Mathematics Commons^™

On The Mann Iteration Process In A Hilbert Space, Troy L. Hicks, John D. Kubicek

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Class Of Singular Neutral-Differential Systems, W. J. Fitzpatrick, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

Noetherian operator theory is used to prove an existence theorem for a singular functional-differential system. An analogue of the standard existence and uniqueness results at an ordinary point follows as a corollary. © 1977 American Mathematical Society.

Regular Singular Differential Equations Whose Conjugate Equation Has Polynomial Solutions, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

Consider the n -dimensional singular differential system defined by the operator $L:(Ly)(z) = z^p y'(z) + A(z)y(z)$, where z is a complex variable and p is a positive integer. The solvability of the nonhomogeneous system $Ly = g$ depends on the solutions of the homogeneous conjugate system, $L^ * f = 0$, where $L^ * $ is the operator conjugate to L. We show that $L^ * f = 0$ has polynomial solutions if the constant matrix in the series expansion of $A(z)$ has at least one nonpositive integer eigenvalue. Also, we show that if $L^ * f = 0$ …

Positive Perturbations Of Unbounded Operators, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.

A Proof Of Convergence For The Tridiagonal Ql Algorithm In Floating-Point Arithmetic, James George Sanderson

Mathematics & Statistics ETDs

Numerous routines are available to find the eigenvalues of a real symmetric tridiagonal matrix. Since it is known to converge in exact arithmetic, the tridiagonal QL algorithm with origin shift is widely used. Here we analyze the algorithm in floating-point arithmetic. This analysis suggests two modifications to the EISPACK implementation TQLl that enable one to prove correctness and hence convergence of the routine.

Also, it is known that the implicit and explicit versions of the QL algorithm produce the same results in exact arithmetic. A counter-example to the floating-point analog of this theorem is presented.

The Use Of Prior Observations In Constructing Prediction Intervals For The Normal Distribution, Charles B. Davis

Mathematics & Statistics ETDs

A prediction interval procedure uses information contained in a sample together with other relevant information to produce an interval which will contain the next observation to be taken from the population with confidence no less than a pre-determined /J. One prediction inter­val procedure renders another "inadmissible" at the fJ level if (1) both procedures maintain the B confidence level and (2) the former produces intervals which are at least as "short" as, and sometimes "shorter" than, those produced by the latter; "short" is defined in a natural fashion in terms of expected length or expected upper (lower) limit. as is …

An Abstract Matrix Model: The Column Model, Tomas Eufracio Salazar

Mathematics & Statistics ETDs

In this dissertation we introduce an abstract model for matrix theory, The Column Model. We investigate some properties of the special class of partially ordered linear algebras that satisfy the conditions of the Model. We use the order structure of the Model to obtain some results on: idempotents in the Model, nonnegative elements of the Model having nonnegative generalized inverses, factor theorems in the Model and concepts in the Model that are related to the usual notion of eigenvalues of an m-by-m matrix. Since the set of m-by-m matrices belongs to the special class of partially ordered linear algebras satisfying …

A Metric Graph Structure For Information Retrieval, Karl Jerry Melendez

Mathematics & Statistics ETDs

Document retrieval systems accept a user request for information and respond with a list of documents which contain information relevant to the request. When the documents (or abstracts of the documents) are stored in a computer memory, a function can be defined which estimates the semantic distance between documents. If this function together with the set of documents forms a metric space, a graph, which I call a progressive graph, can be constructed to aid the search for the documents with relevant information.

Progressive graphs are studied and the search algorithms which use this graph structure are presented. The search …

A Class Of Functional Equations And Mielnik Probability Spaces, S. J. Guccione, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

Let S be the unit sphere of a normed real linear space N and let (S, p) be a Mielnik space of dimension two. For p(x, y) = f(‖x+y‖), x, yєS, where /is a continuous, strictly increasing function from [0, 2] onto [0, 1], it has been shown that (S, p) being two dimensional is equivalent to N being an inner product space. In some polarization problems modeled on the unit sphere of an inner product space, the transition probability p(x, y) may not be as well behaved as p(x, y) = f(‖x + y‖). In order to provide a …

Quasi-Unmixedness And Integral Closure Of Rees Rings, Peter G. Sawtelle

Mathematics and Statistics Faculty Research & Creative Works

For certain Rees rings ℛ of a local domain R, the quasiunmixedness of R is characterized in terms of a certain transform of ℛ being contained in the integral closure of ℛ. © 1976 American Mathematical Society.

