Digital Commons Network^™

Linear Codes Defined From Higher -Dimensional Varieties., Gary Lynn Salazar

LSU Historical Dissertations and Theses

We establish an algebraic foundation to complement the improved geometric codes of Feng and Rao. Viewing linear codes as affine variety codes, we utilize the Feng-Rao minimum distance bound to construct codes with relatively large dimensions. We examine higher-dimensional affine hypersurfaces with properties similar to those of Hermitian curves. We determine a Grobner basis for the ideal of the variety of rational points on certain affine Fermat varieties. This result is applied to determine parameters of codes defined from Fermat surfaces.

Homflypt Skein Modules., Jianyuan Zhong

LSU Historical Dissertations and Theses

Let k be a subring of the field of rational functions in x, v, s which contains x+/-1, v+/-1, s+/-1. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) x --1L+ -- xL -- = (s -- s--1 )L0; (2) L with a positive twist = (xv--1)L; (3) L ⊔ O = u-u-1 s-s-1L where O is the unknot. We give two bases for the relative Homflypt skein module of …

On Some Optimal Control Problems For The Centroaffine Geometry On The Plane., Angel L. Cruz Delgado

LSU Historical Dissertations and Theses

A certain parametrization of substantial planar curves yields a centroaffine arclength s and a centroaffine curvature ks that remain invariant under GL(2, R ) motions. In Chapter 4 we search for those substantial curves with predetermined position and velocity at the initial and terminal points, which minimize the total square curvature 0T k2s 2ds as k varies over all square summable functions on each interval [0, T]. These curves are called centroaffine elastic curves. Thinking of the curvature k as a control, we pose our problem as an optimal control problem over the Lie group GL(2, R ) with fixed …

The Effect Of Antecedent And Consequent Strategies On Increasing Student Homework Compliance And Academic Achievement., Donna Marie Gilbertson

LSU Historical Dissertations and Theses

The primary purpose of this investigation was to evaluate the effects of homework and alternatives to homework on student math completion, accuracy and fluency for low socioeconomic students. To examine possible causes of homework problems as well as the effect of different treatments on math fluency, this study used an idiographic protocol to systematically examine the effects of antecedent and consequential strategies on different types of homework performance problems through several phases. First, a brief experimental analysis was conducted for each student to identify whether poor homework performance was due to a swill deficit or a performance deficit. Next, an …

Collected Papers Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Mathematics And Socio -Cultural Behavior: A Case Study Of The Enculturation Of A New Mathematician, Timothy Byron Gutmann

Doctoral Dissertations

Research has shown that mathematics as we know it is a product of the socio-cultural climate in which it was developed. This research attempts to address the related question of how being involved in mathematics influences the socio-cultural lives of mathematicians. A new Ph.D. mathematician hired in his first faculty position was observed for a period of 13 weeks, most during his first semester. Analysis of this long-term, in depth case study followed ethnographic methods and drew on theories of rites of passage, organizational socialization, self-identity, and evolution. The role of mathematics in the departmental culture and in the newcomer's …

Pre-Service Secondary Mathematics Teachers' Attitudes About The History Of Mathematics, Kelly Marie Sullivan

UNLV Retrospective Theses & Dissertations

This study was conducted to show that using historical material to teach mathematical content to pre-service secondary mathematics teachers could improve their attitudes about incorporating the history of mathematics into the mathematics classroom. A historical module from the Mathematical Association of America was taught to an undergraduate class of pre-service secondary mathematics teachers. Their attitudes regarding the use of the history of mathematics in the mathematics classroom were then compared to the attitudes of students in another undergraduate class, taught by the same researcher, whose instruction did not incorporate history. Results from t-tests indicate that there was a positive change …

The Effect Of In-Class Support On Mathematics Performance Of Classified And Non-Classified High School Students, Lorraine Schlarman

Seton Hall University Dissertations and Theses (ETDs)

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[Introduction To] Mathematics Calculus Bc, John R. Hubbard, David R. Arterburn, Michael A. Perl

Bookshelf

This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests. Our review succinctly covers areas considered most relevant to this exam. Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you.

Phantom Classmates : A Case Study Of Talented Mathematics Students Learning Via Telematics, Leanne S. Clarke

Theses: Doctorates and Masters

The main advantages and disadvantages of the Telematics environment for talented mathematics students were investigated through a case study. The case study considered the interaction of, and opinions of 11 Year 9 students and the teacher/researcher. Participants were from nine schools in regional Western Australia, and were withdrawn from face-to-face classes to attend mathematics transmissions. Qualitative data were collected through student interviews, an anonymous questionnaire, tape recording of lessons, and teacher field notes. Students all agreed the main disadvantage occurred if timetabling for Telematics transmissions did not align with their local school class times for the same subject. The teacher …

On Measuring The Cost Of Children:The Case Of Rural Maharashtra., Manisha Chakrabarty Dr.

