Mathematics Commons^™

Using Environmental News To Help Teach Mathematics, Barry Schiller

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Women In Mathematics By Claudia Henrion, Natasha Keith, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

Use Your Head: Mathematics As Therapy, Miriam Lipschutz-Yevick

Humanistic Mathematics Network Journal

No abstract provided.

Coherence In Theories Relating Mathematics And Language, Carl Winsløw

Humanistic Mathematics Network Journal

No abstract provided.

Operationalizing Interactive Learning Paradigms Through Cooperative Learning Activities 100% Of The Time In Math Classes, Ted Panitz

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Sex, Yan Kow Cheong

Humanistic Mathematics Network Journal

No abstract provided.

Imaginary, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

Cramer-Rao Bound And Optimal Amplitude Estimator Of Superimposed Sinusoidal Signals With Unknown Frequencies, Shaohui Jia

Doctoral Dissertations

This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals.

Molecular Study Of Turbulence In Three Dimensional Cavity Flow, Donald Greenspan

Mathematics Technical Papers - Archive

Three dimensional molecular cavity problems are formulated and solved numerically. The fluid considered is water at 15°C. The turbulent flows generated are characterized by strong crosscurrents over the usual primary vortex direction.

Counting On Continued Fractions, Arthur T. Benjamin, Francis E. Su, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

The Fermat Point And The Steiner Problem, J. N. Boyd, P. N. Raychowdhury

Virginia Journal of Science

We revisit the convex coordinates of the Fermat point of a triangle. We have already computed these convex coordinates in a general setting. In this note, we obtain the coordinates in the context of the Steiner problem. Thereafter, we pursue calculations suggested by the problem.

Explicit Resolutions Of Cubic Cusp Singularities, Helen G. Grundman

Mathematics Faculty Research and Scholarship

Resolutions of cusp singularities are crucial to many techniques in computational number theory, and therefore finding explicit resolutions of these singularities has been the focus of a great deal of research. This paper presents an implementation of a sequence of algorithms leading to explicit resolutions of cusp singularities arising from totally real cubic number fields. As an example, the implementation is used to compute values of partial seta functions associated to these cusps.

Computational Geometry Column 38, Joseph O'Rourke

Computer Science: Faculty Publications

Recent results on curve reconstruction are described.

Diffusion Problems In Wound Healing And A Scattering Approach To Immune System Interactions, Julia Suzanne Arnold

Mathematics & Statistics Theses & Dissertations

A theoretical model for the existence of a Critical Size Defect (CSD) in certain animals is the focus of the majority of this dissertation. Adam [1] recently developed a one-dimensional model of this phenomenon, and chapters I–V address the exist the CSD in a two-dimensional model and a three-dimensional model. The two dimensional (or 1-d circular) model is the more appropriate for a study of CSD's. In that model we assume a circular wound of uniform depth and develop a time-independent form of the diffusion equation relevant to the study of the CSD phenomenon. It transpires that the range of …

An Object-Oriented Algorithmic Laboratory For Ordering Sparse Matrices, Gary Karl Kumfert

Computer Science Theses & Dissertations

We focus on two known NP-hard problems that have applications in sparse matrix computations: the envelope/wavefront reduction problem and the fill reduction problem. Envelope/wavefront reducing orderings have a wide range of applications including profile and frontal solvers, incomplete factorization preconditioning, graph reordering for cache performance, gene sequencing, and spatial databases. Fill reducing orderings are generally limited to—but an inextricable part of—sparse matrix factorization.

Our major contribution to this field is the design of new and improved heuristics for these NP-hard problems and their efficient implementation in a robust, cross-platform, object-oriented software package. In this body of research, we (1) examine …

Lengths Of Geodesics On Klein’S Quartic Curve, Ryan Derby-Talbot

Mathematical Sciences Technical Reports (MSTR)

A well-known and much studied Riemann surface is Klein’s quartic curve. This surface is interesting since it is the smallest complex curve with maximal symmetry. In addition to this high degree of symmetry, Klein’s quartic curve can be tiled by triangles,giving rise to a tiling group generated by reflections. Using the tiling group and the universal cover of the tiling group we are able to compile a list of the lengths of the short,simple,closed geodesics on this surface. In particular,w e are able to determine whether the geodesic loops generated by the tiling are the systoles,i.e.,the shortest closed geodesics.

Feature Evaluation, Classification And Rule Generation Using Fuzzy Sets And Neural Networks., Rajat Kumar De Dr.

Doctoral Theses

Pattern recognition and machine learning form a major area of research and develop- ment activity that encompasses the processing of pictorial and other non-numerical information obtained from the interaction between science, technology and society. A motivation for the spurt of activity in this field is the need for people to com- municate with the computing machines in their natural mode of communication. Another important motivation is that the scientists are also concerned with the idea of designing and making intelligent machines that can carry out certain tasks that we human beings do. The most salient outcome of these is the …

Essays On First Best Implementable Incentive Problem., Manipushpak Mitra Dr.

Doctoral Theses

The theory of mechanism design originated in the mid 1930s with the work of Lange[27], Lerner (28] and Hayek [20] on market socialism'. Further regular was added to their ideas by Arrow and Hurwicz (1). Hurwicz extended them to the general problem of mechanism design. An important aspect of mechanism design is asymmetric information. Information asymmetry typically imposes constraints on the goals which can be attained. For example. in the classic pure public goods problem, mechanisms that achieve truthful revelation of private information are Pareto sub-optimal i.e. these mechanisms lead to a welfare loss (see Hurwicz [24]). When can mechanism …

Rhombic Penrose Tilings Can Be 3-Colored, Thomas Q. Sibley, Stan Wagon

Mathematics Faculty Publications

No abstract provided.

