Digital Commons Network^™

New Topologies And Parallel Algorithms For Static Interconnection Networks., Srabani Sen Gupta Dr.

Doctoral Theses

Many real-life applications in the areas of signal processing, image processing, etc., require a large amount of fast computations to be performed. Although high speed powerful processors are currently available due to the phenomenal advances in VLSI technology, the increasing demand for massive real-time computations can not be met just by a uniprocessor system. One way of achieving the goal of fast computation is through parallel processing. In parallel processing, a problem is broken into several subproblems, which are distributed among different processors so that each of the processors can perform its task simultaneously. Main areas of recent research in …

Some Problems In Estimating Finite Population Total And Variance In Survey Sampling., Saswati Bhattacharya Dr.

Doctoral Theses

The problem of drawing inference concerning the parameters of a finite population of identifiable units has been increasingly engaging the attention of statisticians. The central problem here is to devise a suitable method of selecting a sample from the population and to employ an appropriate estimator to estimate the finite population total or mean. A consider- able progress in this field of study has been made and many authors have contributed towards the development of the theory in this aspect of the problem of statistical inferenceNumerous papers have been written covering the first aspect of the problem, namely, method of …

Foundations Of Object-Based Specification Design, David March Fleming

Graduate Theses, Dissertations, and Problem Reports

To enhance applicability and encourage its use, a component or a component-based system must have a well-designed set of interface features as well as a proper explanation of these features. The dual problem of designing a suitable set of interface features in addition to properly explaining its behavior is termed the specification design problem. This dissertation identifies observability, controllability, and a performance-motivated pragmatic criterion as essential properties of desirable formal specifications for reusable object-based software components. The pragmatic criterion guides the design of component interfaces and component libraries to a suitable set of features so that they are widely applicable, …

Pompeiu Problem And Analogues Of The Weiner-Tauberian Theorem For Certain Homogeneous Spaces., Rama Rawat Dr.

Doctoral Theses

Let G be a connected locally compact unimodular group acting transitively on a locally compact space X. For a function f on X and g € G, define of by 9f(x) = fA 9.a), a € X. One of the recurring themes in analysis is the question of when a function f in a given function space F(X) will have property that Span{gf : g € G} is dense in F(X). If X = R and G = R, the celebrated Wiener-Tauberian theorem answers this question completely for the space L1(R): The span of the translates of fE L1(R) is …

Frequency And Perception Of Mathematics Activities In Family Child Care And Parent-Child Routines, Annette Kari Eddy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The study examined the frequency of preschool mathematics activities at home and in the family child care setting. Provider perception and parent perception of the activities were also surveyed. Twenty-one family child care providers, 38 parents, and 42 preschool children participated in the study. Providers and parents participated in a telephone interview in which they completed either the Day Care Activities Checklist (DAC) or the Parent/Child Activities Checklist (PCAC). Research assistants administered the TEMA-2, a mathematical assessment suitable for preschool children, to the children in the study.

Family child care providers in this study reported engaging in mathematics activities statistically …

Effects Of Computer Assisted Instruction And Pclogo Programs On Math Performance Of Seventh And Eighth Grade Students With Learning Disabilities, Katherine R. Sweeny

Theses & Honors Papers

The purpose of the study was to investigate the effects of computer assisted instruction and Logo programming on the math performance of seventh and eighth grade students with learning disabilities. The sample included thirty (N=30) subjects with learning disabilities. The computer programs used were Deluxe Math Munchers and LOGO for Windows. A three group pretest-posttest experimental design was used to determine if a relationship existed between the three different methods of instruction and achievement, and whether or not a significant difference existed in performance based on grade levels. The 30 subjects were randomly assigned to one of three groups, two …

On Cvt Minimization In Single Machine Scheduling., D. K. Manna Dr.

Doctoral Theses

Scheduling problens are quite common in real life. They arise whenever there is a need to plan execution of various tasks over time and therefore they play very important roles in commercial set-ups concerning manufacturing or service in the optimal use of resources and/or customers satisfaction. The theory of scheduling deals with the construction of suitable models and their analyses. Researchersattention was drawn to the study of scheduling problems using mathematical modeling, probably for the first time when Johnson (1954] published his famous work on flowshop problem. Since then, the study of scheduling problem and its context has gradually attracted …

Fourier Transforms Of Very Rapidly Decreasing Functions On Certain Lie Groups., M. Sundari Dr.