On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that to a certain cosine series f, a Rees-Stanojević cosine sumn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for L1 convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Other corollaries are given concerning the well-known integrability conditions. © 1975, American Mathematical Society.

On L¹ Convergence Of Certain Cosine Sums, John W. Garrett, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

Rees and Stanojevic introduced a new class of modified cosine sums (equation omitted) and found a necessary and sufficient condition for integrability of these modified cosine sums. Here we show that to every classical cosine series f with coefficients of bounded variation, a Rees-Stanqjevic cosine sum gn can be associated such that gn converges to f pointwise, and a necessary and sufficient condition for Lx convergence of gn to f is given. As a corollary to that result we have a generalization of the classical result of this kind. Examples are given using the well-known integrability conditions. © 1976 American …

Univalence Of Derivatives Of Functions Defined By Gap Power Series. Ii, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Extremal Structure Of Locally Compact Convex Sets, J. C. Hankins, Roy M. Rakestraw

Mathematics and Statistics Faculty Research & Creative Works

Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved.

Estimation Of Growth Curves By Least Square Splines, Dorothy Rybaczyk Pathak

Mathematics & Statistics ETDs

The primary object of this dissertation is to present some con­tributions to the theory of estimation of growth curves by least square splines in the presence of unknown unequal variances. The theoretical developments rest heavily on the standard least square theory and the theory of polynomial spline functions. A modifica­tion of the Aitken procedure of weighted least squares is used to estimate regression parameters. It is shown that this modification of the Aitken procedure does not unduly influence the nice least square properties of estimators so obtained; the estimators re­ main unbiased, consistent and asymptotically efficient.

The techniques developed in …

An Evaluation Of Truncated Sequential Test, Ryh-Thinn Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The development of sequential analysis has led to the proposal of tests that are more economical in that the Average Sample Number (A. S. N.) of the sequential test is smaller than the sample size of the fixed sample test. Although these tests usually have a smaller A. S. N. than the equivelent fixed sample procedure, there still remains the possibility that an extremely large sample size will be necessary to make a decision. To remedy this, truncated sequential tests have been developed.

A method of truncation for testing a composite hypotheses is studied. This method is formed by mixing …

Univalence Of Derivatives Of Functions Defined By Gap Power Series, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Coefficient Inequality For Convex Univalent Functions, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

A short proof of formula presented is given for normalized convex univalent functions. © 1975, American Mathematical Society.

On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that the method used by C. V. Stanojevic to obtain a characterization of inner product spaces in terms of a Mielnik probability space of dimension 2 does not admit a generalization to dimension n > 2. © 1975 American Mathematical Society.

The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke

Mathematics and Statistics Faculty Publications

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.

Stiefel-Whitney Homology Classes And Bordism, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

We develop the theory of mod 2 Stiefel-Whitney homology classes for Euler polyhedral. We then describe a simple method of obtaining pJ. bordism theories. Finally, we define the ungraded bordism theory of Euler spaces and show that it is isomorphic to ordinary total homology. © 1975 American Mathematical Society.