Doctoral Theses

In this dissertation we have attempted to measure the cost of children, which plays a crucial role in matters relating to welfare and public policy like child benefits and compensation policies of the government. The cost is measured based on the single equation as well as the systems approach using the 38th round National Sample Survey (NSS) data on household consumer expenditure for rural Maharashtra (relating to the period of January to December, 1983).The first chapter provides a brief account of the basic literature on empirical demand analysis which is relevant for welfare comparison between households. To be specific in …

Redeeming The Symbols: Madeleine L'Engle And The Interpreting Of Contemporary Geometry In The Christian Tradition, C. Christopher Smith

Inklings Forever: Published Colloquium Proceedings 1997-2016

In Madeleine L’Engle’s book, A Stone for a Pillow, she discusses how the Christian faith is often concerned with redeeming symbols into something good. This paper examines the redemption of contemporary geometry and how it reflects the truths of the Christian faith.

Intersecting Chains In Finite Vector Spaces, Eva Czabarka

Faculty Publications

We prove an Erdős–Ko–Rado-type theorem for intersecting k-chains of subspaces of a finite vector space. This is the q-generalization of earlier results of Erdős, Seress and Székely for intersecting k-chains of subsets of an underlying set. The proof hinges on the author's proper generalization of the shift technique from extremal set theory to finite vector spaces, which uses a linear map to define the generalized shift operation. The theorem is the following.

For c = 0, 1, consider k-chains of subspaces of an n-dimensional vector space over GF(q), such that the smallest subspace in any chain has dimension at least …

Various Pushing Methods On Grid Graphs, Jiaxin Wang

Graduate Theses, Dissertations, and Problem Reports (ETD)

This thesis describes algorithms for determining if a grid of switches can be turned into all-off state from any initial configuration by various methods of activation operation (push). Among these push methods, besides the regular "+" push, "+" push with no center, "X" push, "X" push with no center, and a "V"-typed unbalanced push are studied. The research methods used in this work are mainly linear algebra and algorithm analysis. Results obtained include that the grid m x n is completely solvable with push "+" no center, if and only if co-prime (m+1, n+1).

On The Relationships Between Linear Extensions And Multiprocessor Scheduling., Jodi Wineman

Student Work

Scheduling is a classical field with many challenging problems and interesting results. A scheduling problem emerges wherever there is a choice as to the order in which a number of tasks can be performed and/or the assignment of the tasks to the available resources for processing . In this thesis, we focus on a version of the scheduling problem that deals with scheduling precedence constrained tasks onto the multi processors of a given distributed system with the goal of minimizing the schedule time. This scheduling problem has been proven to be NP-hard even when several restrictions are applied. This implies …

An Ellam Scheme For Advection-Diffusion Equations In Two Dimensions, Hong Wang, Helge K. Dahle, Richard E. Ewing, Magne S. Espedal, Robert Sharpley, Shushuang Man

Faculty Publications

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to …

Faculty Profile: Walter Gleason

Bridgewater Review

Profile of Professor Walter Gleason of the Mathematics and Computer Science Department.

Interactive And Zero-Knowledge Proofs, Molli Noland

Theses

An interactive proof involves two parties, the prover and the verifier. The goal of the proof is for the prover to convince the verifier that some instance of a decision problem is true. A zero-knowledge proof is an interactive proof where the only information learned by the verifier of the proof is the outcome of the proof. This thesis contains a theoretical overview of interactive and zero-knowledge proofs and describes experiments with implementations of some of them. Two examples of interactive proofs from number theory are given, a protocol for quadratic non-residues and a protocol for subgroup non-membership. The third …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Use Of Wavelet-Packet Transforms To Develop An Engineering Model For Multifractal Characterization Of Mutation Dynamics In Pathological And Nonpathological Gene Sequences, David Lee Walker

Graduate Theses, Dissertations, and Problem Reports (ETD)

This study uses dynamical analysis to examine in a quantitative fashion the information coding mechanism in DNA sequences. This exceeds the simple dichotomy of either modeling the mechanism by comparing DNA sequence walks as Fractal Brownian Motion (fbm) processes. The 2-D mappings of the DNA sequences for this research are from Iterated Function System (IFS) (Also known as the "Chaos Game Representation" (CGR)) mappings of the DNA sequences. This technique converts a 1-D sequence into a 2-D representation that preserves subsequence structure and provides a visual representation. The second step of this analysis involves the application of Wavelet Packet Transforms, …

The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.

Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.

