Digital Commons Network^™

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Gender Discourse In Small Learning Groups Of College-Level Developmental Mathematics Students, Allen W. Emerson

Dissertations

This study was motivated by the question as to whether women’s and men’s membership in different gender communicative cultures gives rise to gender differentiated ways of talking that are implicated in the failure of a mixed-sex group to achieve good mathematical discourse when women and men sit face to face engaged in various mathematical tasks. If so, in what ways and to what effect is gender discourse implicated in the failure of a mixed-sex group to achieve good mathematical discourse?

Models of feminine and masculine discourse styles based on the theory of communicative cultural difference, as well as a model …

Extensions Of Commutative Rings With Linearly Ordered Intermediate Rings, Michael Scott Gilbert

Doctoral Dissertations

This work concerns λ-extensions of (commutative) rings, which are defined as ring extensions R ⊆ T whose set of intermediate rings is linearly ordered by inclusion. λ-extensions from a subclass of the ∆-extensions of Gilmer-Huckaba and generalize the adjacent extensions of Ferrand-Oliver, Modica, and Dechene.

In Chapter I, we characterize λ-domains (i.e., integral domains R with quotient field K such that R ⊆ K is a λ-extension), showing that they form a subclass of quasilocal i-domains. These results parallel results of Gilmer-Huckaba for ∆-domains. We relate λ-domains to divided domains and pseudovaluation domains.

Chapter II concerns λ-extensions R ⊆ T …

On Three Dimensional Digital Topology And Its Application To Image Processing., Punam Kumar Saha Dr.

Doctoral Theses

Digital topology provides a sound mathematical basis for object classification, counting and labeling, border tracking, contour filling, thinning, segmentation and many other image processing applications. An important characteristic of topo- logical properties is that they are invariant under translation, rotation, and more generally under any elastic deformation. The analysis of three dimensional (3D) digital images has generated increasing interest with the rapid growth of 3D image processing applications including computer vision. 3D digital images are common input/output media in the several application domains of image processing, pattern recognition and computer vision among which 3D medical imaging is of particular interest. …

Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.

Doctoral Theses

Many real-life applications such as image processing, weather forecasting, digital signal processing, etc., require large amount of computations. By distributing the task among several processors, one can appreciably reduce the computation time. To solve complex problems, several computer architectures using multiple processors have been introduced. Recent developments in IC technology have made it economically feasible to construct multiple processor systems consisting of hundreds or thousands of processors.There are two types of multiprocessor systems (PS87). One is tightly coupled, where the processors share a common clock and/or memory. The other is loosely coupled, where each processor runs independently with a local …

A Problem Set In Conditional Probability Using Martingales With A Derivation Of The Gambler’S Ruin Formula, Michael Everett Theriot Jr

Honors Theses

No abstract provided.

A Graph Theoretic Study Of The Similarity Of Discrete Structures, Heather D. Gavlas

Dissertations

A basic problem in drug design consists of finding a compound that satisfies a spectrum of biological and chemical properties. Although drug design problems are central to pharmaceutical research, statisticians have yet to become involved in this area as these problems are viewed statistically as optimization problems. Before statistical optimization procedures can be defined on these spaces whose points are structures and not vectors, very basic mathematical notions of distance must be defined. Graphs have been used as mathematical models to represent the bonding arrangements of molecules for quite some time. In fact, if some of the methodology used by …

Communication Games, Kimberly I. Noonan

Honors Theses

A communication game combines traditional n-person game theory with graph theory. The result is a model of a bargaining situation where communication is restricted. The game's multilinear extension (MLE), a polynomial that summarizes the solutions of the game, is well known for the case where the graph is a tree or simple cycle. This paper simplifies the computation of MLE of the communication game in the case when the graph is a series of simple cycles. The results are then applied to studying the power of each Canadian province in passing an amendment to the constitution, taking geographic location into …

Ideals Of The Lipschitz Class, Konstantin G. Kulev

Honors Theses

In this paper, a classification of the closed ideals of the Little Oh Lipschitz class of functions on the interval [0,1] is provided. The technique used to classify the ideals of the class of continuous functions is modified and applied to the Little Oh Lipschitz class. It is shown that every ideal of these two classes has the form I = {f : flE = 0} for some closed set E C [0, 1]. Furthermore, it is demonstrated that the same technique cannot be successfully applied to the classification of the closed ideals of the Big Oh Lipschitz class.

