Digital Commons Network^™

Model And Design-Based Analysis Of Complex Surveys., Joydip Mitra Dr.

Doctoral Theses

We consider estimating the total Y of a variable y defined on a survey population. The survey is complex only in the sense that we admit sample selection with arbitrary probabilities. Our 'analysis' consists in examining efficacies of conf Idence intervals for the For this we need point estimators and or mean square error (MSE) variance { estimators, respectively say, total. the corresponding e and v. The distribution, resulting from repeated sampling, of the pivotal quantity d = (e-Y)/V 1s supposed to approximate that of standard normal deviate t or of Students t with (n-1) degrees of freedom, assuming large …

Studies On Design, Routing And Fault Tolerance Of Interconnection Network., Krishnendu Mukhopadhyay Dr.

Doctoral Theses

A recent trend in computing is to distribute the computations among a set of processing elements. There are two basic appronches to this - one is to build a loosely-coupled system and the other is to form a tightly-coupled system [PS85].In a loosely-coupled system, the processors do not share common memory or a common clock; but sharing of important resources like data files, softwares, special hardware components etc., is possible without duplicating the resources themselves. The processing nodes may even be geographicully separated from each other and are connected through databuses, telephone/radio links, satellite, etc. Such loosely- coupled systems are …

Markov Dilation Of Nonconservative Quantum Dynamical Semigroups And Quantum Boundary Theory., B. V. Rajarama Bhat Dr.

Doctoral Theses

In classical probability theory, based on Kolmogorov consistency theorem, one can associate a Markov process to any one parameter semigroup of stochastic matrices or transition probability operators. It is indeed the foundation for the theory of Markov processes. Here a quantum version of this theorem has been established. This effectively answers some of the questions raised by P. A. Meyer in his book (see page 220 of (Me).It is widely agreed upon that irreversible dynamics in the quantum setting is de- scribed by contractive semigroups of completely positive maps on C" algebras ([Kr). (AL]). In other words these semigroups, known …

Multivalued Approach For Uncertainty Management., Deba Prasad Mandal Dr.

Doctoral Theses

Real life problems are rarely free from uncertainty which usually emerges from the deficiencies of information available from a situation. The defi- ciencies may result from incomplete, imprecise, not fully reliable, vague or contradictory information depending on the problem. Management of uncer- tainty in a decision making system has been an important research problem for many years.Until the inception of the concept of fuzzy set theory in 1965 (1), the theory of probability and statistics was the primary mathematical tool for modeling uncertainty in a system/situation. Fuzzy set theory has shown enormous proinise in handling uncertaintics to a reasonable extent …

Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.

Doctoral Theses

The main theme of this t hesis is hypergroups. In this thesis the the- ory of hypergroups is applied to study the relation between certain graphs and subfactors of II, factors in the context of principal graphs associated with the inclusions of II, factors. More general classes of hypergroups are iutroduced, new examples of hypergroups associated to certain graphs are coustructed and classification of small order hypergroups is discussed.The text of the thesis is arranged in four chapters. The first chapter is on preliminaries of the theory of hypergroups, the second on the appli- cation of the theory of hyjrrgroups …

Some Limit Theorem On Conditional U-Statistics And Censored Data Non Parametric Regression., Arusharka Sen Dr.

