this thesis, we show how to obtain all line soliton solutions of (2+1)-dimensional ultradiscrete soliton systems from determinant solutions of discrete soliton systems by taking an ultradiscrete limit. Taking an ultradiscrete limit of determinant solutions with non-negativity, we obtain Casorati determinant-like solutions. Starting from Grammian (Gram-type determinant), we obtain another expression of τ-functions, which leads to a perturbed form after the expansion of Grammian. These two different forms are essentially equivalent, i.e., it is possible to transform a form into …

Estimation Of Beta In A Simple Functional Capital Asset Pricing Model For High Frequency Us Stock Data, Yan Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project applies the methods of functional data analysis (FDA) to intra-daily returns of US corporations. It focuses on an extension of the Capital Asset Pricing Model (CAPM) to such returns. The CAPM is essentially a linear regression with the slope coefficient β. Returns of an asset are regressed on index return. We compare the estimates of β obtained for the daily and intra-daily returns. The variability of these estimates is assessed by two bootstrap methods. All computations are performed using statistical software R. Customized functions are developed to process the raw data, estimate the parameters and assess their variability. …

Temperature-Induced Activation Of Freshwater Cyanophage As-1 Prophage, Tin-Chun Chu, Sean R. Murray, Shi-Fang Hsu, Quinn Vega, Lee H. Lee

Department of Mathematics Faculty Scholarship and Creative Works

Synechococcus sp. IU 625 is one of the freshwater cyanobacteria responsible for harmful algal blooms (HAB). Cyanophages can serve as natural control agents and may be responsible for algal bloom prevention and disappearance. Cyanophage AS-1, which infects Synechococcus sp. IU 625 (Anacystis nidulans) and Synechococcus cedrorum, plays an important role in the environment, significantly altering the numbers of its hosts. Since seasonal (temperature-dependent) lytic induction of cyanobacterial prophage has been proposed to affect seawater algal blooms, we investigated if the AS-1 lytic cycle could be induced by a shift to high temperature. Our hypothesis was confirmed, as more phages were …

Negative Dependence And Srinivasan's Sampling Process, Josh Brown Kramer, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics Faculty Scholarship and Creative Works

Dubhashi, Jonasson and Ranjan Dubhashi, Jonasson and Ranjan (2007) study the negative dependence properties of Srinivasan's sampling processes (SSPs), random processes which sample sets of a fixed size with prescribed marginals. In particular they prove that linear SSPs have conditional negative association, by using the Feder-Mihail theorem and a coupling argument. We consider a broader class of SSPs that we call tournament SSPs (TSSPs). These have a tree-like structure and we prove that they have conditional negative association. Our approach is completely different from that of Dubhashi, Jonasson and Ranjan. We give an abstract characterization of TSSPs, and use this …

Graphshop: An Interactive Software Environment For Graph Theory Research And Applications, Aaron Andersen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Graph Theory is the mathematical study of the structure of abstract relationships between objects. Although these constructions (graphs) are themselves purely theoretical, their ability to model pair-wise relationships in systems of arbitrary complexity yields abundant direct correspondence with numerous important physical and societal systems in the real world. Additionally, the simple discrete nature of fundamental graph structures allows for easy pseudo-geometric visualization of graphs in a wide variety of ways. Taken together, these two properties suggest that graph theory teaching, research, and applications would benefit greatly from the use of a unified software environment for graph construction, interaction, and visualization. …

Hermite Polynomials And Sylvester Type Determinants, Kelly C. Stange

Mathematics and Statistics

In this paper, we first recall Hermite polynomials, a particular family of orthogonal polynomials. We then evaluate their recurrence relations in terms of Sylvester type determinants of certain tridiagnoal matrix.

Mathematical Justification Of Introductory Hypothesis Tests And Development Of Reference Materials, Jennifer L. Loveland

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This purpose of this project was to create a set of reference material for an introductory level statistics course. The focus was on the Neyman-Pearson approach to hypothesis testing. A brief historical development of the Neyman-Pearson approach is followed by mathematical proofs of each of the hypothesis tests covered in the reference material. The reference material includes the basic hypothesis tests taught in an introductory statistics course, the accompanying distributions, and prerequisite information.

