Physical Sciences and Mathematics Commons^™

Essay On Deprivation, Poverty And Well-Being., Diganta Mukherjee Dr.

Doctoral Theses

Issues like inequity, deprivation and poverty have been a focus of interest for social scientists for a long time. The present thesis explores a few aspects of the above issues. It ermbodies the fruit of my intellectual perambulation in the Economic Research Unit of Indian Statistical Institute (ISI) during the years 1995 - 97. The text is divided into six chapters. The first chapter gives a general overview of different aspects of measuring inequality, deprivation and poverty. The second, third and fourth chapters take up the issue of deprivation measurement in detail. They contain discussions on deprivation ordering, indices and …

Construction Of Some Combinatorial Designs Arising Out Of Statistical Experiments., Tridib Kumar Dutta Dr.

Doctoral Theses

Chis dissertation considers construction of two kinds of combi natorial sesigns as used by statisticians: repeated measurements designs (RMDS) and symmetric balanced squares (SBSS). 1.1. REPEATED MEASUREMENTS DESIGNS The researchers need to perform experiments where each experimental unit receives some or all of the treatments in an appropriate sequence over a number of successive periods. These designs are known by several names in the statistical 1iterature: repeated measurements designs, crossover or changeover designs, (multiple) time series designs, and before-after designs. If there are n experimental units 1,2, ... n, t treatments and p periods 0,1, .. .p-1, applied, then an …

A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones

Dissertations

A central question in the area of topological graph theory is to find the genus of a given graph. In particular, the genus parameter has been studied for Cayley graphs. A Cayley graph is a representation of a group and a fixed generating set for that group. A group is said to be planar if there is a generating set which produces a planar Cayley graph. We say that a group is toroidal if there is a generating set that produces a toroidal Cayley graph and if there are no generating sets which produce a planar Cayley graph. Characterizations for …

Asymptotic Norming Properties And Related Themes., Sudeshna Basu Dr.

Doctoral Theses

In the first part of this chapter, we explain the main theme of this thesis. The second part consists of some of the notions and results used in subsequent discussions.It is a very familiar fact that a point outside a (bounded) closed convex set in a Banach space can be separated from the latter by a hyperplane. One can ask whether the separation can be effected by disjoint balls. This is a typical example of a ball separation property, study of which has become important in Banach space theory. In this thesis, we study several such properties along with some …

Superconvergence In Iterated Solutions Of Integral Equations, Peter A. Padilla

Mathematics & Statistics Theses & Dissertations

In this thesis, we investigate the superconvergence phenomenon of the iterated numerical solutions for the Fredholm integral equations of the second kind as well as a class of nonliner Hammerstein equations. The term superconvergence was first described in the early 70s in connection with the solution of two-point boundary value problems and other related partial differential equations. Superconvergence in this context was understood to mean that the order of convergence of the numerical solutions arising from the Galerkin as well as the collocation method is higher at the knots than we might expect from the numerical solutions that are obtained …

The Solution Of Hypersingular Integral Equations With Applications In Acoustics And Fracture Mechanics, Richard S. St. John

Mathematics & Statistics Theses & Dissertations

The numerical solution of two classes of hypersingular integral equations is addressed. Both classes are integral equations of the first kind, and are hypersingular due to a kernel containing a Hadamard singularity. The convergence of a Galerkin method and a collocation method is discussed and computationally efficient algorithms are developed for each class of hypersingular integral equation.

Interest in these classes of hypersingular integral equations is due to their occurrence in many physical applications. In particular, investigations into the scattering of acoustic waves by moving objects and the study of dynamic Griffith crack problems has necessitated a computationally efficient technique …

On The Developement Of An Optical Character Recognition(Ocr) System For Printed Bangla Script., Umapada Pal Dr.

Doctoral Theses

This thesis concerns OCR development of machine printed text in an Indian lan- guage, Bangla (Bengali) which is the fourthmost popular language in the world and the secondmost popular language in India.1.1 Optical Character Recognition Optical Character Recognition (OCR) is a process of automatic computer recog- nition of characters in optically scanned and digitized pages of text. OCR is ene of the most fascinating and challenging areas of pattern recognition with various practical applications. It can contribute tremendously to the advancement of an automation process and can improve the interface between man and machine in many applications, including office automation …

Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki

Theses and Dissertations

Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L₂(R) and the Hardy spaces H_p(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …

Units In Integral Group Rings For Direct Products, Richard M. Low

Dissertations

Given a finite group G and the ring of integers, one can form the integral group ring ZG . A natural problem to investigate is to find a description of the group of units for this ring ZG. Since the unit problem for integral group rings arises in the contexts of algebraic topology, number theory, and algebra, it is an important question to try to answer. For this reason, it has drawn the attention of researchers from diverse areas of mathematics.