A Rational Solution To Cootie, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

No abstract provided in this article.

Isometric Extensions Of Zero Entropy Zᵈ Loosely Bernoulli Transformations, Aimee S.A. Johnson, A. A. Şahin

Mathematics & Statistics Faculty Works

In this paper we discuss loosely Bernoulli for Z(d) actions. In particular, we prove that extensions of zero entropy, ergodic, loosely Bernoulli Z(d) actions are also loosely Bernoulli.

A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall

Theses and Dissertations

The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, S(n), which is the set of all …

On Fractal Based Representation Of Image With Application To Image Processing., Suman Kumar Mitra Dr.

Doctoral Theses

The language of an image is universal. Images were the means of communicating infor- mation in ancient days. Even today, although people from different parts of the world speak in different languages, an image conveys almost the same universal meaning to all. With the rapid development of modern computer technologies and with the increasing attempt in getting information at ones finger tips, the importance of communication of information using images can not be ignored.Images are stored in computers in the form of a collection of bits representing pixels (picture elements). Pictures are to be digitized to store them in computers. …

Similarity Based Approximate Reasoning., Swapan Raha Dr.

Doctoral Theses

Many years of research in Artificial Intelligence, Cognitive Science and allied area reveal that the cognitive process of human reasoning deals with imprecise premises. As cognitive process of human reasoning is mainly concerned with the individual's perception, it is liable to be imprecise in nature. Precise traditional two-valued logic and/or multi-valued logics are not effective in handling such reasoning processes. This motivated Zadeh (109) to investigate how these impreciseness in human rea- soning could be modeled through some computable entities. In this regard, Zadeh has shown how such imprecise linguistic terms could be expressed through fuzzy sets over universes of …

Some Contribution To Reliability Analysis Of A Consecutive-K-Out-Of N: F System., Mohammad Khanjari Sadegh Dr.

Doctoral Theses

Present day technology has been characterized by development of complex systems or equipments containing a large number of subaystems and com- ponents. Reliability, as a buman attribute, has been praised for a very long time. For technical systems, however, the reliability concept has not been applied for more than about 50 years. Reliability is the concern of all scien- tists and engineers engaged in developing a system, from design, through the manufacturing, to its ultimate use. Reliability technology has a potentially wide range of application areas like safety or risk analysis, environmental protection, quality, optimization, maintenance, engineering design, etc.For a …

Quantum Stochastic Dilation Of Completely Positive Semigroups And Flows., Debashish Goswami Dr.

Doctoral Theses

The central theme of the present thesia is quantum stochastic dilation af semigroupe of completely panitive mapa on operator algebran. It is the sim of all mathemati- cal, or even all scientific theorics, to understand a given class of objects through a tanonical and simpler subclass of it. For example, abstract C"-algebras are studied through their conerete realisation as elgebra of operators, contractions on a Hilbert space by unitaries. Hilbert modules by the factorissble ones, to mention anly a few. In most af these caes, a general object of the relavant class is sociated with a canonical candidate of the …

Studies On Finite Linear Cellular Automata., Palash Sarkar Dr.

Doctoral Theses

Cellular Automata were originally proposed by John von Neumann as formal models of self reproducing organisms. The structure studied was mostly an ane and two dimensional infinite grida, though higher dimensions were also considered. Computation universality and other computation theoretic questions were considered important. See Burks [24] for a collection of essays on important problems on cellular automata during this period. Later physicists and biologists began to study cellular automsta for the purpose of modelling in their respective domains. In the present era, cellalar automata is being atudied from many widely different angles, and the relationship of these structurea to …

Uncertainity Principles On Some Lie Groups., Swagato Kumar Ray Dr.

Doctoral Theses

The uncertainty principles of Harmonic Analysis say that: a nonzero func- tion and its Fourier transform cannot both be sharply concen- trated. After the initial work on this phenomenon in 1920s, the last two decades witnessed a spurt of activity in this direction (we refer the reader to a very readable survey [FS]). One may notice two broad phases in this activity, the first concentrating on R where the notion of concentration is given different formulations to see whether the phenomenon still holds. In the later phase R is replaced by other commutative or noncommutative groups, or more generally by …

Generalised Bootstrap Techniques., Singdhansu Bhusan Chatterjee Dr.

Doctoral Theses

A typical problem in statistics is as follows: there is some observable data Xn = (X1,..., Xn), and a parameter of interest θ which is related in such a way to the distribution of Xn that meaningful conclusions about θ can be drawn based on Xn. Sometimes data Xn is observed keeping the objective parameter θ in mind, at other times the parameter appears while trying to model the observed data.Once the data is observed and the parameter fixed, the questions that have to be addressed are as follows:(I) How to estimate θ from the data Xn?(II) Given an estimator …

On Quantitative Evaluation Of 3-D Histo-Pathological Images From Confocal Laser Scanning Microscope., P. S. Umesh Adiga Dr.

Doctoral Theses

Automation of image analysis in the bio-medical ficld is one of the important achievements of applied image processing research. The rapid development in the electronic instrumentation during 1960s and 70s made it possible to automate the routine process of diagnosis and prognosis of many discases. Development of high resolution imaging instruments such as X-ray CT, MRI, etc., for macro imaging and electron microscope, confocal microscope, etc., for micro imaging has given a tremendous boost to the advancement of medical field. Advancement in the field of computing has made it possible to reconstruct the pictures of internal organs of the body …