Doctoral Theses

The sequence of polynomials of a single variable known as the Hermite polynomialshala) = ), k21, (-1)* ha(z) =has many close links with the Normal distribution. Their association goes very doep, and extends to several connections bet ween the two-variable Hermite polynomialsHll, 2) = the(z/t), . k21.and the prime example of Gaussian processes, that is Brownian motion, as well. Much of this connection stems from what we term the time-space harmonic property of these polynomials for the Brownian motion process. An exact definition of this property follows later. A natural question that arises is, for stochastic processes in general, when …

Pattern Classification Using Genetic Algorithms., Sanghamitra Bandyopadhyay Dr.

Doctoral Theses

Pattern recognition and machine learning form a major area of research and develop- ment activity that encompasses the processing of pictorial and other non-numerical information obtained from the interaction between science, technology and society. A motivation for the spurt of activity in this field is the need for people to com- municate with the computing machines in their natural mode of communication. Another important motivation is that the scientists are also concerned with the idea of designing and making intelligent machines that can carry out certain tasks that we human beings do. The most salient outcome of these is the …

Muyltivariate And Regression Analysis Based On The Geometry Of Data Clouds., Biman Chakraborty Dr.

Doctoral Theses

Median is a natural estimate of location of a data set, and there are several versions of inultivariate median studied in the literature, each of which is an interesting descriptive statistic for multivariate data and provides some nice geometric insights into the data cloud. One would expect that multidimensional median will be a natural estimate for the center of symmetry of a multivariate distribution. However, there is no unique concept of symmetry in multivariate problems. The center of symmetry can be defined in several ways there. For example, the d-dimensional random variable X is spherically symmetric about e €Rd if …

The Deconstruction Of Mathematics: A Criticism Of Reuben Hersh's What Is Mathematics, Really? And The Humanist Philosophy Of Mathematics, David J. Stucki

Mathematics Faculty Scholarship

Mathematics, as an academic discipline, has stood for many years as the last bastion against a growing tide of intellectual relativism that has become all but ubiquitous. More recently, however, efforts have been made to "humanize" mathematics by advocating a social-constructivist approach to the philosophy of mathematics, both in practice and education. This paper is intended to serve as a critical response to one advocate of this approach, Reuben Hersh (What Is Mathematics, Really?, 1997), and in the process a defense of Platonism.

Dynamic Analysis Of Unevenly Sampled Data With Applications To Statistical Process Control, Laura Ann Mcsweeney

Doctoral Dissertations

Dynamic analysis involves describing how a process changes over time. Applications of this type of analysis can be implemented in industrial settings in order to control manufacturing processes and recognize when they have changed significantly. The primary focus of this work is to construct methods to detect the onset of periodic behavior in a process which is being monitored using a scheme where data is sampled unevenly.

Techniques that can be used to identify statistically significant periodic structure using the periodogram will be reviewed and developed. The statistical properties of the periodogram for unevenly sampled data will be calculated. These …

The Word Problem And The Ideal Membership Problem, Damon Anthony Demas

Doctoral Dissertations

This dissertation concerns two problems from computational algebra, the word problem for semigroups and the ideal membership problem for noncommutative polynomial rings. Historically, the word problem provided one of the first examples of an algorithmically unsolvable problem from outside of logic and computability theory. In terms of solvability, the word problem is equivalent to a restricted version of the membership problem.

For ideals whose membership problem is solvable, computational techniques such as Grobner basis methods often can be used to solve the problem, but not always. In Chapter two, we develop a method which can be used to solve the …

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

Integral Kernel Operators In The Cochran -Kuo -Sengupta Space., John Joseph Whitaker

LSU Historical Dissertations and Theses

This dissertation contains several results about integral kernel operators in white noise analysis. The results found here apply to the space of test functions and generalized functions that were constructed in the paper of Cochran, Kuo, and Sengupta, based on a sequence of numbers &cubl0;an&cubr0; infinityn=0. . We shall prove results about existence, restrictions, and extensions of integral kernel operators based on the conditions on &cubl0;an&cubr0; infinityn=0. contained in the paper of Kubo, Kuo, and Sengupta. Also, we shall prove an analytic property and growth condition of the symbol of a continuous operator in CKS space. Our results are similar …

A Model, Secondary Level, Mathematics Curriculum Developed In Alignment With Washington State Essential Academic Learning Requirements, Easton School District, Seyed Victor Nourani

All Graduate Projects

The purpose ofthis project was to design and develop a model secondary level mathematics curriculum, in alignment with Washington State Essential Academic Learning Requirements, for the Easton School District in Washington. To accomplish this purpose, a review of current research and literature regarding Washington State Essential Academic Learning Requirements related to secondary mathematics was conducted. In addition, related information from selected sources was obtained and analyzed.