Graham Higman (circa 1940) made substantial contributions to the solution of this problem, in the case where G was …

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann

Dissertations

No abstract provided.

The Dirichlet Problem And Its Physical Motivations, Andrew E. Pitts

Honors Theses

In this work, we explore the basics of harmonic function theory and its relationship to problems in the theory of heat diffusion. In particular, we will focus on the classical Dirichlet problem.

Statistical Characterization Of Fluvial-Deltaic Reservoirs With Archetypes, Laura L. Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Optimizing the extraction of oil and other hydrocarbon products from existing sites is important. One source of hydrocarbon products is reservoirs found within sedimentary rock formations. Understanding fluid behavior within such formations can be quite useful in optimizing oil production. Fluid behavior within sedimentary formations is influenced by the bedform structure and permeabilities within the formation. Thus, we are concerned with developing a physically and statistically valid method of characterizing sedimentary rock formations. The use of archetypal analysis to generate synthetic bedforms, as well as the use of Kriging to assign permeabilities within a bedform, was explored. With these tools, …

Problems In Harmonic Function Theory, Ronald A. Walker

Honors Theses

Harmonic Function Theory is a field of differential mathematics that has both many theoretical constructs and physical connections, as well as its store of classical problems.

One such problem is the Dirichlet Problem. While the proof of the existence of a solution is well-founded on basic theory, and general methods for polynomial solutions have been well studied, much ground is still yet to be overturned. In this paper we focus on the examination, properties and computation methods and limitations, of solutions for rational boundary functions.

Another area that we shall study is the properties and generalizations of the zero sets …

Reaction-Diffusion Models Of Cancer Dispersion, Kim Yvette Ward

Mathematics & Statistics Theses & Dissertations

The phenomenological modeling of the spatial distribution and temporal evolution of one-dimensional models of cancer dispersion are studied. The models discussed pertain primarily to the transition of a tumor from an initial neoplasm to the dormant avascular state, i.e. just prior to the vascular state, whenever that may occur. Initiating the study is the mathematical analysis of a reaction-diffusion model describing the interaction between cancer cells, normal cells and growth inhibitor. The model leads to several predictions, some of which are supported by experimental data and clinical observations $\lbrack25\rbrack$. We will examine the effects of additional terms on these characteristics. …

Sparse Equation-Eigen Solvers For Symmetric/Unsymmetric Positive-Negative-Indefinite Matrices With Finite Element And Linear Programming Applications, Hakakizumwami Birali Runesha

Civil & Environmental Engineering Theses & Dissertations

Vectorized sparse solvers for direct solutions of positive-negative-indefinite symmetric systems of linear equations and eigen-equations are developed. Sparse storage schemes, re-ordering, symbolic factorization and numerical factorization algorithms are discussed. Loop unrolling techniques are also incorporated in the coding to enhance the vector speed. In the indefinite solver, which employs various pivoting strategies, a simple rotation matrix is introduced to simplify the computer implementation. Efficient usage of the incore memory is accomplished by the proposed "restart memory management" schemes. A sparse version of the Interior Point Method, IPM, has also been implemented that incorporates the developed indefinite sparse solver for linear …

Mathematical Models Of Tumors And Their Remote Metastases, Carryn Bellomo

Mathematics & Statistics Theses & Dissertations

Clinical observations and indications in the literature have led us to investigate several models of tumors. For example, it has been shown that a tumor has the ability to send out anti-growth factors, or inhibitors, to keep its remote metastases from growing. Thus, we model the depleting effect of such a growth inhibitor after the removal of the primary tumor (thus removing the source) as a function of time t and distance from the original tumor r.

It has also been shown clinically that oxygen and glucose are nutrients critical to the survival and growth of tumors. Thus, we model …

Neuro Fuzzy Reasoning For Pattern Classification And Object Recognition., Jayati Ghosh Dr.

