Optimal Control In Discrete Pest Control Models, 2010 University of Tennessee - Knoxville

#### Optimal Control In Discrete Pest Control Models, Kathryn Dabbs

*University of Tennessee Honors Thesis Projects*

No abstract provided.

An Exploration Of Optimization Algorithms And Heuristics For The Creation Of Encoding And Decoding Schedules In Erasure Coding, 2010 University of Tennessee - Knoxville

#### An Exploration Of Optimization Algorithms And Heuristics For The Creation Of Encoding And Decoding Schedules In Erasure Coding, Catherine D. Schuman

*University of Tennessee Honors Thesis Projects*

No abstract provided.

Assessing The Impact Of A Computer-Based College Algebra Course, 2010 University of Southern Mississippi

#### Assessing The Impact Of A Computer-Based College Algebra Course, Ningjun Ye

*Dissertations*

USM piloted the Math Zone in Spring 2007, a computer-based program in teaching MAT 101and MAT 099 in order to improve student performance. This research determined the effect of the re-design of MAT 101 on student achievements in comparison to a traditional approach to the same course. Meanwhile, the study investigated possible effects of the Math Zone program on students’ attitude toward studying mathematics.

This study shows that there was no statistically significant difference on MAT101 final exam scores between the Math Zone students and the Classroom students in Fall 2007, Spring 2008 and Fall 2008. At the same time ...

Discrete Fractional Calculus And Its Applications To Tumor Growth, 2010 Western Kentucky University

#### Discrete Fractional Calculus And Its Applications To Tumor Growth, Sevgi Sengul

*Masters Theses & Specialist Projects*

Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the *n*-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make *n*- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractional calculus while ...

The Life Of Evariste Galois And His Theory Of Field Extension, 2010 Liberty University

#### The Life Of Evariste Galois And His Theory Of Field Extension, Felicia N. Adams

*Senior Honors Theses*

Evariste Galois made many important mathematical discoveries in his short lifetime, yet perhaps the most important are his studies in the realm of field extensions. Through his discoveries in field extensions, Galois determined the solvability of polynomials. Namely, given a polynomial P with coefficients is in the field F and such that the equation P(x) = 0 has no solution, one can extend F into a field L with α in L, such that P(α) = 0. Whereas Galois Theory has numerous practical applications, this thesis will conclude with the examination and proof of the fact that it is impossible ...

Relative Primeness, 2010 University of Iowa

#### Relative Primeness, Jeremiah N. Reinkoester

*Theses and Dissertations*

In [2], Dan Anderson and Andrea Frazier introduced a generalized theory of factorization. Given a relation *τ* on the nonzero, nonunit elements of an integral domain *D*, they defined a *τ-factorization* of *a* to be any proper factorization *a = λa _{1} · · · a_{n}* where

*λ*is in

*U (D)*and

*a*is

_{i}*τ*-related to

*a*, denoted

_{j}*a*, for

_{i}τ a_{j}*i*not equal to

*j*. From here they developed an abstract theory of factorization that generalized factorization in the usual sense. They were able to develop a number of results analogous to results already known ...

Endomorphisms, Composition Operators And Cuntz Families, 2010 University of Iowa

#### Endomorphisms, Composition Operators And Cuntz Families, Samuel William Schmidt

*Theses and Dissertations*

If b is an inner function and T is the unit circle, then composition with b induces an endomorphism, β, of L^{1}(T) that leaves H^{1}(T) invariant. In this document we investigate the structure of the endomorphisms of B(L^{2}(T)) and B(H^{2}(T)) that implement by studying the representations of L^{1}(T) and H^{1}(T) in terms of multiplication operators on

B(L^{2}(T)) and B(H^{2}(T)). Our analysis, which was inspired by the work of R. Rochberg and J. McDonald, will range from the theory of composition ...

Weighted Inverse Weibull And Beta-Inverse Weibull Distribution, 2010 Georgia Southern University

#### Weighted Inverse Weibull And Beta-Inverse Weibull Distribution, Jing Xiong Kersey

*Electronic Theses and Dissertations*

The weighted inverse Weibull distribution and the beta-inverse Weibull distribution are considered. Theoretical properties of the inverse Weibull model, weighted inverse Weibull distribution including the hazard function, reverse hazard function, moments, moment generating function, coefficient of variation, coefficient of skewness, coefficient of kurtosis, Fisher information and Shanon entropy are studied. The estimation for the parameters of the length-biased inverse Weibull distribution via maximum likelihood estimation and method of moment estimation techniques are presented, as well as a test for the detection of length-biasedness in the inverse Weibull model. Furthermore, the beta-inverse Weibull distribution which is a weighted distribution is presented ...

