Physical Sciences and Mathematics Commons^™

Fractional Derivatives, John M. Beach

Theses and Dissertations

In this thesis, the reader will not find a study of any kind; there is no methodology, questionnaire, interview, test, or data analysis. This thesis is simply a research paper on fractional derivatives, a topic that I have found to be fascinating. The reader should be delighted by a short history of the topic in Chapter 1, where he/she will read about the contributions made by some of the great mathematicians from the last three centuries.

In Chapter 2 the reader will find an intuitive approach for finding the general fractional derivative for functions such as e^ax, x …

Stability And Largeness Of The Core Of Cooperative Games., Amit K. Biswas Dr.

Doctoral Theses

This monograph deals with the area from game theory known as co operativo games. Except the last chapter on NTU games, it deals with transferable utility games. llere we will introiduce and diseus the involved game theuretie notions and set a mathematical hase for the chapters to come.In 1944 von Neamann and Morgenstern(15) introduced a theory of solutions for n-person games in characteristic function form in which cooperation and coalition formation is a crucial aspect. The primary mathematical concern regarding this model is the existence of solutions or stable set. In 1968 Lucas|19 described a tem person game which has …

On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.

Doctoral Theses

Introduction and Summary Consider the problem of classification of an observation into one of two specified populations. Fisher's classification rale, just as several other rules commonly used in practice, depends only on the ratio of the individual densities fi(x), i = 1,2. This led Cox (1966),/27) to model the "posterior odds" by a simple function. Specifically,Cox's logistic discrimination (LGD) rule is then based on the statistic a + 'ßx. This has the advantage that individual densities f.(x) need not be known and we only need to estimate the parameters a and B.Another advantage, which is claimed , is that the …

On Some Self-Organizing Models And Their Applications., Amitava Dutta Dr.

Doctoral Theses

Abstract: Self-organizing neural network models constitute the main theme of this thesis. Some well-known self-organizing models are surveyed and their properties are discussed. The application areas on which the thesis focuses are briefly described.This thesis deals with Artificial Neural Network models, in particular, Self- organizing (unsupervisnd) models. We develop here a few self-organizing neural net- work models to solve certain problems which are well studied in the areas of Image Processing and Computationel Geometry and have wide applications in shape eztrac- tion and optimization.1.1 Artificial neural networkThe study of Biological Neural Networks originally comes under biological sciences. They deal with …

Active Feedback Control Of A Wake Flow Via Forced Oscillations Based On A Reduced Model, Fu Li

Dissertations

As it is well known, the flow past a cylinder consists of a symmetric recirculation bubble of vortices at small Reynolds numbers. As Reynolds number increases, the bubble becomes unstable and develops into a Karman vortex street of alternating vortices. This instability is responsible for the occurrence of large amplitude oscillations in the lift and an increase in the mean drag. It was previously shown by numerical simulation that the mechanism driving the bubble instability is well mimicked by Foppl's four dimensional potential flow model where the bubble is represented by a saddle point. In this work, we design two …

A Study Of Droplet Burning In The Nearly Adiabatic Limit, Juan C. Gomez

Dissertations

We consider a small drop of liquid fuel that burns in an oxidizing gaseous environment and translates slowly (relative to flow 'at infinity') under the action of gravity. Practical applications include the burning of liquid fuels as sprays in domestic and industrial oil-fired burners, diesel engines, and liquid-propellant rocket motors. More relevant to the simple physical set-up of the present study are wellcharacterized laboratory experiments on the burning of a single, isolated fuel drop.

The drop burns in a nearly spherical, diffusion flame, flame sheet regime. We consider a specific example, or limit, referred to as 'nearly adiabatic burning', in …

Numerical Study Of Particle Dynamics In A Falling-Ball Viscometer, Peiwen Hou

Dissertations

The falling-ball viscometer is a device where a spherical particle falls along the axis of a circular cylinder filled with viscous fluid. The various classical results for this device are developed under the assumption that the Reynolds number of the flow is zero, i.e., Stoke's flow. Inertial effects are not taken into account. To better understand the dynamics of the particle sedimentation process and the role of inertia in this process, we implemented a numerical simulation.

The ADI (Alternating Direction Implicit) scheme is widely used to solve the vorticity-stream function formulation of the Navier-Stokes equation in axisymmetric geometries. However, a …

Performance Of Bootstrap Confidence Intervals For L-Moments And Ratios Of L-Moments., Suzanne Glass

Electronic Theses and Dissertations

L-moments are defined as linear combinations of expected values of order statistics of a variable.(Hosking 1990) L-moments are estimated from samples using functions of weighted means of order statistics. The advantages of L-moments over classical moments are: able to characterize a wider range of distributions; L-moments are more robust to the presence of outliers in the data when estimated from a sample; and L-moments are less subject to bias in estimation and approximate their asymptotic normal distribution more closely.

Hosking (1990) obtained an asymptotic result specifying the sample L-moments have a multivariate normal distribution as n approaches infinity. The standard …

Low Seasonal Temperatures Promote Life Cycle Synchronization, Janette Lee Jenkins

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In this paper, we discuss how seasonal temperature variation and dormancy can synchronize the development of exothermic organisms. Using a simple aging model, it is shown that minimal seasonal temperature variation and periods of dormancy during extreme temperature conditions are sufficient to establish stable, univoltine ovipositional cycles. Dormancy, in fact, promotes synchronous oviposition emergence. The mountain pine beetle, an important insect living in extreme temperature conditions and showing no evidence of diapause, invites direct application of this model. Simulations using mountain pine beetle parameters are used to determine temperature regimes for which stable, ovipositional cycles exist.