Controlling Error Rates With Multiple Positively-Dependent Tests, Abdullah Al Masud

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

It is a typical feature of high dimensional data analysis, for example a microarray study, that a researcher allows thousands of statistical tests at a time. All inferences for the tests are determined using the p-values; a smaller p-value than the α-level of the test signifies a statistically significant test. As the number of tests increases, the chance of observing some small p-values is very high even when all null hypotheses are true. Consequently, we make wrong conclusions on the hypotheses. This type of potential problem frequently happens when we test several hypotheses simultaneously, i.e., the multiple testing problem. …

K-Hyponormality Of Powers Of Multivariable Weighted Shifts, Mayra O. Martinez

Theses and Dissertations - UTB/UTPA

In mathematics, weighted shifts, also known as shift operators or translation operators, are examples of linear operators. Single and multivariable weighted shifts have played an important role in the study of (joint) k-hyponormality to LPCS. They have also played a significant role in the study of cyclicity and reflexivity, in the study of C*-algebras generated by multiplication operators on Bergman spaces, as fertile ground to test new hypotheses, and as canonical models for theories of dilation and positivity. We will first consider the hyponormality of powers of commuting multivariable weighted shifts. Specifically, if we let W(α,β) := (T1, T2) denote …

Duffing-Van Der Pol-Type Nonlinear Oscillator System, Jing Cui

Theses and Dissertations - UTB/UTPA

In this thesis, we are concerned with the nonlinear Duffing–van der Pol–type oscillator system by means of the Lie symmetry reduction method. This system has physical relevance as a simple model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. By applying the Lie symmetry analysis, we find two nontrivial infinitesimal generators, and use them to construct canonical variables. Through the inverse analysis, some dynamical properties of the nonlinear system under certain parametric conditions are presented. Comparison with the existing results by the Prelle– Singer procedure is …

Sharp Feature Identification In A Polygon, Joseph P. Scanlan

UNLV Theses, Dissertations, Professional Papers, and Capstones

This thesis presents an efficient algorithm for recognizing and extracting sharp-features from polygonal shapes. As used here, a sharp-feature is a distinct portion of a polygon that is long and skinny. The algorithm executes in O(n^2) time, where n is the number of vertices in the polygon. Experimental results from a Java implementation of the algorithm are also presented.

Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He

Scholarship

We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences. Using a new polynomial sequence transformation technique presented in [12], we give a method to evaluate the measures and their supports of some orthogonal generalized Gegenbauer-Humbert polynomial sequences.

Zero-Sum Magic Graphs And Their Null Sets, Samuel M. Hansen

UNLV Theses, Dissertations, Professional Papers, and Capstones

For any element h of the Natural numbers, a graph G=(V,E), with vertex set V and edge set E, is said to be h-magic if there exists a labeling of the edge set E, using the integer group mod h such that the induced vertex labeling, the sum of all edges incident to a vertex, is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h for which G admits a zero-sum h-magic labeling. A graph G is said to be uniformly …

Modeling Mortality Rates For Leukemia Between Men And Women In The United States, Blessed Quansah

UNLV Theses, Dissertations, Professional Papers, and Capstones

Leukemia related deaths increased dramatically over the last forty years. Leukemia is a malignant disease or cancer of the bone marrow and blood. It is characterized by the uncontrolled accumulation of blood cells. Leukemia is divided into two categories: myelogenous or lymphocytic, each of which can be acute or chronic. The terms, myelogenous or lymphocytic denote the cell type involved.

In this thesis, the proposed modeling techniques are applied to leukemia deaths data from the Surveillance Epidemiology and End Results (SEER). In particular, annual deaths data from 1969 to 2007 are used in the data analysis, which includes three major …

The Minimum-Norm Least-Squares Solution Of A Linear System And Symmetric Rank-One Updates, Xuzhou Chen, Jun Ji

Faculty Articles

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able …