The Effect Of Explicit Timing On Math Performance Using Interspersal Assignments With Students With Mild/Moderate Disabilities, 2010 Utah State University

#### The Effect Of Explicit Timing On Math Performance Using Interspersal Assignments With Students With Mild/Moderate Disabilities, Fangjuan Hou

*All Graduate Theses and Dissertations*

Explicit timing and interspersal assignments have been validated as effective methods to facilitate students' math practice. However, no researchers have explored the combinative effect of these two methods. In Study 1, we extended the literature by comparing the effect of explicit timing with interspersal assignments, and interspersal assignments without timing. Generally, participants' rate of digits correct on easy and hard addition problems was higher during the explicit timing condition than during the untimed condition. However, the participants' rate of digits correct decreased after initial implementation of the explicit timing condition.

Motivation plays a crucial role in maintaining performance levels and ...

Option Pricing And Stable Trading Strategies In The Presence Of Information Asymmetry, 2010 Western Michigan University

#### Option Pricing And Stable Trading Strategies In The Presence Of Information Asymmetry, Anirban Dutta

*Dissertations*

Pricing derivatives is one of the central issues in mathematical finance. The seminal work of Black, Scholes and Merton has been the cornerstone of option pricing since their introduction in 1973. Their work influenced the pricing theory of other derivatives as well.

This derivative pricing theory has two primary shortcomings. Firstly, the theoretical pricing in such theories are not accompanied by a stable trading strategy. Secondly, they often assume that the market agents use a uniform model for the underlying instrument and that the market prices of the derivatives reveal all the information about the underlying instrument.

Theoreticians like Grossman ...

Analysis Of Discrete Data Under Order Restrictions, 2010 Georgia Southern University

#### Analysis Of Discrete Data Under Order Restrictions, Jeff Campbell

*Electronic Theses and Dissertations*

Strategies for the analysis of discrete data under order restrictions are discussed. We consider inference for sequences of binomial populations, and the corresponding risk difference, relative risk and odds ratios. These concepts are extended to deal with independent multinomial populations. Natural orderings such as stochastic ordering and cumulative ratio probability ordering are discussed. Methods are developed for the estimation and testing of differences between binomial as well as multinomial populations under order restrictions. In particular, inference for sequences of ordered binomial probabilities and cumulative probability ratios in multinomial populations are presented. Closed-form estimates of the multinomial parameters under order restrictions ...

Carleson-Type Inequalitites In Harmonically Weighted Dirichlet Spaces, 2010 University of Tennessee - Knoxville

#### Carleson-Type Inequalitites In Harmonically Weighted Dirichlet Spaces, Gerardo Roman Chacon Perez

*Doctoral Dissertations*

Carleson measures for Harmonically Weighted Dirichlet Spaces are characterized. It is shown a version of a maximal inequality for these spaces. Also, Interpolating Sequences and Closed-Range Composition Operators are studied in this context.

On The Irreducibility Of The Cauchy-Mirimanoff Polynomials, 2010 University of Tennessee - Knoxville

#### On The Irreducibility Of The Cauchy-Mirimanoff Polynomials, Brian C. Irick

*Doctoral Dissertations*

The Cauchy-Mirimanoff Polynomials are a class of polynomials that naturally arise in various classical studies of Fermat's Last Theorem. Originally conjectured to be irreducible over 100 years ago, the irreducibility of the Cauchy-Mirimanoff polynomials is still an open conjecture.

This dissertation takes a new approach to the study of the Cauchy-Mirimanoff Polynomials. The reciprocal transform of a self-reciprocal polynomial is defined, and the reciprocal transforms of the Cauchy-Mirimanoff Polynomials are found and studied. Particular attention is given to the Cauchy-Mirimanoff Polynomials with index three times a power of a prime, and it is shown that the Cauchy-Mirimanoff Polynomials of ...

