Digital Commons Network^™

Boundary Approximation Methods For Some Free And Moving Boundary Problems, David Gerald Meredith

Digitized Theses

Numerical methods for a class of free and moving boundary problems are considered. The class involves the solution of Laplace's equation on a domain which is changing shape with time. The position of the boundary is described by an evolution equation. With the time fixed, a boundary approximation method is employed to solve the potential problem. The boundary location at the next time is determined from the evolution equation using standard techniques and the process is repeated.;Two boundary methods are examined. Both are characterized by representing the approximate solution of the potential problem as a series of known basis functions, …

On Compact Finite Difference Schemes With Applications To Moving Boundary Problems, Michel Francois Pettigrew

Digitized Theses

Compact finite differences are introduced with the purpose of developing compact methods of higher order for the numerical solution of ordinary and elliptic partial differential equations.;The notion of poisedness of a compact finite difference is introduced. It is shown that if the incidence matrix of the underlying interpolation problem contains no odd unsupported sequences then the Polya conditions are necessary and sufficient for poisedness.;A Pade Operator method is used to construct compact formulae valid for uniform three point grids. A second Function-Theoretic method extends compact formulae to variably-spaced three point grids with no deterioration in the order of the truncation …

Order Automata, William Herbert Sulis

Digitized Theses

We define an order automaton to be a 4-tuple (M,X,R, {dollar}\eta{dollar}) where ({dollar}X,\eta{dollar}) is a {dollar}M{dollar}-automaton and {dollar}R{dollar} a partial ordering on {dollar}X{dollar} such that {dollar}x \leq y{dollar} if and only if there exists an {dollar}a \in M{dollar} such that {dollar}\eta(x,a) = y{dollar}. The monoid {dollar}M{dollar} is said to generate the order {dollar}R{dollar} on {dollar}X{dollar}. Some relationships between the algebraic properties of {dollar}M{dollar} and the order {dollar}R{dollar} are determined. A monoid {dollar}M{dollar} is shown to be the monoid for some order automaton if and only if it has a homomorphic image {dollar}M\sp\prime{dollar} which is ordering, i.e. for all {dollar}x,a,b \in …

Design And Analysis For Bayesian Approximation Of Solutions To Linear Differential Equations, Karole Herzog

Honors Capstones

The problem we are addressing is that of designing and analyzing experiments for numerically solving linear differential equations of the form: Σ-(i=0)^n [g_i (t) y^((i) ) = h(t)] for all t in a specified domain. In general, for a linear differential equation of the order n, we are given n pieces of information to use as boundary conditions. This information may consist of a boundary condition for y and each derivative of y up to y(n-1); or, we may be given multiple boundary conditions for y and/or any of the (n-1) derivatives, as long as there are n pieces of …

The Problem Of Adequately Defining Numbers, D. Stephan Delong

Honors Capstones

Natural numbers, although they pervade much of mathematics, are among the most difficult entities for which to provide definitions. Although it is often overlooked, as the efforts of pure mathematics are directed toward the maximization of rigor, the development of sound definitions for numbers can be viewed as one of the most critical objectives of the discipline. This paper is an examination and a support for the efforts in this area of the German logician Gottlob Frege, and in particular of his landmark treatise die Grundlagen der Arithmetik. This work marked the first successful attempt to define numbers through appeal …

A Workshop For Building Confidence In Learning Mathematics, Joseph David Rich

Honors Capstones

This study was undertaken in an attempt to decrease the mathematics anxiety and thereby improve the performance of a group of twenty-four freshmen college students in a special admissions program at Northern Illinois University. The study was conducted in an intermediate algebra class and used a behavior modification approach for reducing anxiety. A book entitled Building Confidence in Mathematics was written by the experimenter and provided for the students’ use. The workshop met twice a week for three weeks and was run by the experimenter and a counselor. The students were given a pre-test and post-test of the Phobos anxiety …

Finiteness Theorems For Forms Over Number Fields., Jenna Price Carpenter

LSU Historical Dissertations and Theses

In 1932, E. Witt showed how the collection of bilinear forms over a field $E$ can be made into a ring called the Witt ring, $W(E)$, of $E$. Properties of bilinear forms over a field often are reflected in the algebraic properties of its Witt ring. Perlis, Szymiczek, and Conner give criteria for global fields to be Witt equivalent; that is, to have isomorphic Witt rings. We refine these criteria to obtain finite, necessary and sufficient conditions to insure Witt equivalence of number fields. These conditions yield several finiteness statements for forms over number fields. Among them, for a fixed …

