Digital Commons Network^™

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Chaotic Behaviour In Three Dimensional Quadratic Systems., Fu Zhang

Student Work

This thesis presents a part of the proof of that there is no chaos in three dimensional autonomous quadratic systems of four terms with one nonlinear term and without constant terms. The first step of the proof is identifying equivalent systems from all possible systems by the 3rd order permutation group and as a result 138 inequivalent patterns are found(refer to appendix A). And then for the solvable systems we show how to solve them. Some of the nonsolvable systems turn out to be 2nd order autonomous systems and they are resolved by analyzing the monotonicity of the solutions and/or …

Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.

Doctoral Theses

Many real-life applications such as image processing, weather forecasting, digital signal processing, etc., require large amount of computations. By distributing the task among several processors, one can appreciably reduce the computation time. To solve complex problems, several computer architectures using multiple processors have been introduced. Recent developments in IC technology have made it economically feasible to construct multiple processor systems consisting of hundreds or thousands of processors.There are two types of multiprocessor systems (PS87). One is tightly coupled, where the processors share a common clock and/or memory. The other is loosely coupled, where each processor runs independently with a local …

Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.

Doctoral Theses

No abstract provided.

Wilderness Survival Basic Skills: A Model Seventh Grade Science Curriculum With Integrated Math Concepts, Layne B. Hutchins

All Graduate Projects

The purpose of this project was to design and implement a model 7th grade science program with integrated mathematics concepts using an outdoor survival theme. The developed program focused on mathematics and science topics related to exploration and survival in the wilderness and enjoyment of the outdoors in order to connect mathematics and science concepts with real life experiences. Current research and literature on integration and multiple intelligences, integration of mathematics and science as well existing outdoor programs was reviewed. Finally, section overviews, student learning objectives, learning activities and teaching strategies were adapted and developed.

The Development And Design Of Activities To Support Performance Based And Integrated Math Instruction For Fifth Grade Students, Lelia L. Coghill

All Graduate Projects

The purpose of the project was to develop and design activities and materials to support performance based integrated mathematics instruction for fifth grade students in the concept areas of place value, decimals, percents, and fractions. The activities and materials were prepared in conjunction with other disciplines, namely reading, writing, art, science, and social studies. The intent was to make mathematics relevant to real life with stress on student performance as an indicator of knowledge, understanding, and application. The activities make use of performance based, integrated, and real life situations, and the materials include technology, field trips, gaming, manipulatives, recording sheets, …

Literature And Writing Connections With Mathematics In A First Grade Classroom, Linda Joan Sheeler Sorenson

All Graduate Projects

The National Council of Teachers of Mathematics Standard #2, communication in mathematics, is addressed. The benefits of integrating writing and the use of children's literature in mathematics are studied. Writing strategies and an annotated bibliography of children's literature that address instruction of first grade mathematics outcomes prescribed by the Yakima (WA) School District are developed. Recommendations for implementing the project are given.

The Effects Of Analytic Reading Skills On Sixth Graders' Ability To Solve Mathematical Story Problems., Linda Hale Eilers

LSU Historical Dissertations and Theses

The purpose of the present study was to determine the effects of two levels of instructional treatment on sixth graders' ability to solve mathematical story problems. The two levels of instructional treatment were instruction in the use of graphic organizers in conjunction with specific analytic reading skills and instruction in specific analytic reading instruction alone. These were compared to the absence of either treatment. The steady decline in students' scores on measures of ability to read and solve story problems over the past decade prompted research in three sixth-grade public school classes in northeast Louisiana. The study employed an experimental/control, …

On The Homology Of Branched Cyclic Covers Of Knots., Wayne H. Stevens

LSU Historical Dissertations and Theses

We consider the sequence of finite branched cyclic covers of $S\sp3$ branched along a tame knot $K : S\sp1\to S\sp3$ and prove several results about the homology of these manifolds. We show that the sequence of cyclic resultants of the Alexander polynomial of K satisfies a linear recursion formula with integral coefficients. This means that the orders of the first homology groups of the branched cyclic covers of K can be computed recursively. We further establish the existence of a recursion formula that generates sequences which contain the square roots of the orders of the odd-fold covers and that contain …

Composition Operators On Riemann Surfaces, Ioana Crenguta Mihaila

Doctoral Dissertations

General background. Composition operators are defined on a Hilbert (or Banach) spaces of complex valued functions defined on some set X. For the big majority of cases the set X is the unit disc in the complex plane, and the space of functions is one of the Hardy or Bergman spaces (weighted or not). This is due, without doubt, to the richness of those spaces, and the high degree of interest in them. There have been also important papers on the study of the Hardy spaces on the unit ball of n-dimensional complex space.