Banach Spaces Of Analytic Functions, Michael T. Nimchek

Honors Theses

In this paper, we explore certain Banach spaces of analytic functions. In particular, we study the space A-1, demonstrating some of its basic properties including non-separability. We ask the question: given a class C of analytic functions on the unit disk D and a sequence [Zn] = 0 for all n? Finally, we explore Mz invariant subspaces of A-1, demonstrating that they may possess the codimension-2 property.

Geršgorin And Beyond•••, Jason Knight Belnap

Undergraduate Honors Capstone Projects

Eigenvalues are useful in various areas of mathematics, such as in testing the critical values of a multi variable function to see if it is a local extrema. One of the more common ways to define eigenvalues is:

Definition (1): Given that A is an n by n matrix, λ is an eigenvalue of A if and only if det(A - λI_n) = 0. Any nonzero vector in Null(A - λI) is called an eigenvector associated with λ.

History Of Fermat's Last Theorem, Amanda Brown

Undergraduate Honors Capstone Projects

Around 1637, Pierre de Fermat made a now-famous mathematical conjecture. However, Fermat's conjecture neither began nor ended with him. Fermat's last theorem, as the conjecture is called, has roots approximately 3600 years old. The proof of the theorem was not realized until 1994, over 350 years after it was proposed by Fermat.

Applications Of Optimal Control, Katherine Renee Fister

Doctoral Dissertations

In this dissertation, we investigate optimal control of partial and ordinary differential equations. We prove the existence of an optimal control for which the objective functional is maximized. The goal is to characterize the optimal control in terms of the solution of the optimality system. The optimality system consists of the state equations coupled with the adjoint equations. To obtain the optimality system we differentiate the objective functional with respect to the control. This process is applied to harvesting in a predator-prey parabolic system, to analyzing surface runoff in a parabolic problem, and to controlling the effect of the HIV …

The Use Of Non-Commutative Algebra In Cryptographically Secure Pseudo-Random Number Generators, Brian M. Mckeever

Honors Theses

This thesis begins with a general overview of pseudo-random number generators and some of their applications. This thesis then describes their applications to cryptography, and some additional requirements imposed by cryptography. This thesis then provides an introduction to the ring of quaternions, and discusses how they can be included in pseudo-random number generators. Finally, this thesis provides a description of the performance of these generators.

Exact Solutions For Orthogonal And Non-Orthogonal Magnetohydrodynamic Stagnation-Point Flow, Shahrooz Moosavizadeh

Mathematics & Statistics Theses & Dissertations

The viscous plane flow of an electrically conducting fluid towards an infinite wall is solved in the presence of a magnetic field which is aligned with the flow far from the wall. The problem has two dimensionless parameters-- ε, the magnetic Prandtl number, and β, the square of the ratio of Alfven velocity to fluid velocity far from the wall. The problem has a similarity solution which reduces the governing equations to a system of coupled ordinary differential equations which can be solved numerically. For extreme values of ε, both large and small, singular perturbation techniques are used to derive …

Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.

Doctoral Theses

No abstract provided.

Employement Fluctuations In Rural India:A Statistical Analysis With Special Reference To Maharsatra., Kaushik Bhattacharya Dr.

Doctoral Theses

This dissertation attempts to find out the nature and the extent of employment fluctuation in rural India. The dissertation is partly theoretical and partly empirical in nature. On the methodological side, it builds up a consistent analytical frame- work. Employment fluctuation is measured in terms of a new mobility measure proposed in this dissertation. The empirical work is basod on the data collected by the National Sample Survey Organisation (NSSO), Government of India, in their 38-th round survey operation. I, therefore, thank NSSO for allowing me to work with the data. The views expressod in this dissertation or the errors …

Degenerating Variations Of Mixed Hodge Structures, Eric C. Gaze

Open Access Dissertations

Pure Hodge structures degenerating along a normal-crossings divisor determine variations of mixed Hodge structures on the latter, whose properties as described by the Orbit theorems are well known. We are interested in extending these results to more general variations of mixed Hodge structures.