Doctoral Theses

In Statistics, a classical problem is that of estimating the regression function which is defined as m{t) := E(Y|X = ), te R, for two random variables X and Y such that EY < 0o. The estimators are constructed iased on a sample {(Xi, Yi.)}, 1sis n,n 2 1, from the distribution of (X, Y). Throughout this thesis, we assume X and Y to be real-valued for the sake of convenience. The classical approach to this problem is to assume a parametrized, polynomial form for nt-), i.e., m(t) := Bo + E-1 P,ti, p 21, and obtain estimates of the unknown paraineters Bo, Bj,, 1sjsp. Later, with the development of techıniques for non-parametrie density estimation, it was sought to extend these techniques to regression estimation. Heuristically, the two problems can be seen to be related as follows : let fi(-) be the marginal density of X and note that E1(X S x) = h(t)dt, z € R, whereas EY 1(X Sx) = m(t)fi(t)dt, x E MR. (1.0.2) In other wordds, (1.0.1) can be looked upon as a special case of (1.0.2), with Y = 1. + similarity, as we shall see later on, has been the underlying theme in Chapters 2 and 4 of the present work.) The following non-parametric regression estimator was proposed independently by Nadaraya (1964) and Watson (1964): "(): := m.(Y,)/m.(1, ), te R, (1.0.3) where m,(Y, t) = (nan)- E-, Y;K((t - X:)/an). (1.0.4) m,(1,1) (na,)-E, K((I - X)/a,). Here K(), the so-called kernel function, is chosen to satiafy various analytical conditions (typically, K(-) is taken to be a density function), and a, 1 0 are the bandwidths which go to zero sufficiently slowly (e.g., na,0o as n00) in order to ensure consistency of the estimator mW (). The intuition behind such an estimator is that m,(Y,) is an estimator of mt-)fi() while m,(1,) cstimates the density fa(-). See Prakasa Rao (1983), Chapters 1-4. for an introduction to non-parametric density and regression estimation. Now, m(t) is a functional of the conditional distribution of Y, given X = t. A natu- ral generalisation of the regression estimation problem seems to be the estimation of the following functionals: mh(t1,....tk) := E{h(Y1,.....Yk) | X1, = t1.,Xk. = tk), (t....) € R*, k 2 1, (1.0.5) where h: R*- R is such that Elh(Y...., Y) < 0. A similar generalisation led Hoelfding (1948) from the sample mcan to the theory of so-called U-statistics, in the uncondilional set-up. The estimation of (1.0.5) were considerexl, for the first time in published form, in Stute (1991) where the following conditional U-statistics were proposed as estimators;where Fn(-) := n-1E, 1(Xi; < ) denotes the empirical distribution function (c.d.f Bochynek discussed the asymptotic normality of conditional U- and V-statistics and pei formed simulation studies on them. Stute (1991) established weak and strong pointwis consistency and asymptotic normality of U(t). Liero (1991) studied uniform strong con sistency of conditional U-statistics and established asymptotic normality of the integrate squared error (ISE) statistic:for suitable A c R* and weight function w(-). We quote the following examples to illustrate the possible use of conditional U-statistics See Stute (1991) and Bochynek (1987) for other examples. Throughout this thesis, our set up will be as foliows: {(Xn, Yn)}n>ı is a bi-variate i.i.d sequence, with (X1, Y1) having join density f(,-) and X, having marginal density fi(-). Consequently,

Discrete Singularity Method And Its Application To Incompressible Flows., S K. Venkatesan Dr.

Doctoral Theses

The smooth flow of a fluid has sprung many surprises. A flow which at an instant of time is quite regular and orderly could produce on the slightest of disturbance a complex bewildering varieties of flows, broadly termed as turbulence. Direct numerical simulation of the Navier-Stokes equations have shown that it is quite possible that these turbulent flows are solutions of the Navier-Stokes equations. In fact it is by now well recognized that many non-linear systems produce chaos quite similar to turbulence. However the large number of scales and their complex interactions involved make turbulence difficult to understand. Direct numerical …

Study Of Moduli Of Bundles., Indranil Biswas Dr.

Doctoral Theses

Hitchin (Hi2) realized the importance of studying pairs (E,∅) where E is a vector bundle and ∅ is a homomorphism of E into EOL for a fixed line bundle L. When C is a smooth pro jective algebraic curve this has since been studied quite extensively. One can construct a covering of C in this situation and the given data can be completely recovered by this covering map and a line bundle on the covering curve (see Beauville, Narasimhan and Ramanan (BNR]). When L is the canonical bundle this procedure gives a completely integrable system on the cotangent bundle of …

Parametric Homotopy Principle Of Some Practical Differential Relations., Mahuya Datta Dr.