I have been working with my …

Profiles Of Reform In The Teaching Of Calculus: A Study Of The Implementation Of Materials Developed By The Calculus Consortium Based At Harvard (Cch) Curriculum Project, Alice Darien Lauten

Doctoral Dissertations

The research question addressed in this study is: What profiles of interpretation and implementation of reform in the teaching of calculus emerge from data obtained from mathematics faculty members using Calculus Consortium Based at Harvard (CCH) Curriculum Project materials? Site liaisons from mathematics departments using CCH Curriculum Project materials in 117 academic institutions, consisting of 13 secondary schools, 30 two-year colleges, 19 doctoral and research universities, and 55 other colleges and universities, completed Initial and Site Liaison Surveys. Site liaisons and 266 other instructors from 117 academic institutions completed a Faculty Survey. Six clustering scales were developed from the survey …

Curriculum In Mathematics For Air Conditioning And Refrigeration, Darrow P. Soares

Theses Digitization Project

No abstract provided.

An Interdisciplinary Unit On The Renaissance, Sarah Elizabeth Hughes

Theses Digitization Project

No abstract provided.

The Galois Group Of The Maximal 2-Extension Of A Field, Wenfeng Gao

Digitized Theses

This work is on the structure of the Galois groups of the maximal 2-extensions of a field. This work is closely related to many famous open questions (Galois representations, the elementary conjecture, Fermat prime numbers, the level and u-invariant of a field, etc.).;Let F be a field of characteristic not 2 and {dollar}F\sb{lcub}q{rcub}{dollar} the maximal 2-extension of F. Let {dollar}G\sb{lcub}q{rcub}{dollar} be the Galois group of {dollar}F\sb{lcub}q{rcub}/F.{dollar} This work deals with the connections among the Galois theory of F, the structure of {dollar}G\sb{lcub}q{rcub}{dollar} and the mod 2 Galois cohomology of {dollar}G\sb{lcub}q{rcub}.{dollar};One of the most famous questions about Galois cohomology theory and …

A Study To Determine The Relationships Between A Local School Division's Middle School System's Technology, Science, And Mathematics Course Curricula And The Accommodation Of State And National Goals, Standards Or Objectives, William C. Reed

OTS Master's Level Projects & Papers

The goals of the study were to determine if: A state's learning standards, for this study the Virginia Standards of Learning, acknowledged, accommendations for technology, science, and mathematics curricula at the middle school level as set forth in a published, national level coordination/integration standard; A local school division's curricula, for this study the Virginia Beach City public School's middle school technology, science and mathematics curricula, complied with the established state standards; and The Virginia Beach City Public School's middle school technology, science and mathematics curricula were related, associated, coordinated or integrated in any fashion.

Existence And Uniqueness Theorems For Some White Noise Integral Equations., Dongya Zou

LSU Historical Dissertations and Theses

Let $({\cal S})\sbsp{\beta}{*},0\le\beta<1,$ be the Kondratiev-Streit spaces of generalized functions. Let $f:\lbrack 0,T\rbrack\times ({\cal S})\sbsp{\beta}{*}\to ({\cal S})\sbsp{\beta}{*},$ be weakly measurable, and satisfy a growth condition and a Lipschitz condition. Let $\theta :\lbrack 0, T\rbrack\to ({\cal S})\sbsp{\beta}{*},$ be weakly measurable and satisfy a growth condition. Then it is shown that the white noise integral equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t}f(s, X\sb{s})ds,0\le t\le T,$ has a unique solution in $({\cal S})\sbsp{\beta}{*}$, where the integral is a white noise integral in the Pettis or Bochner sense. This result is extended to ${\cal M}\sp*$, the Meyer-Yan distribution space. Some special equations are also solved explicitly. For $F\in L\sp2({\bf R}\sp+)$, let $A\sb{s}=\int\sbsp{-\infty}{s} F(s-u)\partial\sb{u}du,\ E\sb{s}= {\rm exp}(A\sb{s}),$ and $A\sbsp{s}{*},\ E\sbsp{s}{*}$ be their duals, respectively. The equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t} A\sbsp{s}{*}X\sb{s}ds, t\in\lbrack 0,T\rbrack,$ is solved in $({\cal S})\sp*$ or $(L\sp2)$, and the equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t} E\sbsp{s}{*}X\sb{s}ds, t\in\lbrack 0, T\rbrack,$ is solved in ${\cal M}\sp*,$ where $\theta$ is as above. Moreover, under certain conditions on $\theta,\Phi:\lbrack 0,T\rbrack\to ({\cal S})\sp*$ and $\sigma:\lbrack 0,T\rbrack\sp2\to{\bf R},$ the Volterra equation $X\sb{t}=\theta\sb{t}+\int\sbsp{0}{t}\sigma(t,s)\Phi\sb{s}\ {\rm o}\ X\sb{s}ds, t\in\lbrack 0,T\rbrack,$ is also solved, and its solution is in ${\cal M}\sp*, ({\cal S})\sbsp{\beta}{*},$ or $(L\sp2),$ depending on the growth conditions for $\theta$ and $\Phi.$ Finally, for a suitable deterministic function f, the white noise partial differential equation ${\partial u\over\partial t}=\Delta u+:e\sp{\dot B\sb{x}}: {\rm o}\thinspace u, u(0,x)=f(x),x\in{\bf R}\sp{n}, t\in\lbrack 0,\infty),$ is solved in ${\cal M}\sp*$.

