Mathematics Commons^™

Best Lp Aapproximation With Multiple Constraints For 1 ⩽ P < ∞, J. J. Swetits, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The problem considered in this paper is best L_p approximation with multiple constraints for 1 ⩽ p < ∞. Characterizations of best L_p approximations from multiple n-convex splines and functions are established and the relationship between them is investigated. Applications to best monotone convex approximation are studied.

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

An Artificial Neural Approach To The Decomposition Problem, Chandrashekar L. Masti

Electrical & Computer Engineering Theses & Dissertations

The goal of this thesis is to develop an artificial neural approach toward addressing the intractability involved with the decomposition problem. The search for the lattice of substitution property (s. p.) partitions essential to decompositions is cast into the framework of constraint satisfaction. An artificial neural network is developed to provide solutions by performing optimization of a mathematically derived objective function over the problem space. The issue of transitivity is verified to belong to a class of problems beyond the scope of solvability for conventional quadratic-order constraint satisfaction neural networks. A theorem is stated and proved establishing that third-order correlations …

A Root Finding Algorithm For Parallel Architecture Machines, Stuti Moitra

Computer Science Theses & Dissertations

In this thesis a parallel algorithm for determining the zeros of any given analytic function is described. Parallelism is achieved by modifying the traditional bisection algorithm for architecture machines.

Given any user supplied function f(X), continuous on the interval A_o ≤ x ≤ B₀, and the tolerance of accuracy an algorithm of determining up to ten roots, with error of approximation less than or equal to tolerance, on parallel systems like Distributed Array Processor (OAP) and N-cube is considered.

A variation of the bisection method has been adapted for this purpose. At each level of iteration a …

Stability Of A Viscoelastic Burgers Flow, D. Glenn Lasseigne, W. E. Olmstead

Mathematics & Statistics Faculty Publications

The system of equations proposed by Burgers to model turbulent flow in a channel is extended to include viscoelastic affects. The stability and bifurcation properties are examined in the neighborhood of the critical Reynolds number. For highly elastic fluids, the bifurcated state is periodic with a shift in frequency.

Boundary Value Problems In Elasticity And Thermoelasticity, Stuart Davidson

Mathematics & Statistics Theses & Dissertations

In this dissertation the author solves a series of mixed boundary value problems arising from crack problems in elasticity and thermoelasticity. Using integral transform techniques and separation of variables appropriately, it is shown that the solutions can be found by solving a corresponding set of triple or dual integral equations in some instances, while in others the solutions of triple or dual series relations are required. These in turn reduce to various singular integral equations which are solved in closed form, in two cases, or by numerical methods. The stress intensity factors at the crack tips, the physical parameters of …

Evaluation Of The Function Exp (X2) Erfc (X) To Higher Precisions For Higher-Order Derivative Polarography Of Ce-Type Electrode Process, Myung-Hoon Kim, Veriti P. Smith, Tae-Kee Hong

Chemistry & Biochemistry Faculty Publications

The function exp(x2)erfc(x), which is often encountered in studies of electrode kinetics, is evaluated to an extended precision with 32 significant decimal digits in order to find theoretical relationships used in derivative polarography/voltammetry for a chemically-coupled electrode process. Computations with a lower precision are not successful. Evaluation of the function is accomplished by using three types of expansions for the function. Best ranges of arguments are selected for each equation for particular precisions for efficiencies. The method is successfully applied to calculate higher-order derivatives of the current-potential curves in all potential ranges for a reversible electron transfer reaction coupled with …

Construction Of The Best Monotone Approximation On Lp [0, 1], J. J. Swetits, S. E. Weinstein

Mathematics & Statistics Faculty Publications

(First paragraph) For 1 ≤ p < ∞, let L_p, denote the Banach space of pth power Lebesgue integrable functions on [0, l] ∥ƒ∥_p = (∫¹₀∣ƒ∣ ^p)^1/p Let M_p denote the set of nondecreasing functions in L_p. For l < p < ∞ , each ƒ∊L_p has a unique best approximation from M_p, while, for p = 1, existence of a best approximation from M₁ follows from Proposition 4 of [6].