Doctoral Theses

Recall that for a function f ϵ L1(Rn ), its Fourier transform fÌ‚ is definedby: fÌ‚ (ƹ) = ʃ Rnf(x)ei(ƹ,x)dx ( 0.1.1)where (.,.) denotes the standard inner product on Rn and dr the Lebesgue measure on Rn. A celebrated theorem of L. Schwartz asserts that a function f on Rn is rapidly decreasing (or in the Schwartz class ) if and only if its Fourier transform is rapidly decreasing . In sharp contrast to Schwartz s theorem, is a result due to Hardy ([18) which says that ʃ and fÌ‚ cannot both be very rapidly decreasing . More precisely, if …

On Some Problems Related To Hermite And Laguerre Expansions., P. K. Ratnakumar Dr.

Doctoral Theses

The first three chapters of this thesis are concerned with the spherical means associated to the Hermite and Laguerre expansions. The study of spherical means has a very long history. The classic work of F. John deals with various applications of the spherical means to the theory of partial differential equations. They entered Fourier analysis with the celebrated theorem of E. Stein on spherical analogue of the Lebesgue differentiation theorem. Ever since they have appcared again and again in several areas of analysis like integral geometry, inversion of Fourier transforms and related arcas.

The Fixed Point Index As A Local Lefschetz Number., Neeta Pandey Dr.

Doctoral Theses

In this thesis we defitne a class of self maps of connected compact polyhodza - those which prmserve erpanding directions - and define the fixed point indices of such maps at an isolated set of fixed points of the map as a local Lefschets rumber. Our definition uses simplicial approximations of the given map in the spirit of O Nell (I19| and Fournier (71) and is intrinsic so that it is computable.Let X be a connected compact polyhedron and f:X→ X be a map an X. The Lefscheta number L() of / is then defined to be ([13]),L) -E(-1)jTrace {, …

Recurrence And Transience Of Reflecting Diffusions., S. Balaji Dr.

Doctoral Theses

An attempt to obtain conditions for certain stability properties of reflecting diffusions in unbounded domains with boundary has been made in this thesis. For diffusions in R', such stability properties like recurrence, transience and positive recurrence have been studied extensively; see Bhattacharya (1978), Kliemann (1987), Pinsky (1987). One might see Pinsky (1995) for an up-to-date review of kuown methods and results in this all case. (For corresponding recurrence classification results on Markov chains using martin- gale ideas based on stoxchastic analogues of Lyapunov functions, see Meyn and Tweedie (1993a), (1993b) and the references given therein). The main concern in this …

Designing And Developing A Model Applied Mathematics Curriculum For Taiwanese-Canadian Extension School Students, In Grades Ten Through Twelve In Vancouver, British Columbia, Canada, Timothy Kuo-Tung Liu

All Graduate Projects

The purpose of the project was to design and develop a model applied mathematics curriculum for Taiwanese-Canadian extension school students, in grades ten through twelve in Vancouver, British Columbia, Canada. To accomplish this purpose, a review of current research and literature regarding curriculum and instruction related to applied mathematics was conducted. Additionally, related information from selected schools with applied mathematics programs in Taiwan, Canada, and the United States of America, was obtained and analyzed. A handsearch of various other sources was also conducted.

Literature-Based Supplimental Activities In A Second Grade Classroom, Heidi Stevens

All Graduate Projects

The National Council of Teachers of Mathematics recommendations and the Washington State Commission on Student Learning Essential Academic Learning Requirements are addressed. The benefits of integrating mathematics and literature are studied. Integrated activities, materials, and a bibliography of children's literature that supplement a traditional mathematics CUITiculum for primary students are developed. Recommendations for implementing the project are given.

