Digital Commons Network^™

Some Aspects Of Multi Source Satellite Image Processing., L. Lalitha Dr.

Doctoral Theses

The observation of a target by a device plaoed at some distance from it is cal.led remote sensing as ngainst in situ sensing where the sensor is kept in contact with the target. Usually physical emanations such as the electr omagnetic radiation from the target s observed by the sensing device. Sensors mounted on aircraft or satallite platforms measure the amount of energy reflected from or emitted by the earth's surface. Sensors scan the ground below a nd to either side of the satellite platform and as the platform noves forward, an image of the earths surface is formed.A satellite …

Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.

Doctoral Theses

Neyman and Scott (1948) were the first to point out that the method of maximum likelihood fails to provide elfficient estimates when the number of parameters grows with the sample size n. Consider the following examples introduced by them:Ezample 1.1 Let { Xi } be a sequence of independent random vectors in I", components Xij of Xi being independent normal with mean u, and variance o2 Ilere o2 is the parameter of interest. It is casy to sce that the maxinum likelihood estimate for o2 is not even consistent. It is also known (see Lindsay (1980), Pfanzagl (1982), van der …

The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.

Doctoral Theses

In the first part of this chapter we explain in general terms the main theme of this thesis and provide a chapter wise summary of its principal results. The second part recapitulates some of the known notions and results used in the subsequent chapters. The numbers given in parentheses correspond to those in the list of references on page 70.S. Mazur (40] was the first to consider the following smoothness property in normed linear spaces, called the Mazur Intersection Property (MIP), or, more briefly, the Property (1):Every closed bounded convex set is the intersection of closed balls containing it.He showed …

Tournaments And Ideal Class Groups., Robert John Kingan

LSU Historical Dissertations and Theses

In a series of papers published in the 1930's, L. Redei and H. Reichardt established a method for determining the 4-rank of the narrow ideal class group of a quadratic number field, essentially by finding the rank over ${\bf F}\sb2$ of a $\{0,1\}$-matrix determined by applying the Kronecker symbol to the prime divisors of the field discriminant. When this field is of the form ${\bf Q}(m\sp{1\over2}),$ with $m={\pm}p\sb1{\cdots}p\sb{n},$ each $p\sb{i}\equiv3$ (mod 4) prime, this matrix takes a form similar to that of the adjacency matrix for a tournament graph. Also, in this case we can find the 4-rank of the …

Finite Groups As A Generalization Of Vector Spaces Through The Use Of Splitting Systems, Joseph Kirtland

Doctoral Dissertations

The structure of a finite group is investigated through a geometry induced by the splitting systems of the group. The method is based on the one used to induce a geometry on a finite dimensional vector space over a finite field and as a result, concepts related to the special and projective linear group are extended to arbitrary groups. One major by-product is the classification of solvable multiprimitive groups of arbitrary derived length. This leads to a necessary and sufficient condition for a solvable nC-group to be multiprimitive.

Beliefs, Autonomy, And Mathematical Knowledge, Judy Ann Rector

Doctoral Dissertations

The purpose of this study was to investigate the apparent effects of students' beliefs about mathematics and autonomy on their learning of mathematics. The study utilized a multiple-case study design with analysis by and across cases. The cases represented six high school students enrolled in either Algebra II or Algebra II/Trigonometry. Data was collected in three phases: (a) classroom observations and assessment of the teacher's perception of her role in the learning process, (b) an assessment of students' beliefs about mathematics and autonomy, and (c) an assessment of students' newly formed mathematical constructs on functions.

The beliefs' assessment included observing …

Attitudes And Beliefs Of Preservice Elementary School Teachers Towards Mathematics, Deborah Beam Ingalls

UNLV Retrospective Theses & Dissertations

This study purposed to see if measurable changes could be detected in prospective teachers' attitudes or beliefs about mathematics as teachers progressed through their required courses of study in mathematics and mathematics education. The study included 164 prospective elementary school teachers who were enrolled in one of three mathematics or mathematics education courses. The subjects responded to a survey based on common "mathematics myths." The mathematics myths correspond to mathematical beliefs shown in other research to be held by severely math anxious or math avoidant people. The study found that students disagreed more with the mathematics myths as they progressed …