An Extension Of Essentially Non-Oscillatory Shock-Capturing Schemes To Multi-Dimensional Systems Of Conservation Laws, Jay Casper

Mathematics & Statistics Theses & Dissertations

In recent years, a class of numerical schemes for solving hyperbolic partial differential equations has been developed which generalizes the first-order method of Godunov to arbitrary order of accuracy. High-order accuracy is obtained, wherever the solution is smooth, by an essentially non-oscillatory (ENO) piecewise polynomial reconstruction procedure, which yields high-order pointwise information from the cell averages of the solution at a given point in time. When applied to piecewise smooth initial data, this reconstruction enables a flux computation that provides a time update of the solution which is of high-order accuracy, wherever the function is smooth, and avoids a Gibbs …

Best Approximation With Geometric Constraints, Yuesheng Xu

Mathematics & Statistics Theses & Dissertations

This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best L_p approximation to a function in L_p (0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.

Corrigendum, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Fixed Point Theorems For Compatible Multi-Valued And Single-Valued Mappings, Hideaki Kaneko, Salvatore Sessa

Mathematics & Statistics Faculty Publications

The notion of compatibility for point-to-point mappings recently defined by Jungck is generalized to include multi-valued mappings. This idea is used to establish a fixed point theorem for a generalized contractive multi-valued mapping and a single-valued mapping.

A Nonlinear Eigenvalue Problem In Astrophysical Magnetohydrodynamics: Some Properties Of The Spectrum, John A. Adam

Mathematics & Statistics Faculty Publications

The equations of ideal magnetohydrodynamics (MHD) with an external gravitational potential—a ‘‘magnetoatmosphere’’—are examined in detail as a singular nonlinear eigenvalue problem. Properties of the spectrum are discussed with specific emphasis on two systems relevant to solar magnetohydrodynamics. In the absence of a gravitational potential, the system reduces to that of importance in MHD and plasma physics, albeit in a different geometry. This further reduces to a form isomorphic to that derived in the study of plasma oscillations in a cold plasma, Alfvén wave propagation in an inhomogeneous medium, and MHD waves in a sheet pinch. In cylindrical geometry, the relevant …

The Strong Perfect Graph Conjecture For Pan-Free Graphs, Stephan Olariu

Computer Science Faculty Publications

A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the largest number ω(F) of pairwise adjacent vertices in F. Berge's famous Strong Perfect Graph Conjecture asserts that a graph G is perfect if and only if neither G nor its complement G contains an odd chordless cycle of length at least five. Its resolution has eluded researchers for more than twenty years. We prove that the conjecture is true for a class of graphs which strictly contains the claw-free graphs.

On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge

Mathematics & Statistics Theses & Dissertations

This dissertation is devoted to the acceleration of convergence of vector sequences. This means to produce a replacement sequence from the original sequence with higher rate of convergence.

It is assumed that the sequence is generated from a linear matrix iteration x_i+ i = Gx_i + k where G is an n x n square matrix and x_I+1 , x_i,and k are n x 1 vectors. Acceleration of convergence is obtained when we are able to resolve approximations to low dimension invariant subspaces of G which contain large components of the error. When …

A New Conjecture About Minimal Imperfect Graphs, H. Meyniel, Stephan Olariu

Computer Science Faculty Publications

H. Meyniel proved that in every minimal imperfect graph, every pair of vertices is joined by a chordless path containing an odd number of edges. We conjectured that in every minimal imperfect graph, every pair of vertices is joined by a path containing an even number of edges. We give an equivalent version of this new conjecture.

Atamm Multicomputer System Design, William Robert Tymchyshyn

Electrical & Computer Engineering Theses & Dissertations

The Algorithm To Architecture Mapping Model, or ATAMM, is a graph theoretic design methodology that has been created to resolve design and performance issues involved with concurrent processing. Petri-net marked graphs are used to represent the computational environment.

This thesis describes the development of a multicomputer system which will operate within the bounds specified by the ATAMM model. The system is first designed and implemented using the framework of standard multicomputer design theory. A validation is then performed by the comparison of the system's computational performance to results predicted by ATAMM. This validation is shown to be successful for three …

Self Consistent Model Of The Glow Discharge, Hao Chen

Electrical & Computer Engineering Theses & Dissertations

The strong spatial variation of the electric field intensity in the vicinity of the cathode of a gas discharge requires the use of microscopic methods to describe the nonequilibrium behavior of the electron dynamics in this region. A one-dimensional Monte Carlo code was developed. It allows one to obtain the distribution of the electron drift velocity and rate coefficients for a given electric field intensity in the cathode fall. The results of this calculation are used to find the density distribution of charged particles in this region and consequently, by means of Poisson's equation, a corrected electric field intensity. In …

A Mathematical Model Of Tumor Growth By Diffusion, John A. Adam

Mathematics & Statistics Faculty Publications

A diffusion model of the prevascular stage of tumor growth is presented. The basic feature of such a model is the diffusion of growth inhibitor, which is produced at a spatially non-uniform rate within the tissue. Regimes of limited and unlimited tissue growth are determined, and the consistency of this and simpler models is discussed in the light of observational results.