An Evaluation Of Bartlett's Chi-Square Approximation For The Determinant Of A Matrix Of Sample Zero-Order Correlation Coefficients, Stephen M. Hattori

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

The single equation least-squares regression model has been extensively studied by economists and statisticians alike in order to determine the problems which arise when particular assumptions are violated. Much literature is available in terms of the properties and limitations of the model. However, on the multicollinearity problem, there has been little research, and consequently, limited literature is available when the problem is encountered. Farrar & Glauber (1967) present a collection of techniques to use in order to detect or diagnose the occurrence of multicollinearity within a regression analysis. They attempt to define multicollinearity in terms of departures from a hypothesized …

Models For Estimating Psychiatric Bed Needs, Patricia A. Brenneman

Loma Linda University Electronic Theses, Dissertations & Projects

Inland Counties Comprehensive Health Planning Council wished to estimate the psychiatric bed needs by type (such as state hospitals, board and care homes, etc.) in San Bernardino County from the distributions of patient arrivals and of lengths of stay. A statistical description of the system during 1973 was considered the first step toward estimating future bed needs. A computer simulation model using IBM's programming language General Purpose Simulation System (GPSS) was developed and was found to be unsatisfactory.

Theorems were then developed for a statistical model, seeking to predict future bed needs. The most convenient of these theorems states that …

Levi Structures For Polynomial Ideals., Richard Michael Grassl

Mathematics & Statistics ETDs

Let R be the ring of polynomials in a denumerable set of independent indeterminates over a field F and let I be an ideal (Xo,x1,x2, ... ) in R. A Levi structure for I provides bases for I and R as vector spaces over F and an associated algorithm for determining whether an element of R is in I.

Such structures have been developed previously for certain principal differential ideals [i.e., ideals (Xc),x1 , ... ) with xj the j-th derivative of Xol in which the generator is homogeneous and isobaric and for a family of related ordinary ideals. The …

Branching Processes With Cataclysmic Environmental Changes., Juan F. Corona-BurgueñO

Mathematics & Statistics ETDs

In this dissertation we consider a continuous time branching process with a random environment in which the environment changes according to a continuous time Markov chain. The extinction problem for this model is posed and solved by two distinct methods: by the method of random evolutions of Griego and Hersh and by the results of Athreya and Karlin on branching processes with random environments. Limit theorems for the population size as well as a system of partial differential equations for the expected number of particles (as functions of time) are obtained.

The Numerical Solution Of The Generalized Eigenvalue Problem For Rectangular Matrices, Charles Henry Burris Jr.

Mathematics & Statistics ETDs

This paper studies the Generalized Eigenvalue Problem Ax=λBx for real, rectangular matrices A and B. Several current algorithms for solving this problem are examined, most of which involve a determination of the rank of B, or one of its submatrices. An example is given in which such a decision cannot be made without introducing unnecessary error into the problem. The QZR Algorithm is then introduced as an algorithm which uses unitary transformations to reduce the matrices to a prescribed canonical form. This canonical form provides the information necessary for making decisions about rank. Since A and B can be non …

Independence, Essential Independence And Zero Correlation Of Two Random Variables Conditioned On A Third., Chester Raymond Crain Jr.

Mathematics & Statistics ETDs

In a recent paper Stoughton Bell and William J. Zimmer defined three distinct types of conditional independence; which they call pointwise, intervalwise and strong; of two random variables given a third. They considered these and four closely related independence properties, and they examined the relationships among the 128 (=23+4) Boolean combinations. Bell and Zimmer also considered the kinds of assumptions in applied research that would give rise to each type of conditional independence.

I have searched published texts and papers in probabil­ity and statistics for the three types of conditional inde­pendence. The type considered by Alfred Renyi [Foundations of Probability …

The Order Of An Entire Function With Some Derivatives Univalent, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Note On T, Topologies, Wilson R. Crisler, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Let t be a T. topology for a set X. The problem of representing t as the lattice product (intersection) of stronger topologies is considered. © 1974 American Mathematical Society.

A Method Of Moments Applied To An Invariant Imbedding Solution Of A Certain Class Of Fredholm Integral Equations., Grenfell Paul Boicourt

Mathematics & Statistics ETDs

This dissertation first develops a method for solving the integral equation when y(z') is a constant and then extends it to the case where y(z') is a step function. The solution of the integral equation is achieved by solving the integro differential invariant imbedding equations derived from the integral equation by varying the limits of integration. The imbedding equations are solved using a moment method which reduces the calculation to an initial value problem. Proofs of the existence and convergence of the method are given. In the case where y(z') is a constant, the solution of the integral equation is …