Doctoral Theses

A system uf r-th order partial differential inequalities is a subspace in the space of r-jets of CT" maps between manifolds. The problem of homotopy classification of C solutions of such systems is stauliel in this thesis. The text roughly divides into two parts. In the first part, the problem is considered in an equivariant setting when the system is open and invariant under the action of a compact L.ie group, but may not be invariant under the action of the pseudogroup of equivariant local diffeomorphisms. The second part concerns a non-equivariant set-up without the openness condition on the systern. …

Decomposable Functions And Universal C*-Algebras, Llolsten Kaonga

Doctoral Dissertations

This paper deals with universal $C\sp\*$-algebras generated by matricial relations on the generators, for example, the universal $C\sp\*$-algebra with generators $a\sb{ij}, 1 \leq i,j \leq n$, subject to the condition that the matrix ($a\sb{ij}$) be normal and have spectrum in a designated compact subset ${\cal K}$ of the complex plane.

The main thrust of the paper is to compute the K-groups of some of these $C\sp\*$-algebras and to determine when they contain non-trivial projections. In the above example, we show that the K-groups of the algebra coincide with the topological K-groups of the set ${\cal K}$. We show, in general, …

Stability Properties For The Constant Of Hyperreflexivity, Ileana Ionascu

Doctoral Dissertations

Let H be a separable, complex, Hilbert space and let ${\cal B}(H$) be the algebra of all (bounded linear) operators on H. We define a function$$\kappa:{\cal B}(H) \to \lbrack 1,\infty\rbrack;\qquad \kappa(T) = K({\cal A}\sb{w}(T)),\qquad \forall T \in {\cal B}(H),$$where ${\cal A}\sb{w}(T$) is the unital weakly closed algebra generated, in ${\cal B}(H$), by T, and $K({\cal A}\sb{w}(T$)) is the constant of hyperreflexivity of ${\cal A}\sb{w}(T$). If H is finite-dimensional, we show that $\kappa$ is continuous at $T \in {\cal B}(H$) if and only if T is non-reflexive or has dimH distinct eigenvalues (Theorem 2.6). An auxiliary result (Theorem 2.1) states that …

On The Berezin Symbol, Semra Kilic-Bahi

Doctoral Dissertations

Let ${\cal H}$ be a functional Hilbert space of analytic functions on a complex domain $\Omega,$ with the normalized reproducing kernel function $k\sb{z},\ z\in\Omega.$ If A is a linear map of ${\cal H}$ into itself, the Berezin symbol, A, of A is defined on $\Omega$ by $\tilde{A}(z) = \langle Ak\sb{z},\ k\sb{z}\rangle.$ The purpose of this research is to study how the properties of an operator are reflected in the properties of its Berezin symbol. In summary, I have (1) studied the properties of the Berezin symbol as a complex-valued function; (2) characterized multiplication operators, induced by a multiplier of ${\cal …

Reflexive Subspaces And Lattices Of Pairs Of Projections, Deborah Narang

Doctoral Dissertations

Consider the sets ${\cal P}\sb{\cal H}$ and ${\cal P}\sb{\cal K}$ of the projections onto closed subspaces of Hilbert spaces ${\cal H}$ and $\cal K$ respectively. From the usual partial orders (based upon set containment) on $\cal P\sb{\cal K}$ and $\cal P\sb{\cal H}$, we can define a partial order on $\cal P\sb{\cal K}\times\cal P\sb{\cal H}$ by ($Q\sb1,P\sb1)\le(Q\sb2, P\sb2)$ if and only if $P\sb1\le P\sb2$ and $Q\sb2\le Q\sb1.$ Then the map $\alpha : \cal P\sb{\cal K}\times \cal P\sb{\cal H}\to \cal P\sb{\cal K\oplus\cal H}$ given by $\alpha(Q,P)=(1-Q)\oplus P$ is an order-preserving map. In particular, if $\cal L\subseteq\cal P\sb{\cal K\times\cal H}$ is a lattice, …