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

No Antitwins In Minimal Imperfect Graphs, Stephan Olariu

Computer Science Faculty Publications

It is customary to call vertices x and y twins if every vertex distinct from x and y is adjacent either to both of them or to neither of them. By analogy, we shall call vertices x and yantitwins if every vertex distinct from x and y is adjacent to precisely one of them. Lovász proved that no minimal imperfect graph has twins. The purpose of this note is to prove the analogous statement for antitwins.

An Application Of Global Optimization Algorithm For Modal Parameter Identification, Chung-Men Chen

Mechanical & Aerospace Engineering Theses & Dissertations

Single-mode projection filters for modal parameter identification for flexible structures are introduced. An effective two-dimensional global optimization method using interval analysis is combined with the projection filters to facilitate identification for modal frequency and damping. A numerical simulation of a ten-mode structure is presented to illustrate the feasibility of the new method. The projection filters are practical for parallel processing implementation.

Model Of Hot-Film Sensor With Substrate Effects, David Mcalpine Judge

Electrical & Computer Engineering Theses & Dissertations

A detailed mathematical model is constructed to investigate the frequency response of a hot-film anemometer system. Since several diverse factors affect the frequency response, the analysis is broken down into three main parts. Each part is a detailed mathematical model. The first model consists of the ordinary differential equations which govern the electronics of the feedback system and heat transfer of the sensor. An important simplification in this model is that the rate of heat conduction from the sensor to its substrate is constant.

In the second model the unsteady state heat transfer properties of the substrate are examined by …

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQ_n(x) = z_n^-1 exp[ -H_n(x)]Π dP(x_j), where x = (x₁,..., x_n) ∈ Rⁿ, where H_n is the Hamiltonian, z_n is …

On The Thermal Stresses Due To A Uniform Heat Flow Past A Circular Hole With A Radial Edge Crack, George F. Edmonds

Mathematics & Statistics Theses & Dissertations

The problem solved in this dissertation is that of finding the stresses in an isotropic, linear, thermoelastic solid when a uniform heat flow is disturbed by the presence of an insulated circular hole with a radial edge crack. By superimposing a Mellin transform solution of the equations of thermoelasticity on a Michell series solution the author reduces the problem to a pair of singular integral equations which are then solved numerically. The stress intensity factors and crack formation energies, quantities of interest to workers in fracture mechanics, are then calculated.

Estimation In Truncated Exponential Family Of Distributions, Laxman M. Hegde

Mathematics & Statistics Theses & Dissertations

Estimating the parameters of a truncated distribution is a well known problem in statistical inference. The non-existence of the maximum likelihood estimator (m.l.e.) with positive probability in certain truncated distributions is not well known. To mention a few results in the literature:

(i) Deemer and Votaw 1955 show that the maximum likelihood estimator does not exist in a truncated negative exponential distribution on 0,T , T > 0 known, whenever the sample mean x (GREATERTHEQ) T/2.

(ii) Broeder 1955 shows that the maximum likelihood estimator of the scale parameter of a truncated gamma distribution, with the shape parameter being known, becomes …

Algebraic Grid Generation Using Tensor Product B-Splines, Bonita Valerie Saunders

Mathematics & Statistics Theses & Dissertations

In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.

Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.

The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the …

Minimal Norm Constrained Interpolation, Larry Dean Irvine

Mathematics & Statistics Theses & Dissertations

In computational fluid dynamics and in CAD/CAM a physical boundary, usually known only discreetly (say, from a set of measurements), must often be approximated. An acceptable approximation must, of course, preserve the salient features of the data (convexity, concavity, etc.) In this dissertation we compute a smooth interpolant which is locally convex where the data are locally convex and is locally concave where the data are locally concave.

Such an interpolant is found by posing and solving a minimization problem. The solution is a piecewise cubic polynomial. We actually solve this problem indirectly by using the Peano kernel theorem to …