Fourier Transform And Heat Equation In White Noise Analysis., Jung-Soon Kim Lee

LSU Historical Dissertations and Theses

In this dissertation, we study the Fourier transform and heat equation in the white noise set-up. It is known that the Fourier transform ${\cal F}$ can be defined on the space (${\cal S}$)* of generalized white noise functionals. We prove that ${\cal F}$ is the adjoint of a certain linear operator on the space (${\cal S}$) of test functionals. On the other hand, it is known that if f is a bounded Lip-1 function on an abstract Wiener space with Gaussian measures $P\sb{t},$ then $u(t)=P\sb{t}f$ solves the heat equation ${d\over dt}u(t)={1\over2}\Delta\sb{G}u(t)$ with initial condition u(0) = f where $\Delta\sb{G}$ is …

Banach Space Valued Stochastic Differential Equations., Fariborz Asadian

LSU Historical Dissertations and Theses

Let $W(t,\omega)$ be a Brownian motion on an abstract Wiener space (i,H,B) corresponding to the canonical normal distribution on H. The well known theorem of Girsanov is proved for such a process with the perturbing term taking values in the Hilbert space H. Consider the stochastic integral equation $\xi(t) = x+\int\sbsp{0}{t}A(s,\xi(s))dW(s)+\int\sbsp{0}{t}\sigma(s,\xi(s))ds$ where x is in $B,\ A(\cdot,\cdot)$ and $\sigma(\cdot,\cdot)$ are bounded continuous functions from $\lbrack 0,\infty)\times B$ to $I+L\sb2(H)$ and H respectively. Here $L\sb2(H)$ denotes the collection of Hilbert Schmidt operators on H. Furthermore, suppose for every $s\ge 0$ the restriction of $A(s,\cdot)$ to H is invertible and $A(s,\cdot)$ and …

Sex-Related Differences In Autonomous Learning Behaviours And Mathematics Achievement, Laura Beahan

Theses : Honours

The autonomous learning behaviour model proposed by Fennema and Peterson (1985a, 1985b) hypothesises that sex- related differences in mathematics are a result of sex-related differences in autonomous learning behaviours. Autonomous learning behaviours include choosing to engage in high-level tasks, preferring to work independently on such tasks and persisting at them. The purpose of this study was to investigate sex-related differences in autonomous learning behaviours and to determine any relationship between the presence of these behaviours and achievement in mathematics. Twelve students studying the Year 1 unit "Foundations of Mathematics" were selected for the study, including two males and two females …

Lattice Statistics Of Polymer Adsorption, Dongming Zhao

Digitized Theses

The interaction of branched polymers with an adsorption surface is studied using rigorous and numerical methods. For a polymer network with a fixed topology and consisting of self-avoiding chains, we prove that the reduced free energy is the same as that for self-avoiding walks interacting with a surface. For a network modelled by a lattice animal, we prove that a phase transition exists when such an animal interacts with a surface. The transition points are numerically studied by one and two variable Pade approximants. A number of rigorous results for the statistics of lattice animals are also obtained.

Pseudo Almost Periodic Functions And Their Applications, Chuanyi Zhang

Digitized Theses

The space of pseudo almost periodic functions on {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}{dollar} (denoted by {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} when they are vector-valued and {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}){dollar} when they are scalar-valued, {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\lbrack a,\infty){dollar} for {dollar}a\in\IR{dollar} and {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\IR{dollar} for {dollar}a={lcub}-\infty{rcub}{dollar}, X is a Banach space) is defined and its properties are studied. A decomposition theorem is given showing that a function is in {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} if and only if it is the sum of an almost periodic function and an ergodic perturbation. The relation between a pseudo almost periodic function and its almost periodic component is discussed. It is shown that {dollar}{lcub}\cal …

Hopf Algebras And Cohomology Operations, Zaiqing Li

Digitized Theses

The main purpose of this thesis is to study product structures of Hopf algebras, in particular for the cases of the Steenrod algebra and the Brown-Peterson algebra. In Chapter 1, we are given a Hopf algebra with basic operations {dollar}\{lcub}D\sp{lcub}R{rcub} \vert R :{dollar} exponential sequences{dollar}\{rcub}{dollar}, the coalgebra structure being the Cartan Formula. The main theorem is a formula expressing the products {dollar}D\sp{lcub}R{rcub}\cdot D\sp{lcub}S{rcub}{dollar} of basic operations using a star operation of scalar parameters. In Chapter 2, the Milnor Product Formula for the Steenrod algebra is shown to be a consequence of the main theorem in Chapter 1. The weighted symmetrical …