A Paley-Wiener Theorem For All Two And Three-Step Nilpotent Lie Groups., Robert Reeve Park

LSU Historical Dissertations and Theses

A Paley-Wiener Theorem for all connected, simply-connected two and three-step nilpotent Lie groups is proved. If f $\epsilon \ L\sbsp{c}{\infty}({G}),$ where G is a connected, simply-connected two or three-step nilpotent Lie group such that the operator-valued Fourier transform $\\varphi(\pi)$ = 0 for all $\pi$ in E, a subset of G of positive Plancherel measure, then it is shown that f = 0 a. e. on G. The proof uses representation-theoretic methods from Kirillov theory for nilpotent Lie groups, and uses an integral formula for the operator-valued Fourier transform $\\varphi(\pi)$. It is also shown by example that the condition that G …

To Track Or Not To Track : Refining Middle School Mathematics, Jennifer E. Patton

Honors Capstones

This research project discusses the issue of tracking, or ability grouping, in the education system. Using this type of system, students are grouped into low, medium,and high ability groups in all or at least several of their subjects in school. This type of grouping is the most commonly used instructional method to facilitate for students' differences. However, educational literature and research shows that although students have differences in abilities and learning styles, tracking is not the most effective, efficient, or equitable way of accommodating for these differences. Hence, this research project not only discusses the evidence for and against tracking, …

Intersections Of Hyperconics And Configurations In Classical Planes, James Michael Mcquillan

Digitized Theses

Let {dollar}\pi{dollar} = PG(2,F), where F is a field of characteristic 2 and of order greater than 2. Given a conic, its tangents all pass through a common point, the nucleus. A conic, together with its nucleus, is called a hyperconic. All conics considered are non-degenerate.;First, a relationship is established between hyperconics and certain symmetric unipotent Latin squares for all finite projective planes.;Intersection properties of hyperconics in PG(2,F), Fano configurations containing points of a hyperconic, as well as certain subplanes of PG(2,F) are studied. An open question in {dollar}\pi{dollar} = PG(2,q), q even, is: what is the size and structure …

A Study To Determine The Relationship Between Students Who Excel In Mathematics And Students Who Excel In Technology Education, Kevin L. Pace

OTS Master's Level Projects & Papers

This study was used to gain information about the success of high school students in mathematics and technology. The goals established for this research are: 1. Students who excel in mathematics courses will also excel when studying technology education.

Structural Results For Matroids., Sandra Reuben Kingan

LSU Historical Dissertations and Theses

This dissertation solves some problems involving the structure of matroids. In Chapter 2, the class of binary matroids with no minors isomorphic to the prism graph, its dual, and the binary affine cube is completely determined. This class contains the infinite family of matroids obtained by sticking together a wheel and the Fano matroid across a triangle, and then deleting an edge of the triangle. In Chapter 3, we extend a graph result by D. W. Hall to matroids. Hall proved that if a simple, 3-connected graph has a $K\sb5$-minor, then it must also have a $K\sb{3,3}$-minor, the only exception …

Graphs In Number Theory., Leigh Ann Myers

LSU Historical Dissertations and Theses

In the 1930's L. Redei and H. Reichardt established methods for determining the 4-rank of the narrow ideal class group of a quadratic number field, Q($D\sp{1/2}).$ One of these methods involves determining the number of D-splittings of the discriminant, D, of the number field. Later, this method was revised so that we need only find the rank of a matrix over F$\sb2$. In some cases, these Redei matrices can be viewed as adjacency matrices of graphs or digraphs. In Chapter I we introduce the graphs and matrices mentioned above, the method for finding 4-ranks, and present some preliminary results on …

The Generalized Distributive Law As Tacit Knowledge In Algebra., Juanita Lavall Bates