Pure Framed Braids And 3-Manifolds., Jonathan Natov

LSU Historical Dissertations and Theses

This dissertation looks at representations of framed pure braids and compact orientable three manifolds. A representation, $\Phi:Z\sp{n}\oplus P\sb{n}\to \Gamma\sb{n},$ is constructed from the framed pure braid group on n strands to the mapping class group on a surface of genus n. The representation is used to obtain a presentation of the fundamental group. The representation, like that of (M-P), is compatible with Heegaard and Surgery descriptions. An algorithm is presented for transforming mapping class group elements to a stably equivalent pure framed braid, under the correspondence given by the representation. A geometric description, using the representation, is given for multiplication …

Contributions To The Theory Of Neighborhoods And Its Applications, Michael Joseph Cullinane

Doctoral Dissertations

Neighborhoods have played a fundamental role in general topology since the birth of the field. This work outlines the historial evolution of the notion of neighborhood and employs neighborhood assignments, weak neighborhood assignments, and a naturally induced notion of duality in a study of non-Hausdorff topological spaces. Neighborhood characterizations of various classes of spaces, among them the developable and the pseudometrizable spaces, are obtained. A generalization of topological spaces based upon a primitive notion of neighborhood is explored and examples are supplied to motivate the investigation.

Contributions To The Theory Of Distance Functions And Its Application In General Topology, Lawrence Valery Neveu

Doctoral Dissertations

As non-Hausdorff spaces are becoming more important in topology, there is a need to consider new notions in topology to supplement the usual structures. This work uses distance functions to find useful generalizations (in a non-Hausdorff context) of the classes of spaces that are important in the Hausdorff setting. We begin, in the first part, with a historical overview that traces the evolution of the notion of distance and its role in the development of general topology.

In the second part of this work, we launch our study of distance functions. Using non-symmetric distance functions, called asymmetric, we generalize the …

Student Interactions And Mathematics Discourse: A Study Of The Development Of Discussions In A Fifth-Grade Classroom, Sharon Marie Soucy Mccrone

Doctoral Dissertations

Mathematics reform efforts are gaining attention and support in the years since the dissemination of the National Council of Teachers of Mathematics (NCTM) Standards documents. Encouraging student interactions in small and large group settings, and promoting discussion and argumentation of mathematical ideas among students are two possible implications of the vision presented in the Standards. The goal of having mathematics discussions, however, can present a variety of classroom challenges. Many factors influence classroom discourse and need to be addressed in ways that inform teachers as they work toward creating a more interactive, discussion-based mathematics classroom.

The study examines the development …

Perfect Matchings: Modified Aztec Diamonds, Covering Graphs Andn-Matchings, Adriana Badauta Cransac

Doctoral Dissertations

In the Introduction, we present the problems we are going to study and we establish the basic definitions, concepts and results that are used throughout.

We begin the first chapter with a presentation of the Aztec diamond and the behaviour of its random domino tilings. We introduce the dual-matching-problem and we explore the structure of the perfect matchings of modified Aztec diamonds. We show that some of these matchings can be extended to matchings of the dual Aztec diamond, pointing out a bijection between these types of matchings. We determine the number of perfect matchings for each of the modified …

On Some Range Inclusions, Mihaela Anca Poplicher

Doctoral Dissertations

The de Branges-Rovnyak spaces have been introduced by Louis de Branges and James Rovnyak, and have been studied by several authors, in particular by Donald Sarason. The object of this thesis is to study more extensively some properties of this class of spaces. In particular, which of these spaces are invariant under the action of which composition operators, or adjoints of composition operators.

Some known facts and a couple of new properties are included in Chapter 1. There it is shown that the norm of the kernel function for evaluation at a point in the unit disc (in the de …

Vertical Equating Of Curriculum-Based Tests In Reading, Mathematics, And Language Arts, Judith Susan Gage Costa

UNLV Retrospective Theses & Dissertations

Vertical equating of a large urban school district's curriculum-based achievement tests for students in grades one through five was performed by using the BILOG-MG software package produced by Zimowski, Muraki, Mislevy, and Bock. This software extends the application of the item response theory (IRT) approach to test analysis to testing situations involving multiple groups BILOG-MG, item parameter estimates were derived using a marginal maximum a posteriori approach in combination with an expectation-maximization algorithm (EM). Estimates of examinee ability were produced using the Bayesian, or expected a posteriori, estimate with a normal prior distribution; Linkage of successive test forms was accomplished …

The Development Of Curriculum For A High School Course Integrating Drafting And Mathematics, Diana Lynn Mcvicker

Theses Digitization Project

No abstract provided.