Pooled And Individual Bycatch Quotas: Exploring Tradeoffs Between Observer Coverage Levels, Bycatch Frequency, Pool Size, And The Precision Of Bycatch Estimates, Landon S. Jensen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The North Pacific Ocean is highly productive, hosting many of the world's largest groundfish populations and supporting a thriving fishing industry. Numerous regulations have been implemented to control the incidental take of non-target bycatch. Individual and Pooled Bycatch Quotas have recently been proposed as instruments that could further encourage the avoidance of such bycatch and increase enforceability of bycatch caps at less-than-entire-fishery levels of operation. The recent advent of fishing cooperatives such as the Pacific Whiting Conservation Cooperative and the Pollock Conservation Cooperatives create an additional impetus for examining the characteristics of pool and vessel specific bycatch quotas.

We have …

Mode Vertices And Mode Graphs., Jobriath Scott Kauffman

Electronic Theses and Dissertations

The eccentricity of a vertex, v, of a connected graph, G, is the distance to a furthest vertex from v. A mode vertex of a connected graph, G, is a vertex whose eccentricity occurs as often in the eccentricity sequence of G as the eccentricity of any other vertex. The mode of a graph, G, is the subgraph induced by the mode vertices of G. A mode graph is a connected graph for which each vertex is a mode vertex. Note that mode graphs are a generalization of self-centered graphs. This paper presents some …

A New Perspective On Classification, Guohua Zhao

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The idea of voting multiple decision rules was introduced in to statistics by Breiman. He used bootstrap samples to build different decision rules, and then aggregated them by majority voting (bagging). In regression, bagging gives improved predictors by reducing the variance (random variation), while keeping the bias (systematic error) the same. Breiman introduced the idea of bias and variance for classification to explain how bagging works. However, Friedman showed that for the two-class situation, bias and variance influence the classification error in a very different way than they do in the regression case.

In the first part of …

Mean-Square Error Bounds And Perfect Sampling For Conditional Coding, Xiangchen Cui

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, new theoretical results are obtained for bounding convergence and mean-square error in conditional coding. Further new statistical methods for the practical application of conditional coding are developed.

Criteria for the uniform convergence are first examined. Conditional coding Markov chains are aperiodic, π-irreducible, and Harris recurrent. By applying the general theories of uniform ergodicity of Markov chains on general state space, one can conclude that conditional coding Markov chains are uniformly ergodic and further, theoretical convergence rates based on Doeblin's condition can be found.

Conditional coding Markov chains can be also viewed as having finite state space. …

Positive Solutions Obtained As Local Minima Via Symmetries, For Nonlinear Elliptic Equations, Florin Catrina

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, we establish existence and multiplicity of positive solutions for semilinear elliptic equations with subcritical and critical nonlinearities. We treat problems invariant under subgroups of the orthogonal group. Roughly speaking, we prove that if enough "mass " is concentrated around special orbits, then among the functions with prescribed symmetry, there is a solution for the original problem.

Our results can be regarded as a further development of the work of Z.-Q. Wang, where existence of local minima in the space of symmetric functions was studied for the Schrödinger equation. We illustrate the general theory with three examples, all …

Comparing Nonlinear And Nonparametric Modeling Techniques For Mapping And Stratification In Forest Inventories Of The Interior Western Usa, Gretchen Gengenbach Moisen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Recent emphasis has been placed on merging regional forest inventory data with satellite-based information both to improve the efficiency of estimates of population totals, and to produce regional maps of forest variables. There are numerous ways in which forest class and structure variables may be modeled as functions of remotely sensed variables, yet surprisingly little work has been directed at surveying modem statistical techniques to determine which tools are best suited to the tasks given multiple objectives and logistical constraints. Here, a series of analyses to compare nonlinear and nonparametric modeling techniques for mapping a variety of forest variables, and …

Vertices In Total Dominating Sets., Robert Elmer Dautermann Iii

Electronic Theses and Dissertations

Fricke, Haynes, Hedetniemi, Hedetniemi, and Laskar introduced the following concept. For a graph G = (V,E), let rho denote a property of interest concerning sets of vertices. A vertex u is rho-good if u is contained in a {minimum, maximum} rho-set in G and rho-bad if u is not contained in a rho-set. Let g denote the number of rho-good vertices and b denote the number of rho-bad vertices. A graph G is called rho-excellent if every vertex in V is rho-good, rho-commendable if g > b > 0, rho-fair if g = b, and …

A Survey Of The Taniyama-Shimura Conjecture, Kady Schneiter

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Perhaps the most famous problem in all of mathematics is the theorem that states that the equation aⁿ + bⁿ = cⁿ has no non-trivial solutions for integers a, b, and c, and n ≥ 2. This theorem was proposed by a seventeenth century French mathematician named Pierre de Fermat. Though the theorem is easy to understand, the proof has been elusive. Over the past 350 years many mathematicians have attempted to prove Fermat's theorem. They have used a variety of methods and many have been successful in proving the theorem in specific cases. …

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.

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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. …

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 …

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 …

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 …