A Study Of The Relationship Between Use Of Technology In Math And Higher Test Scores, Mary Ann Grooters

Masters Theses

This thesis explored the relationship of a technology enhanced curriculum to higher test scores and higher student motivation. This thesis involved two seventh grade math classes in Kentwood, Michigan. A control class received instruction including lectures, written assignments, and projects. The test group received similar assignments and projects and in addition were given technology supported exercises. A survey given to the test group examined motivation levels, and end of chapter tests compared achievement scores of both groups. The findings indicate that a technology enhanced curriculum does not lead to higher test scores but does impact student motivation to learn math.

The Role Of The Federal Aid In Sportfish Restoration Program In Promoting State Marine Artificial Reef Development Activities, Loren Clark Evans

Theses and Major Papers

The passage of the Wallop-Breaux Amendments to the Federal Aid in Sportfish Restoration Program (FASRP), in 1984, significantly increased the funding available to states participating in the Program. Subsequently, the FASRP became the largest single source of funding for state marine artificial reef development activities. In recent years, there has been concern among program constituents that FASRP funds are not being utilized as intended. The principle question of the current research focused on how effective FASRP subsidies have been in providing meaningful benefits to state fisheries management programs. Specifically, the research focused on the application of FASRP monies in promoting …

Massachusetts Angler Typologies: The Recreation Specialization Approach, Jonathan S. O'Neil

Theses and Major Papers

As the abundance of fish stocks in the Northeast continues to decline, the need to regulate the marine recreational catch is a topic receiving much attention. Yet, the move to manage recreational anglers' fishing activities raises a host of new questions. How should the resource be allocated among different groups of fishermen? Which group should take precedence over others; or should resources be divided equally among all? To manage the Massachusetts recreational fishery, many of these questions will have to be answered to ensure the success of conservation goals. With a comprehensive understanding of anglers and their relationship to fishery …

Sturm-Liouville Theory, Lycretia Englang Ting

Theses Digitization Project

No abstract provided.

Semisimplicity For Hopf Algebras, Michelle Diane Stutsman

Theses Digitization Project

No abstract provided.

A Study Of Finite And Linear Elasticity, Fen Rui Johnson

Theses Digitization Project

No abstract provided.

The Mandelbrot Set, Jeffrey Francis Redona

Theses Digitization Project

No abstract provided.

Structured Eigenvectors, Interlacing, And Matrix Completions, Brenda K. Kroschel

Dissertations, Theses, and Masters Projects

This dissertation presents results from three areas of applicable matrix analysis: structured eigenvectors, interlacing, and matrix completion problems. Although these are distinct topics, the structured eigenvector results provide connections.;It is a straightforward matrix calculation that if {dollar}\lambda{dollar} is an eigenvalue of A, x an associated structured eigenvector and {dollar}\alpha{dollar} the set of positions in which x has nonzero entries, then {dollar}\lambda{dollar} is also an eigenvalue of the submatrix of A that lies in the rows and columns indexed by {dollar}\alpha{dollar}. We present a converse to this statement and apply the results to interlacing and to matrix completion problems. Several corollaries …

Applications Of Hyperbolic Geometry In Physics, Scott Randall Rippy

Theses Digitization Project

The purpose of this study was to see how the fundamental properties of hyperbolic geometry applies in physics.

Convex Functions, Susanna Maria Zagar

Theses Digitization Project

No abstract provided.

Polynomial Equations And Solvability: A Historical Perspective, Laurie Jan Riggs

Theses Digitization Project

No abstract provided.

Topological Classification Of Non-Degenerate Quadratic System, Aleksandr Voldman

Theses Digitization Project

No abstract provided.