LSU Historical Dissertations and Theses

The purposes of this study were to investigate theories that explain why common errors of the type ($a \pm b)\sp{c} = a\sp{c} \pm b\sp{c}$ and $\root c \of {a \pm b} = \root c \of {a} \pm \root c \of {b}$ occur in algebra problem solving by novices; and to develop and assess techniques for remediating these errors. The meaning theory of learning (ML), procedural learning theory (PL), and implicit structure learning theory (ISL) are alternative frameworks for the explanation of the errors. The ML theory hypothesizes that experts have rich semantic connections to the procedures and symbols of algebra, …

Generalizations Of The Optimal Control Problem For The Vidale-Wolfe Advertising Model., Richard Dale Edie

LSU Historical Dissertations and Theses

The purpose of this dissertation is to study two different generalizations of the optimal control problem based on the Vidale-Wolfe Advertising Model. The first problem is an infinite horizon free endpoint one-dimensional version of the Vidale-Wolfe optimal control problem of advertising in time varying markets. A solution is obtained for this problem. Then a thorough proof using the method of dynamic programming is presented to verify that this solution is optimal under reasonable market conditions. The second problem is a finite time fixed endpoint two-dimensional version of the Vidale-Wolfe optimal control problem. Normal optimal trajectories are obtained for this problem. …

Centralizer Of A Semisimple Element On A Reductive Algebraic Monoid, Marjoie Eileen Hull

Digitized Theses

Let M be a reductive linear algebraic monoid with unit group G and let the derived group of G be simply connected. The purpose of this thesis is to study the centralizer in M of a semisimple element of G. We call this set {dollar}M\sb0.{dollar};We use a combination of the theories of algebraic geometry, linear algebraic groups and linear algebraic monoids in our study. One of our main tools is Renner's analogue of the classical Bruhat decomposition for reductive algebraic monoids. Our principal result establishes an analogue of the Bruhat decomposition for {dollar}M\sb0.{dollar} This is a more general result than …

Determining The Validity And Reliability Of An Instrument Designed To Measure Metacognitive Behaviours, Anne L. Martin

Theses : Honours

This project was designed to study the role of metacognition in mathematical problem solving. More specifically, it was designed to determine the validity and reliability of an instrument proposed to identify metacognitive behaviours in Year 7 children solving problems. The instrument was used to analyse audio tapes of pairs of students working on a non-routine problem (i.e., a problem that cannot be solved solely by the direct application of the basic operations). Analysis of the audio tapes involved categorizing metacognitive decisions as: orientation, organization, execution, and verification behaviours. A "cognitive-metacognitive" framework (Garofalo & Lester, 1985) was used as a basis …

Digital Morphometry : A Taxonomy Of Morphological Filters And Feature Parameters With Application To Alzheimer's Disease Research, Andrew Mehnert

Theses: Doctorates and Masters

In this thesis the expression digital morphometry collectively describes all those procedures used to obtain quantitative measurements of objects within a two-dimensional digital image. Quantitative measurement is a two-step process: the application of geometrical transformations to extract the features of interest, and then the actual measurement of these features. With regard to the first step the morphological filters of mathematical morphology provide a wealth of suitable geometric transfomations. Traditional radiometric and spatial enhancement techniques provide an additional source of transformations. The second step is more classical (e.g. Underwood, 1970; Bookstein, 1978; and Weibull, 1980); yet here again mathematical morphology is …

Bounded Linear Operators On Banach Sequence Spaces, Xiaopeng Gao

Digitized Theses

We investigate matrices and sequences of operators as bounded linear operators on Banach sequence spaces in various situations, and some topics related to these matrices and sequences. This thesis consists of five chapters.;In the first chapter we study whether an infinite matrix, particularly a summability matrix, is a bounded linear operator on {dollar}l\sb{lcub}p{rcub} (p \ge{dollar} 1). Some restrictive conditions for Norlund and weighted mean matrices to be in {dollar}B(l\sb{lcub}p{rcub}){dollar} imposed by earlier authors we eliminated. Some results for weighted mean matrices are proved as consequences of more general results for generalized Hausdorff matrices.;A necessary and sufficient condition for a non-negative …