Density Theorems For Reciprocity Equivalences., Thomas Carrere Palfrey

LSU Historical Dissertations and Theses

The author studies reciprocity equivalence and the wild set of a reciprocity equivalence. He proves that if two algebraic number fields K and L are reciprocity equivalent then there exists a reciprocity equivalence between them with an infinite wild set. In particular, there always exists a self-equivalence with an infinite wild set on any algebraic number field. Even though a wild set of an equivalence can be infinite, he proves that its Dirichlet density is always zero. The structure of a reciprocity equivalence is examined. He proves that the bijection on primes determines the group isomorphism on global square classes …

L(P) Regularity And Extrapolation., Michael Helmuth Ruge

LSU Historical Dissertations and Theses

The goal of this thesis was to isolate classes of bounded linear operators in $L\sb{p}(I)$ which on the one hand still have some of the well-known and useful properties of positive operators, but which on the other hand are large enough to include some important classes of operators (e.g. the Hilbert transform and the singular operators derived from it) that cannot be dominated by positive operators. In Chapter I, we study as a first class of this kind the $L\sb{p}$ regular operators. By definition such operators map equiintegrable sets in $L\sb{p}(I)$ into equiintegrable sets in $L\sb{p}(I)$ and sets compact in …

Differences In The. Reading And Mathematics Achievement Between Asian American And Non Asian American Children, Linda B. Price

Theses and Dissertations

Explanations for the achievement or overachievement of Asian Americans are often conflicting and subject to debate among researchers. Four major theories for this achievement are explored in the review of literature. One of these theories concerns the idea that Asian American's beliefs are the result of Confucianism and its influence on the lives of Asian Americans. Another theory examines the parent's positive attitude toward education and its influence on achievement. A third theory suggests that Asian American babies are more alert and sensitive at birth. The final theory examined proposes that the Asian American immigration to the United States is …

Differences Between The High School Grade Point Average And The Sat Mathematics Score In Predicting Success In The Three-Quarter Mathematics Sequence At A Post-Secondary Vocational Education Institution, Steve A. Hicks

Theses and Dissertations

Thirty-seven current and former Engineering Technology students at a postsecondary vocational education institution were used as subjects for a comparison of the high school grade point average and the SAT mathematics score as predictors of success in the three-quarter mathematics sequence during the first year of the two-year program: The Pearson Product-Moment Correlation was used to compute two correlation coefficients; one between the high school GPA and the mathematics sequence average, and the other between the SAT mathematics score and the mathematics sequence average. These correlation coefficients were then compared, using a z calculation, to determine that the difference between …

Perfil Quali-Quantitativo Dos Currículos Do Ensino Secundário Brasileiro No Século Xix [A Quali-Quantitative Profile Of The Curricula Of The Brazilian Secondary School Of The Xix Century], Karl M. Lorenz, Ariclê Vechia

Education Faculty Publications

O trabalho caracteriza a organização e os conteúdos dos currículos adotados na escola secundária brasileira de 1838 a 1900, tomando como referência o Colégio Pedro II. O estudo classifica as disciplinas em quatro conjuntos curriculares: Humanidades, Ciências, Matemáticas e Estudos Sociais. Analise, quantitativamente, as disciplinas dos conjuntos curriculares, sua frequência e distribuição nas series, e a carga horaria atribuída elas.

The paper describes the organization and contents of the curricula adopted in the Brazilian secondary school for the years 1838 to 1900, using as its reference the College Pedro II. The study classifies the curricular disciplines in four groups: Humanities, …

The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner

Pitzer Faculty Publications and Research

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.

On Sequential Test Procedure With Application In Identification And Selection., Atasi Basu Dr.