Computational Circle Packing: Geometry And Discrete Analytic Function Theory, 2010 University of Tennessee, Knoxville

#### Computational Circle Packing: Geometry And Discrete Analytic Function Theory, Gerald Lee Orick

*Doctoral Dissertations*

Geometric Circle Packings are of interest not only for their aesthetic appeal but also their relation to discrete analytic function theory. This thesis presents new computational methods which enable additional practical applications for circle packing geometry along with providing a new discrete analytic interpretation of the classical Schwarzian derivative and traditional univalence criterion of classical analytic function theory. To this end I present a new method of computing the maximal packing and solving the circle packing layout problem for a simplicial 2-complex along with additional geometric variants and applications. This thesis also presents a geometric *discrete Schwarzian* quantity whose value ...

Fractions Of Numerical Semigroups, 2010 University of Tennessee - Knoxville

#### Fractions Of Numerical Semigroups, Harold Justin Smith

*Doctoral Dissertations*

Let S and T be numerical semigroups and let k be a positive integer. We say that S is the quotient of T by k if an integer x belongs to S if and only if kx belongs to T. Given any integer k larger than 1 (resp., larger than 2), every numerical semigroup S is the quotient T/k of infinitely many symmetric (resp., pseudo-symmetric) numerical semigroups T by k. Related examples, probabilistic results, and applications to ring theory are shown.

Given an arbitrary positive integer k, it is not true in general that every numerical semigroup S is ...

A Criterion For Identifying Stressors In Non-Linear Equations Using Gröbner Bases, 2010 The University of Southern Mississippi

#### A Criterion For Identifying Stressors In Non-Linear Equations Using Gröbner Bases, Elisabeth Marie Palchak

*Honors Theses*

No abstract provided.

Pre-Service Teachers’ Knowledge Of Algebraic Thinking And The Characteristics Of The Questions Posed For Students, 2010 Marquette University

#### Pre-Service Teachers’ Knowledge Of Algebraic Thinking And The Characteristics Of The Questions Posed For Students, Leigh A. Van Den Kieboom, Marta Magiera, John Moyer

*Mathematics, Statistics and Computer Science Faculty Research and Publications*

In this study, we explored the relationship between the strength of pre-service teachers’ algebraic thinking and the characteristics of the questions they posed during cognitive interviews that focused on probing the algebraic thinking of middle school students. We developed a performance rubric to evaluate the strength of pre-service teachers’ algebraic thinking across 130 algebra-based tasks. We used an existing coding scheme found in the literature to analyze the characteristics of the questions pre-service teachers posed during clinical interviews. We found that pre-service teachers with higher algebraic thinking abilities were able to pose probing questions that uncovered student thinking through the ...

Pre-Service Middle School Teachers’ Knowledge Of Algebraic Thinking, 2010 Marquette University

#### Pre-Service Middle School Teachers’ Knowledge Of Algebraic Thinking, Leigh A. Van Den Kieboom, Marta Magiera, John Moyer

*Mathematics, Statistics and Computer Science Faculty Research and Publications*

In this study we examined the relationship between 18 pre-service middle school teachers’ own ability to use algebraic thinking to solve problems and their ability to recognize and interpret the algebraic thinking of middle school students. We assessed the pre-service teachers’ own algebraic thinking by examining their solutions and explanations to multiple algebra-based tasks posed during a semester-long mathematics content course. We assessed their ability to recognize and interpret the algebraic thinking of students in two ways. The first was by analyzing the preservice teachers’ ability to interpret students’ written solutions to open-ended algebra-based tasks. The second was by analyzing ...

Sets Definable Over Finite Fields: Their Zeta-Functions, 2010 University of Massachusetts Medical School

#### Sets Definable Over Finite Fields: Their Zeta-Functions, Catarina I. Kiefe

*Catarina I. Kiefe*

Sets definable over finite fields are introduced. The rationality of the logarithmic derivative of their zeta-function is established, an application of purely algebraic content is given. The ingredients used are a result of Dwork on algebraic varieties over finite fields and model-theoretic tools.

Pseudodefinite Fields, Procyclic Fields And Model-Completion, 2010 Massachusetts Institute of Technology

#### Pseudodefinite Fields, Procyclic Fields And Model-Completion, Allan Adler, Catarina I. Kiefe

*Catarina I. Kiefe*

In this paper, it is shown that the theory of pseudofinite fields is, with respect to a suitable language, the model completion of the theory of procyclic fields. Also, procyclic fields are characterized as the class of relatively algebraically closed subfields of pseudofinite fields.