Doctoral Theses

In real world, pattern classification and object recognition problems are faced with fuzzi- ness that is connected with diverse facets of cognitive activity of the human being. An origin of sources of fuzziness is related to labels expressed in feature space as well as to labels of classes taken into account in classification and /or recognition procedures. Though a lot of scientific efforts have already been dedicated to pattern recognition problems, especially to classification procedures, still pattern recognition is confronted with a continuous challenge coming from a human being who can perform lot of ex- tremely complex classification tasks by …

Wiener Tauberian Theorems On Semisimple Lie Group., Rudra Pada Sarkar Dr.

Doctoral Theses

In their celebrated study of Harmonic analysis on semi-simple Lie groups Ehrenpreis and Mautner [E-M] noticed that the analogue of the claasical Wiener Tauberian theorem resting on the unitary dual does not hold for semisimple Lle groups. A simple proof of this fact due to M. Duflo appears in (H). Ehrenpreis and Mautner went on in (E-M] to formulate the problem on the commutative Banach algebra of the SO2(R)-biinvariant functions in L1(SL2(R))1, and obtained two different versions of the theorem involving, this time, the dual of the Banach algebra which includes, beside the unitary dual of G, a part of …

Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.

Doctoral Theses

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.

Doctoral Theses

GraphsA graph G = (VE) consists of a finite set V and a subset E of ). (Here () denotes the set of all 2-subsets of V.) Elements of Vare called the vertices and the elements of E are called the edges of the graph. So Vis the vertex set and E is the edge set of the graph G. Two vertices a, y are said to be adjacent if the pair {a, y} is an edge; otherwise they are non-adjacent. If two vertices are adjacent then each is called a neighbour of the other vertex.Sometimes the edges of a …

On Lipschitzian, And Connected Matrices In: Linear Complementarity Problem., Sriparna Bandyopadhyay Dr.

Doctoral Theses

This dissertation deals with a number of questions related to the linear complementarity problem (LCP). Given A ∈ Rn*n and q ∈ Rnthe LCP is to find a vector z ∈ R" such that Az+q ≥0,≥ and 2'(Az + 9) = 0. There is a vast literature on LCP developed during the last four decades. LCP plays a crucial role in the study of Mathematical Progranming from the point of view of algorithms as well as applications. The questions on existence and multiplicity of solutions in LCP has led researchers to introduce and study a variety of matrix classes. Most …

A Study In Geometric Construction, Nichola Sue Mcclain

Theses Digitization Project

No abstract provided.

Using Symbolic Dynamical Systems: A Search For Knot Invariants, Russell Clark Wheeler

Theses Digitization Project

No abstract provided.

Stochastic Analysis Of Quality Control Charts Using Integral Equations, Kenneth Adam Scharnagl

Legacy ETDs

No abstract provided.

A Bayesian Meta-Analysis Using The Gibbs Sampler, Shannon Marie Fair

UNF Graduate Theses and Dissertations

A meta-analysis is the combination of results from several similar studies, conducted by different scientists, in order to arrive at a single, overall conclusion. Unlike common experimental procedures, the data used in a meta-analysis happen to be the descriptive statistics from the distinct individual studies.

In this thesis, we will consider two regression studies performed by two scientists. These studies have one common dependent variable, Y, and one or more independent common variables, X. A regression of Y on X with other independent variables is carried out on both studies. We will estimate the regression coefficients of X …

Cyclic Cutwidth Of Three Dimensional Cubes, Ray N. Gregory

Theses Digitization Project

No abstract provided.

A Study Of Optimization In Hilbert Space, John Awunganyi

Theses Digitization Project

No abstract provided.

State Sum Invariants Of Three Manifolds, Sharon Angela Newman-Gomez

Theses Digitization Project

No abstract provided.

Torus Embedding And Its Applications, Rick Hung Nguyenhuu

Theses Digitization Project

No abstract provided.

Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups, Iem H. Heng

Mathematics & Statistics Theses & Dissertations

Classical Hadamard matrices are orthogonal matrices whose elements are ±1. It is well-known that error correcting codes having large minimum distance between codewords can be associated with these Hadamard matrices. Indeed, the success of early Mars deep-space probes was strongly dependent upon this communication technology.

The concept of Hadamard matrices with elements drawn from an Abelian group is a natural generalization of the concept. For the case in which the dimension of the matrix is q and the group consists of the p-th roots of unity, these generalized Hadamard matrices are called “Butson Hadamard Matrices BH(p, q)”, …