Digital Commons Network^™

Differentiation And Composition On The Hardy And Bergman Spaces, Neil Portnoy

Doctoral Dissertations

Banach spaces of analytic functions are defined by norming a collection of these functions defined on a set X. Among the most studied are the Hardy and Bergman spaces of analytic functions on the unit disc in the complex plane. This is likely due to the richness of these spaces.

An analytic self-map of the unit disc induces a composition operator on these spaces in the natural way. Beginning with independent papers by E. Nordgren and J. V. Ryff in the 1960's, much work has been done to relate the properties of the composition operator to the characteristics of the …

On The Value Functions Of Some Singular Optimal Control Problems., Jesus Alberto Pascal

LSU Historical Dissertations and Theses

Infinite horizon singular optimal control problems with control taking values in a closed cone U in Rn lead to a dynamic programming equation of the form: maxF2x,v, v',v'' ,F1x,v,v' =0, forall x∈Q, where Q , the state space of the control problem, is some nonempty connected open subset of Rn , and F1, F2 are continuous real-valued functions on QxR2 and QxR3 respectively, with the coercivity assumption for F 2, that is, the function r&rarrr;F2x,u,p,r is nonincreasing on R . A major concern is to determine how smooth the value function v is across the free boundary of the problem. …

On The Second Stiefel-Whitney Class Of Scaled Trace Forms Of Central Simple Algebras., Rosali Brusamarello

LSU Historical Dissertations and Theses

In this work we compute the second Stiefel-Whitney class $w\sb2$ of the scaled trace form $Q\sb{A,a}(x)={\bf tr}\sb{A/k}(ax\sp2),$ where A is a central simple algebra over a perfect field k of characteristic different from two, $a\in A$ is a fixed element, and ${\bf tr}\sb{A/k}$ is the reduced trace. The first three chapters provide background material about quadratic forms, central simple algebras, group cohomology, and representations of linear algebraic groups. The fourth chapter presents two known results about the second Stiefel-Whitney class of trace forms: Serre's formula for the case of etale algebras and Saltman's formula for the case of central simple …

Spikes In Matroid Theory., Zhaoyang Wu

LSU Historical Dissertations and Theses

For an integer $n\ge 3,$ a rank-n matroid is called an n-spike if it consists of n three-point lines through a common point t such that, for all k in $(1, 2,\..., n - 1),$ the union of every set of k of these Lines has rank $k + 1.$ The point t is called the tip of the n-spike. Ding, Oporowski, Oxley, and Vertigan proved that, for all $n\ge 3,$ there is an integer $N(n)$ such that every 3-connected matroid with at least $N(n)$ elements has a minor isomorphic to a wheel or whirl of rank $n,\ M(K\sb{3,n})$ or …

Maximal Circuits In Matroids., Pou-Lin Wu

LSU Historical Dissertations and Theses

Lovasz, Schrijver, and Seymour have shown that if a connected matroid M has a largest circuit of size c and a largest cocircuit of size c*, then M has at most 2c+c*-1 elements. A question of Oxley that has attracted considerable recent attention is whether there is an upper bound on the size of M that is polynomial in terms of c and c*. In particular, Bonin, McNulty, and Reid conjectured that 12cc* is such a bound. In Chapter 1, we prove this conjecture for an connected graphic and cographic matroids. In Chapter 2, we give a constructive description of …

A Study Of Secondary Mathematics: Reports Impacting Curriculum, Philip B. Nelson

OTS Master's Level Projects & Papers

The research goals of this study include: 1. What influence did societal pressures of the time have toward the reports recommended curriculum? 2. What influences did technological developments of the time have toward the reports recommended curriculum? 3. What were or are unique (if any) mechanisms of the time that initiated the perceived need for reform in mathematics education? 4. What influence did changing college entrance requirements of the time have towards the reports recommended curriculum? 5. What curricula was recommended to ensure student study achieved the desired performance in mathematics?

Research In Mathematics Education: A Contemporary Perspective, Alistair Mcintosh (Ed.)