Doctoral Theses

The area of sequential testing of statistical hypothesss is an important part of sequential analysis. The idea of a sequential test goes back to Dodge and Romig (1929) who cons tructed a double sampling procedure for sampling inspection. They wers motivated by the obser- vation that the double sampling plan requires a smaller number of observations on the average when compared uith the corresponding single sampling plan, Later schemes like multiple sampling vide Wlalter Bartky (1943) and interesting practical application of large scale experimente in successive stages vide Mahalanobis (1940) started comni ng up.The formal theory in sequential analysis began …

Some Aspects Of Majorization And Their Applications In Statistics., Subir Kumar Bhandari Dr.

Doctoral Theses

The works in this dissertation are primarily baset ur. difterent concepts of majorization and the results thereof. True first part of this dissertation is a study on dirfferent concepts of uni variate and multivariate majorization. The latter part of this dissertation includes studies on some problems in Sample Survey, and problems relating to ranking and selection with the use of some results, old and new, in majorization.The concept of univariate majorization has been consi- dered by economists in relation to Lorenz ourve, as well as by mathematicians and statisticians, especially in the field of reliability. It appears that the results …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

The Linear Algebra Of Interpolation With Finite Applications Giving Computational Methods For Multivariate Polynomials, Coert D. Olmsted

Mathematics and Statistics

Linear representation and the duality of the biorthonormality relationship express the linear algebra of interpolation by way of the evaluation mapping. In the finite case the standard bases relate the maps to Gramian matrices. Five equivalent conditions on these objects are found which characterize the solution of the interpolation problem. This algebra succinctly describes the solution space of ordinary linear initial value problems. Multivariate polynomial spaces and multidimensional node sets are described by multi-index sets. Geometric considerations of normalization and dimensionality lead to cardinal bases for Lagrange interpolation on regular node sets. More general Hermite functional sets can also be …

Study On Mappings And Maniforlds Of Fueter Hypercomplex And Almost Complex Types., Basudeb Dutta Dr.

Doctoral Theses

This thesis ie concerned chiefly with oertain families of smooth ... mappinga from domains in IRn to IRn which arise as natural generali- setione of complex anelytio mappinge. Thess Fueter families heve important hypercomplex aubfamilies defined via convergent Laurent series in one queternionio or actonionio veriable (with central coeffi- ofents). The various families and subfamdlies are olosed under compositior and inversion (when defined) of, meppinge consequently they form pseudo- groups on which one can model manifolds. The geometry of manifolde which oerry such ;Fueter or hypercomplex structure turna out to be qui ta %3D rich. In particular, they heve oanonioal …

On A Class Of Stochastic Approximation -Type Parameter-Learning Algorithms For Pattern Recognition., Amita Pal Dr.

Doctoral Theses

The first tank can involve one or more subtasks. For instance, it may require the design of a classifier on the basis of whatever prior knowledge there is of the feature space, or given the design, to estimate efficiently the parameters of the classifier. The latter might involve the estimation of the density function itself if very little is known about the class-conditional fenture distribution, or it may necessitate the entimation of the parameters of the fenture distribution, if one can assume it to have some known form. It may also involve estimating the boundaries of the classes, if even …

Generalizations Of The Segal Conjecture, Piotr Mavian Zelewski

Digitized Theses

The main result of this thesis may be described in the following manner: Let G be a finite group and let {dollar}\pi{dollar} be a compact Lie group. Define A(G,{dollar}\pi{dollar}) to be the free abelian group generated by equivalence classes of subhomomorphisms (G {dollar}\supset{dollar} H {dollar}{lcub}\buildrel\rho\over\longrightarrow{rcub}\ \pi){dollar}. A(G,{dollar}\pi{dollar}) is a module over the Burnside ring A(G). Define a map to stable homotopy which sends this subhomomorphism to the stable map BG{dollar}\sb+{dollar} {dollar}{lcub}\buildrel\rm transfer\over\longrightarrow{rcub}{dollar} BH{dollar}\sb+{dollar} {dollar}{lcub}\buildrel\rm B\rho\sb+\over\longrightarrow{rcub}{dollar} B{dollar}\pi\sb+{dollar}. This recipe defines a map {dollar}\Psi{dollar}: A(G,{dollar}\pi)\sbsp{lcub}\rm IA(G){rcub}{lcub}\{rcub}{dollar} {dollar}\to{dollar} {dollar}\{lcub}{dollar}BG{dollar}\sb+{dollar}, B{dollar}\pi\sb+\{rcub}{dollar}. Our main result states that {dollar}\Psi{dollar} is an isomorphism. This generalises Carlsson's proof …

