Fraction-Free Methods For Determinants, 2011 University of Southern Mississippi

#### 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 ...

Ultrametric Properties Of Homotopy And Refinement Critical Values, 2011 University of Tennessee, Knoxville

#### Ultrametric Properties Of Homotopy And Refinement Critical Values, Steven Derochers

*Chancellor’s Honors Program Projects*

No abstract provided.

Tqft Diffeomorphism Invariants And Skein Modules, 2011 University of Iowa

#### Tqft Diffeomorphism Invariants And Skein Modules, Paul Harlan Drube

*Theses and Dissertations*

There is a well-known correspondence between two-dimensional topological quantum field theories (2-D TQFTs) and commutative Frobenius algebras. Every 2-D TQFT also gives rise to a diffeomorphism invariant of closed, orientable two-manifolds, which may be investigated via the associated commutative Frobenius algebras. We investigate which such diffeomorphism invariants may arise from TQFTs, and in the process uncover a distinction between two fundamentally different types of commutative Frobenius algebras ("weak" Frobenius algebras and "strong" Frobenius algebras). These diffeomorphism invariants form the starting point for our investigation into marked cobordism categories, which generalize the local cobordism relations developed by Dror Bar-Natan during his ...

Bifurcation Theory For A Class Of Second Order Differential Equations, 2011 University of Iowa

#### Bifurcation Theory For A Class Of Second Order Differential Equations, Alvaro Correa

*Theses and Dissertations*

We consider positive solutions of the nonlinear two point boundary value problem *u‘‘+λf(u)=0, u(-1)=u(1)=0 *, *f(u)=u(u-a)(u-b)(u-c)(1-u), 0*, depending on a parameter λ. Each solution *u(x)* is even function, and it is uniquely identified by *α=u(0)*. We will prove, using delicate integral estimates that *α=b,1* are not bifurcations points. We explore and prove a series of properties which restrict the location of a bifurcation point by studying the change of concavity of the graph of *f* and the points where the rays from *0 ...*

On Commutativity Of Unbounded Operators In Hilbert Space, 2011 University of Iowa

#### On Commutativity Of Unbounded Operators In Hilbert Space, Feng Tian

*Theses and Dissertations*

We study several unbounded operators with view to extending von Neumann's theory of deficiency indices for single Hermitian operators with dense domain in Hilbert space. If the operators are non-commuting, the problems are difficult, but special cases may be understood with the use representation theory. We will further study the partial derivative operators in the coordinate directions on the L^{2} space on various covering surfaces of the punctured plane. The operators are defined on the common dense domain of C^{∞} functions with compact support, and they separately are essentially selfadjoint, but the unique selfadjoint extensions will be non-commuting ...

A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, 2011 Missouri University of Science and Technology

#### A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le

*Mathematics and Statistics Faculty Research & Creative Works*

In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.

Sharp Feature Identification In A Polygon, 2011 University of Nevada, Las Vegas

#### 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.

Zero-Sum Magic Graphs And Their Null Sets, 2011 University of Nevada, Las Vegas

#### 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 ...

Statistical Inference Of A Measure For Two Binomial Variates, 2011 University of Nevada, Las Vegas

#### 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 ...

Euler E271 : A Link Between Mathematics Of Yesterday, Today, And Tomorrow, 2011 University of Tennessee at Chattanooga

#### 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 ...

Comparison Study Between Mapreduce (Mr) And Parallel Data Management Systems (Dbms) In Large Scale Data Analysis, 2011 Macalester College

#### 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 ...

On The Homology Of Automorphism Groups Of Free Groups., 2011 University of Tennessee, Knoxville

#### On The Homology Of Automorphism Groups Of Free Groups., Jonathan Nathan Gray

*Doctoral Dissertations*

Following the work of Conant and Vogtmann on determining the homology of the group of outer automorphisms of a free group, a new nontrivial class in the rational homology of Outer space is established for the free group of rank eight. The methods started in [8] are heavily exploited and used to create a new graph complex called the space of good chord diagrams. This complex carries with it significant computational advantages in determining possible nontrivial homology classes.

Next, we create a basepointed version of the Lie operad and explore some of it proper- ties. In particular, we prove a ...

Row Reduction Of Macaulay Matrices, 2011 University of Southern Mississippi

#### 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 ...

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, 2011 Utah State University

#### 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 ...

Modules Over Localized Group Rings For Groups Mapping Onto Free Groups, 2011 Boise State University

#### 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 of *H *with *F*, so that the group ...

Interplay Between Anomalous Transport And Catalytic Reaction Kinetics In Single-File Nanoporous Systems, 2011 Iowa State University

#### Interplay Between Anomalous Transport And Catalytic Reaction Kinetics In Single-File Nanoporous Systems, Dajiang Liu, Jigang Wang, David Ackerman, Igor I. Slowing, Marek Pruski, Hung-Ting Chen, Victor S.-Y. Lin, James W. Evans

*Ames Laboratory Publications*

Functionalized nanoporous materials have broad utility for catalysis applications. However, the kinetics of catalytic reaction processes in these systems can be strongly impacted by the anomalous transport. The most extreme case corresponds to single-file diffusion for narrow pores in which species cannot pass each other. For conversion reactions with a single-file constraint, traditional mean-field-type reaction-diffusion equations fail to capture the initial evolution of concentration profiles, and they cannot describe the scaling behavior of steady-state reactivity. Hydrodynamic reaction-diffusion equations accounting for the single-file aspects of chemical diffusion can describe such initial evolution, but additional refinements are needed to incorporate fluctuation effects ...

A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance, 2011 Bryant University

#### A Multiple Regression Analysis Of Personality’S Impact On Actuarial Exam Performance, Matthew Ciaffone

*Honors Projects in Mathematics*

Existing literature indicates that there is some connection between personality and both academic and work-related performance. The author's intent for the research described herein is to explore this connection for students majoring in actuarial mathematics with regard to their performance on actuarial certification exams. Specifically, using the five-factor model of personality, the author seeks to predict the number of attempts required to pass the first two exams in the process (Exam 1/P - probability; Exam 2/FM - financial mathematics) using measures of the five dimensions of the five-factor model (openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability) through ...

Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, 2011 Bryant University

#### Factors Related To Math Performance And Potential Benefits Of One-On-One Instruction, Amanda Zagame

*Honors Projects in Mathematics*

This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This ...

Convolution Equations In Spaces Of Distributions Supported By Cones, 2011 University of Bordeaux

#### Convolution Equations In Spaces Of Distributions Supported By Cones, Alex Meril, Daniele C. Struppa

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We describe some examples of surjective convolutors on D'(T), for T a closed convex cone in Rn. We also give necessary and suffficient conditions on Si,..., Sm in S'(T) to be generators of the whole convolution algebra S'(F).

Continuous Blooming Of Convex Polyhedra, 2011 Massachusetts Institute of Technology

#### Continuous Blooming Of Convex Polyhedra, Erik D. Demaine, Martin L. Demaine, Vi Hart, Joan Iacono, Stefan Langerman, Joseph O'Rourke

*Computer Science: Faculty Publications*

We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number of cuts) to have a continuous blooming.