Research outputs pre 2011

The twelve chapters in this book-all but two written by researchers in Australian universities-provide ample evidence of the impressive contributions currently being made by Australia to research in mathematics education. The authors' fields of inquiry are diverse: they include discussion of the roles of language and imagery, problem posing and problem solving, students' beliefs and students' thinking, gambling and mental computation. T!1eir methodologies are no less diverse, incorporating descriptions of both quantitative and qualitative research projects, including action research in classrooms, theoretical perspectives and the development of theoretical models, reviews of research, surveys, clinical interviews and descriptions of new research …

How Can We Make Our Mathematics Lessons Meaningful And Enjoyable?, Takbir Ali

Book Chapters / Conference Papers

No abstract provided.

Characterisations Of Slender Groups, Thomas Kelly

Masters

Chapter 1 summarises some necessary results concerning free, divisible, algebraically compact and cotorsion groups. A detailed proof of the well-known result that the Specker group P is ℵ1 free but not free is included and the structure of the quotient group P/S is determined. The basic properties of slender groups are examined and cotorsion groups of cardinality less than or equal to that of the continuum are shown to be epimorphic images of P. Chapter II presents Nunke’s characterisation of slender groups. This approach establishes that homomorphic images of the Specker group P are the direct sum of a cotorsion …

Evaluating Action Research As A Model For School-Based Professional Development Of Secondary Mathematics Teachers In The Philippines, Florenda L. Gallos

Theses: Doctorates and Masters

This study documented a school-based professional development activity conducted in a secondary school in the Philippines where five secondary mathematics teachers and the head of the school participated in a program of action research. The effectiveness of action research as a form of professional development and the constraints in using this form of professional development in the Philippines were evaluated based on the changes on teachers in terms of pedagogical knowledge, practices and beliefs. Qualitative research techniques were used. The methodology included questionnaires, interviews, class observations and diaries. The results indicated that the involvement of the participants in the action …

How Schools In Western Australia Are Responding To The Pressures Of Accountability In Mathematics Education, Lynne Messenger

Theses: Doctorates and Masters

Western Australian primary schools have responded to the Education Department's call for school accountability in many areas of the school accountability. This study focuses on the endeavours that schools have made to demonstrate their accountability in the subject area of Mathematics. The document "Improving and Reporting Schools' Performance" was made available to all state primary schools at the beginning of the 1996 school year as part of the Student Outcome Statement package. However, only a small number of primary schools have used the Student Outcome Statements in Mathematics in the National Professional Development Program trial conducted by the Commonwealth Department …

Professional Development And Practice: A Study Of Early Childhood Teachers Of Mathematics, Wendy Hawthorne

Theses: Doctorates and Masters

In the past twenty years there has been increased interest in the ways in which teachers construct their professional lives. It is no longer assumed that preservice education alone will enable teachers to meet the challenges of their teaching lives. Ongoing professional development is seen as an essential component of contemporary teachers' lives but remains a challenge for professional development planners and providers. The nature and extent of teachers' participation in professional development was a significant dimension of the investigation of professional development contained in this thesis. The research questions which formed the basis for the data collection in this …

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 …

Implications Of Extended College Algebra On Western Kentucky University Students, Julie Anne Baker

Mahurin Honors College Capstone Experience/Thesis Projects

College algebra has the highest enrollment of any mathematics course at Western Kentucky University. In an effort to increase the success rate in this course, Western Kentucky University added an extended version of college algebra to the curriculum in the fall of 1997. The extended version incorporates two days of supervised study per week in addition to traditional lectures. This study investigates the success of the extended college algebra course on achievement rates of Western Kentucky University students.

Foundations Of Object-Based Specification Design, David March Fleming

Graduate Theses, Dissertations, and Problem Reports (ETD)

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 …

Using The Simplex Code To Construct Relative Difference Sets In 2-Groups, James A. Davis, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Relative Difference Sets with the parameters (2^a, 2^b, 2^a, 2^a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

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 …

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 {, …

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.

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 …

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 …

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

Theses Digitization Project

No abstract provided.

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

Theses Digitization Project

No abstract provided.

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.

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 …