Invariant Operator Ranges Of Operator Algebras, D Benjamin Mathes

Doctoral Dissertations

Given a norm closed unital algebra ${\cal A}$ of operators on Hilbert space, a sublattice of Lat$\sb{1/2}{\cal A}$ is identified, which we denote Lat$\sb{\rm cb}{\cal A}$. It is proved that Lat$\sb{\rm cb}{\cal A}$ is lattice isomorphic to Lat$\sb{1/2}{\cal A}\otimes{\cal K}$ (where ${\cal K}$ denotes the ideal of compact operators on an infinite dimensional separable Hilbert space). This isomorphism is used to prove theorems describing Lat$\sb{\rm cb}{\cal A}$ by carrying over know results concerning Lat$\sb{1/2}{\cal A}\otimes{\cal K}$. It is then shown that Lat$\sb{\rm cb}{\cal A}$ can always be written as the set of ranges of operators that intertwine the algebra with …

Applications Of Lattice Filters To Quadrature Mirror Filter Banks, Gregory R. Jaspers

Retrospective Theses and Dissertations

Presented is a method for designing and implementing lattice filters to be used in Quadrature Mirror Filter (QMF) Banks. Quadrature Mirror Filter Banks find use in applications where a signal must be spilt into subbands operated on then reconstructed in the output. Because of their structure, lattice filters do this very well and allow perfect reconstruction, even when the lattice coefficients must be quantized. In this paper QMF's and Lattice Filters are derived and analyzed. Application of the lattice filter is presented along with a design program and example of its use to implement a QMF. The computer aided design …

Variables : What Are They And Why Are They Important?, Kathleen A. Gavin

Honors Capstones

As a student in MATH 412 last semester, I encountered literature that suggested Algebra I students’ difficulty with that subject stemmed from their misconceptions concerning the concept of variable. Indeed, the transition from junior high school to high school mathematics is challenging enough and these things that we call variables truly form the base from which the concepts of Algebra develop. A variable can be identified as a special type of mapping, from a set of objects onto a number system. This mapping is based upon the measurement of some characteristic of the objects. Frequently, a variable is not named …

Fractal Geometry : Mathematics And Applications, Eileen Buckingham

Honors Capstones

The first section, entitled “Introduction and Applications,” is self-descriptive. The paper begins by introducing and defining the new terms “fractals” and “fractal geometry.” At the same time, Benoit B. Mandelbrot is accredited for having developed this new field. The introduction is followed by simple examples. This section is completed with a number of practical applications involving a variety of sciences. Section 2 consists of the background mathematics necessary to understand the Mandelbrot set and the computer program illustrating it. To fully understand the section, some prior knowledge of complex analysis is necessary. Sections 3 and 4 are the program description …

Gender Differences In Mathematics Achievement, Denise D'Antonio

Honors Capstones

Current research on gender differences in mathematics achievement is summarized. A cross-cultural study of sex differences in attitudes towards mathematics (confidence, individuality and liking) and in attributional patterns in mathematics (ability, effort, task, environment/luck) included American sixth graders (n=155, m=70, f=85) and British 11-12 year olds (n=42, m=18, f=24). Comparisons based on responses to a two-part survey concerning sex of student, sex of teacher, nationality, and achievement level were made. Significant results were obtained in the following categories concerning attitudes about mathematics. American female students with a female teacher liked mathematics more than American female students with a male teacher …

Stacker : A Microworld For Algebra, Melissa Elli Hauser

Honors Capstones

Research has been done which shows students have difficulty bridging the gap between arithmetic and basic algebra. Often, students who are able to perform symbolic manipulations still have an inadequate understanding of the underlying concepts involved. Further research has shown that emphasizing the link between arithmetic and algebra aids students in acquiring these concepts. A microworld is a type of computer program which allows exploration within the confines of an environment which models a conceptual framework. Research suggests that this kind of exploration is especially conducive to internalization of the framework being modeled. “Stacker: A Microworld for Algebra,” pictorially models …

Ergodic Actions Of Semi-Direct Product Groups., Edgar Navarro Reyes

LSU Historical Dissertations and Theses

We describe ergodic Borel actions of a semi-direct product group $K$ $\times\sb{s}$ $G$ on a standard Borel space where G is a group acting on a compact group K by automorphisms. In the canonical action of G on the dual K of K we assume each G-orbit in K is finite. This condition is automatically satisfied if K is a compact connected semi-simple Lie group. We discuss amenable actions and relatively weakly-mixing actions of this semi-direct product group.