Arboreal Adventure: A Cross Curricular Unit On Trees, Anne Elizabeth Boshoven

Theses Digitization Project

No abstract provided.

Lie Theory Of Differentiable Transformations On Banach-Type Manifolds., Amadou Belly Guisse

LSU Historical Dissertations and Theses

Let M be a manifold modeled on a Banach space B, and let U be an open subset of M containing the domain of some chart $\varphi$. The aim of this work is to set mathematical foundations (topological, algebraic geometrical) for the theory of pseudosemigroups of local transformations S on M and their infinitesimal generators $L\sp{r}(S,\ U).$ In the first part of this dissertation we define the topology of local uniform convergence, the most suitable in this case, similar to the compact open topology in the finite dimensional case, and show what relationship it has with different topologies. In the …

A Vector-Valued Operational Calculus And Abstract Cauchy Problems., Boris Baeumer

LSU Historical Dissertations and Theses

Initial and boundary value problems for linear differential and integro-differential equations are at the heart of mathematical analysis. About 100 years ago, Oliver Heaviside promoted a set of formal, algebraic rules which allow a complete analysis of a large class of such problems. Although Heaviside's operational calculus was entirely heuristic in nature, it almost always led to correct results. This encouraged many mathematicians to search for a solid mathematical foundation for Heaviside's method, resulting in two competing mathematical theories: (a) Laplace transform theory for functions, distributions and other generalized functions, (b) J. Mikusinski's field of convolution quotients of continuous functions. …

Unavoidable Minors Of Graphs Of Large Type., John Joseph Dittmann Jr

LSU Historical Dissertations and Theses

In this paper, we study one measure of complexity of a graph, namely its type. The type of a graph G is defined to be the minimum number n such that there is a sequence of graphs $G = G\sb0, G\sb1,\... , G\sb{n},$ where $G\sb{i}$ is obtained by contracting or deleting one edge from each block of $G\sb{i-1}$, and where $G\sb{n}$ is edgeless. We show that a 3-connected graph has large type if and only if it has a minor isomorphic to a large fan. Furthermore, we show that if a graph has large type, then it has a minor …

Graphs And Number Theory., Brian Heck

LSU Historical Dissertations and Theses

In the 1930's, L. Redei and H. Reichardt used certain matrices to aid in the determination of the structure of ideal class groups of quadratic number fields. This is a classical number theoretic problem which in general presents diffculties. Ideal class groups are finite abelian groups, and it is a result of Gauss that allows us to determine their 2-rank, in other words the number of cyclic factors of even order. Redei and Reichardt worked on determining the 4-rank, the number of factors of order divisible by 4. Later, the classical study of circulant graphs was utilized to further help …

Weak Convergence Of Interacting Stochastic Systems., George William Paslaski

LSU Historical Dissertations and Theses

The aim of the dissertation is to establish the weak convergence of mean-field interacting particle systems driven by Poisson random measures and semimartingales. The limit of the stochastic systems is identified by the use of martingale problems and Picard iteration schemes. The interacting systems driven by Poisson random measures are shown to be stable with respect to the coefficients of the system as well as the driving terms. The same results can be achieved when a random interaction term independent of the driving terms is introduced into the coefficients of the system. Equations driven by semimartingales do not neccesarily possess …

Teachers Of Mathematics Teach Mathematics Differently : A Case Study Of Two Teachers, Jennie Bickmore-Brand

Theses: Doctorates and Masters

This thesis investigates the different approaches adopted by two teachers for teaching mathematical content at the upper primary level of education. Questions have been raised by researchers about the impact teachers' philosophical background may have on their perception of how mathematics should be taught. Similarly questions have been asked about the role of content in mathematics education in relation to the process of education. The two teachers held different beliefs about what they were doing when they were teaching mathematics and why they were teaching that way. Their methodological emphases were different; one could be described as being more learner-centred …

Extending And Exploring Students' Problem Solving Via Problem Posing, Elena N. Stoyanova

Theses: Doctorates and Masters

Despite the fact that problem posing has been recommended as a useful mathematical activity in the curriculum documents of several countries, research about the types of problem-posing situations in which students could be involved, and about the effects of these problem-posing activities on students' mathematical performance is limited. The application of problem posing in school mathematics has been hindered by the absence of a framework which links problem posing, problem solving and mathematics curricula