Szasz-Muntz Theorems For Nilpotent Lie Groups., Darwyn C. Cook

LSU Historical Dissertations and Theses

The classical Szasz-Muntz theorem says that for $f\ \in\ L\sp2(\lbrack 0, 1\rbrack )$ and $\{n\sb{k}\}\sbsp{k=1}{\infty}$ a strictly increasing sequence of positive integers,$$\int\limits\sbsp{0}{1}x\sp{n\sb{j}}f(x)dx=0\ \forall j\Rightarrow f=0\Leftrightarrow\sum\sbsp{j=1}{\infty}{{1}\over{n\sb{j}}}=\infty.$$We have generalized this theorem to compactly supported functions on $\Re\sp{n}$ and to an interesting class of nilpotent Lie groups. On $\Re\sp{n}$ we rephrased the condition above on an integral against a monomial as a condition on the derivative of the Fourier transform $\ f$. For compactly supported f this transform has an entire extension to complex n-space, and these derivatives are coefficients in a Taylor series expansion of $\ f$. In the nilpotent Lie groups …

Some Lifting Problems In Arithmetic Equivalence., Nancy C. Colwell

LSU Historical Dissertations and Theses

The main theorem in this dissertation provides a partial answer to the following question: Given a $\doubz\sb{p}$-extension $F{\sb\infty} /F$ and a finite extension $K/F$, where F is a number field and p a prime number, to what extent does the K-splitting behavior the prime ideals of F determine the Iwasawa invariants of the $\doubz\sb{p}$-extension $K{\cdot}F{\sb\infty}/K$. The answer is that if two fields K and L are arithmetically equivalent over F, then $K{\cdot}F{\sb\infty} /K$ and $L{\cdot}F{\sb\infty} /L$ have exactly the same Iwasawa invariants for any $\doubz\sb{p}$-extension $F{\sb\infty} /F$, so long as p is not an exceptional divisor for K and L …

The Generalized Kompaneets Equation., Kunyang Wang

LSU Historical Dissertations and Theses

In the dissertation, the generalized Kompaneets equation$${\partial u\over\partial t}={1\over\beta(x)}\lbrack\alpha(x)(u\sb{x}+ku+F(x,u))\rbrack\sb{x}$$(for $x,t>0)$ is studied. For the linear case, when $F\equiv0,$ a complete theory is given. A brief discussion is carried for the nonlinear case when $F(x,u)=f(x)g(u).$. For the following equation,$$v\sb{t}=\varphi(y,v\sb{y})v\sb{yy}+\psi(y,v,v\sb{y}),$$Goldstein and Lin's result is extended to degenerate case. Also, for the following linear operator,$$Au=\alpha(x)u\prime\prime+\beta(x)u\prime$$(for $x\in \lbrack 0,$ 1)), Clement and Timmermans' result is extended to the case of discontinuous coefficients $\alpha$ and $\beta$.

A Polynomial Invariant Of Links In A Solid Torus., Jaehoo Park Kim

LSU Historical Dissertations and Theses

A polynomial invariant of links in a solid torus is defined through an algebra $H\sb{n}({1\over2}$). $H\sb{n}({1\over2}$) modulo by an ideal is the type-B Hecke algebra. This invariant satisfies the $S\sb3$-skein relation as in the 1-trivial links case of dicromatic link invariant discovered by J. Hoste and M. Kidwell. A link in the solid torus is isotopic to a closed braid which is a braid in the braid group of the annulus. We find an invariant of links through a represention $\pi$ of the braid group of the annulus to the algebra $H\sb{n}({1\over2}$). A trace map X is defined on a …

Jordan Algebras And Lie Semigroups., Yongdo Lim

LSU Historical Dissertations and Theses

For a Euclidean Jordan algebra V with the corresponding symmetric cone $\Omega$, we consider the semigroup $\Gamma\sb{\Omega}$ of elements in the automorphism group $G(T\sb{\Omega})$ of the tube domain $V$ + $i\Omega$ which can be extended to $\Omega$ and maps $\Omega$ into itself. A study of this semigroup was first worked out by Koufany in connection to Jordan algebra theory and Lie theory of semigroups. In this work we give a new proof of Koufany's results and generalize up to infinite dimensional Jordan algebras, so called $JB$-algebras. One of the nice examples of the semigroup $\Gamma\sb{\Omega}$ is from the Jordan algebra …

Matroid Connectivity., John Leo

LSU Historical Dissertations and Theses

This dissertation has three parts. The first part, Chapter 1, considers the coefficient $b\sb{ij}(M)$ of $x\sp{i}y\sp{j}$ in the Tutte polynomial of a connected matroid M. The main result characterizes, for each i and j, the minor-minimal such matroids for which $b\sb{ij}(M)>0.$ One consequence of this characterization is that $b\sb{11}(M)>0$ if and only if the two-wheel is a minor of M. Similar results are obtained for other values of i and j. These results imply that if M is simple and representable over $GF(q),$ then there are coefficients of its Tutte polynomial which count the flats of M that …