Class Numbers And Units Of Number Fields E With Elementary Abelian K(2)O(E)., Ruth Ilse Berger

LSU Historical Dissertations and Theses

This is a contribution to the research that is going on in Algebraic Number Theory, relating classical questions on class numbers and units of a number field F to the structure of $K\sb2$($O\sb{F}$), the Milnor K-group $K\sb2$ of the ring of integers. We are interested in number fields F where the 2-primary subgroup of $K\sb2$($O\sb{F}$) is elementary abelian of rank $r\sb1$(F), the number of real embeddings of F. In (C-$H\sb1$) it is proven that the 2-primary subgroup of $K\sb2(O\sb{F}$) is of the above type if and only if the number field has the following properties: (a) the number field has …

White Noise Approach To Multiparameter Stochastic Integration., Mylan Redfern Betounes

LSU Historical Dissertations and Theses

In this dissertation we will set up the Hida theory of generalized Brownian functionals, or white noise analysis, on ${\cal L}\sp{\*}(\IR\sp{\rm d})$, the space of tempered distributions, and apply it to multiparameter stochastic integration. With the partial ordering on $\IR\sbsp{+}{\rm d}$: (s$\sb1$, dots,s$\sb{\rm d}$) $<$ (t$\sb1$, dots,t$\sb{\rm d}$) if s$\sb{\rm i}$ $<$ t$\sb{\rm i}$, 1 $\leq$ i $\leq$ d, the Wiener process W((t$\sb1$, dots,t$\sb{\rm d}$),x) = $\langle$x,1$\sb{\rm \lbrack 0,t\sb1)\times\cdots \times\lbrack 0,t\sb{d})}\rangle$, x $\in {\cal L}\sp{\*}(\IR\sp{\rm d})$ is a generalization of a Brownian motion and there is the Wiener-Ito decomposition: L$\sp2({\cal L}\sp{\*}(\IR\sp{\rm d}))$ = $\sum\sbsp{\rm n = 0}{\infty}\times$K$\sb{\rm n}$, where K$\sb{\rm n}$ is the space of n-tuple Weiner integrals. As in the one-dimensional case, there are the continuous inclusions (L$\sp2)\sp+ \subset$ L$\sp2({\cal L}\sp{\*}(\IR\sp{\rm d})) \subset$ (L$\sp2)\sp-$, and (L$\sp2)\sp-$ is considered the space of generalized Wiener functionals. We will define the differentiation operator $\partial\sb{\rm (t\sb1,\dots,t\sb{d}})$ and its adjoint $\partial\sp{\*}\sb{\rm (t\sb1,\dots,t\sb{d})}$ and give some properties. We prove that the multidimensional time Ito stochastic integral is a special case of a white noise integral and give conditions for its existence. For d = 2 the Ito integral is not sufficient for representing elements of L$\sp2({\cal L}\sp{\*}(\IR\sp2))$. We show that the other integral involved can also be realized in the white noise setting. For F $\in {\cal L}\sp{\*}(\IR\sp{\rm d}$) we will then define F(W((s,t),x) as an element of (L$\sp2)\sp-$ and obtain a generalized Ito formula.

On Prime Powers And Symbolic Prime Powers., Patrick Hall Phenis

LSU Historical Dissertations and Theses

We study the conditions under which the power of a prime ideal is equal to the corresponding symbolic prime power. We begin by extending a result of Villamayor(h). We consider a smooth k-algebra S(S$\sp\prime$) which is the localization of a finite k-algebra where k is a field of characteristic zero. For a prime ideal P (P$\sp\prime$) we show that if $S\over P$ $\cong$ $S\sp\prime\over P\sp\prime$ then P$\sp{n}$ = P$\sp{(n)}$ if and only if P$\sp\prime\sp{n}$ = P$\sp\prime\sp{(n)}$, for n $\geq$ 1. In the proof we use a generalization of the notion of a truncated cotangent complex introduced by Illusie. We then …