Mathematics Commons^™

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. …

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. …

Ranking Score Vectors Of Tournaments, Sebrina Ruth Cropper

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

Given , a tournament on vertices, Landau derived a method to determine how close is to being transitive or regular. This comparison is based on the tournament’s hierarchy number, ̅, a value derived from its score vector ̅ ( ). Let be the set of all score vectors of tournaments on vertices with the entries listed in non-decreasing order. A partial order, poset, exists on the set using the following binary relation. Given ̅ ̅ such that ̅ ̅, let ̅ ̅ if Σ Σ for and Σ Σ . Let this poset be represented as ( ) ( ) …

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.

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 …

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, Morgan E. Summers

Undergraduate Honors Capstone Projects

This qualitative research project focuses on the issues facing middle and secondary mathematics placement through an extensive literature review as well as a case study of a local school district. As students move from elementary school to middle and secondary schools, they are placed into classes that appear to be based on ability. One of the driving questions of this project is how is this ability level determined? Through an in-­‐depth look at one school district, it is found that a primary source of information is both norm-­‐referenced and criterion-­‐referenced assessments given to students in fifth and eighth grades. In …

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 …

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 …

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 …

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 …

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 …

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.

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. …

“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler

Mathematics Faculty Publications

During Spring 2009, Dr. Kessler created and published a comic book series that embedded math content into the story for 4th-6th grade students. The comics were well received in the classrooms at Cumberland Trace Elementary. Dr. Kessler contends that this approach to teaching and learning can be used in any content area, and is useful for engaging students who might not be as interested otherwise. This session will explore ways of utilizing the skills of your students to construct learning comics in your classes, regardless of the funds, technology, and artistic experience at your disposal. The session will include a …

2011 Sonia Kovalevsky Math For Girls Day Flyer, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

2011 Sonia Kovalevsky Math For Girls Day Evaluation Forms, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Presenter, student and teacher evaluation forms for the 6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

Integer Optimization And Computational Algebraic Topology, Bala Krishnamoorthy

Systems Science Friday Noon Seminar Series

We present recently discovered connections between integer optimization, or integer programming (IP), and homology. Under reasonable assumptions, these results lead to efficient solutions of several otherwise hard-to-solve problems from computational topology and geometric analysis. The main result equates the total unimodularity of the boundary matrix of a simplicial complex to an algebraic topological condition on the complex (absence of relative torsion), which is often satisfied in real-life applications . When the boundary matrix is totally unimodular, the problem of finding the shortest chain homologous under Z (ring of integers) to a given chain, which is inherently an integer program, can …

Public Policy, Long Run Growth And Economic Transition From Agriculture To Industrial Mass Production., Rudrani Bhattacharya Dr.

Doctoral Theses

It has been recognized that the heart of the development process lies on the transformation of an economy from traditional activities in agriculture to industrial activities. As emphasized by Lewis (1954), the movement of labor from primary sector to industry is conducive to the rise of economy’s savings and investment rate and thus fostering economic growth. The core of this paradigm is the historically observed rapid growth in today’s developed countries associated with expansion of industrial activities.It is well-documented by now that at least over a few centuries leading up to 1800 AD there was little change in the world …

Packings And Realizations Of Degree Sequences With Specified Substructures, Tyler Seacrest

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation focuses on the intersection of two classical and fundamental areas in graph theory:  graph packing and degree sequences.  The question of packing degree sequences lies naturally in this intersection, asking when degree sequences have edge-disjoint realizations on the same vertex set.  The most significant result in this area is Kundu's k-Factor Theorem, which characterizes when a degree sequence packs with a constant sequence.  We prove a series of results in this spirit, and we particularly search for realizations of degree sequences with edge-disjoint 1-factors.  

Perhaps the most fundamental result in degree sequence theory is the Erdos-Gallai Theorem, characterizing …