Mathematics Commons^™

Tolerance Intervals For A Class Of Ifr Distributions With A Threshold Parameter, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

One-sided upper and lower tolerance intervals based on type II censored data are obtained. Under certain conditions the tolerance factors can be obtained from known results on the 2-parameter exponential distribution. Copyright © 1980 by the Institute of Electrical and Electronics Engineers, Inc.

Algorithms For Fixed Points Of Nonexpansive Operators, Michael Donald Humphries

Doctoral Dissertations

"Browder proved that in a Hilbert space or a uniformly convex Banach space every non-expansive self-map of a closed, bounded, and convex set has a fixed point. This dissertation contains two algorithms for finding a fixed point of such an operator. The first is a special case of the Mann process. It averages two points which are relatively distant to obtain a better approximation to a fixed point. Under Browder's hypotheses, there is a fixed point which is the limit of a sequence of fixed points of contractions. The second algorithm uses Richardson extrapolation to accelerate the convergence of this …

Solutions Of Differential Inequalities And Existence Theorems For Multi-Point Boundry Value Problems, Paul W. Eloe

Doctoral Dissertations

"Consider the boundary value problem y = 0, y(a) = 0, y(b) = O. The Green's function G(x,s) for this problem is negative for all (x,s) in (a,b) x (a,b). More generally, define the operator L by (formula presented).

If L is disconjugate on [a,b], then the Green's function for the problem

Ly = 0,

y⁽ⁱ⁾ (x.) = O, j=1, ..., k and i=0, ..., n^j-1

where rn_j = n and a= x₁ < x₂ < ... < x_k = b, satisfies the inequality (formula presented)

This implies G(x,s) satisfies the condition, called Condition S, that its sign is independent …

Newtruck: A Comprehensive Long-Term Project In Computer Science, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Fixed Point Theorems In Generalized Hilbert Spaces, Troy L. Hicks, Ed W. Huffman

Mathematics and Statistics Faculty Research & Creative Works

Some fundamental fixed point theorems are proved for locally convex spaces whose generating family of semi norms satisfies the parallelogram law. © 1978.

Convergent Factorial Series Solutions Of Linear Difference Equations, W. J. Fitzpatrick, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Conjugate Of A Singular Functional Differential Operator, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

An explicit representation of the conjugate of a singular functional differential operator is given. Some theorems and their corollaries are proven.

K-Theory Doesn't Exist, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Locally Quasi-Uniform Structures And Strongly Complete Quasi-Uniform Structures, Shirley Carpenter Huffman

Doctoral Dissertations

"Locally quasi-uniform spaces are studied, and it is shown that a topological space (X,t} admits exactly one compatible locally quasi-uniform structure if and only if tis finite.

A general topological result is given showing that a topological space with an infinite topology has either an infinite ascending or an infinite descending sequence of open sets.

The concept of aw-space is introduced, and it is ii shown that every w-space admits a strongly complete quasi-uniform structure. Also, a characterization of w-spaces is given showing when the fine quasi-uniform structure is equal to the fine locally quasi-uniform structure.

An example is given …

Inferences On The Shape Parameter Of The Gamma Distribution And Cramer-Rao Lower Bounds From Censored Data, James Wyckoff

Doctoral Dissertations

"This dissertation is presented in publication form and consists of two articles. The first article considers inferential procedures on the shape parameter of a gamma distribution from censored sampling. Moments for the statistic T = log(x̅_r/x͠_r) are found and used to derive a two-moment chi-square approximation for T. This approximation is then used for testing, estimating, and setting confidence bounds on the shape parameter of a gamma distribution. The second article concerns the Cramér-Rao lower bounds for the variances of estimators, where the estimators are based on censored data. Convenient techniques are derived to evaluate the …

Some Results On Inferences For The Gamma And Double Exponential Distributions, John Victor Grice

Doctoral Dissertations

"This dissertation is presented in publication form and consists of two articles. The first article considers testing the mean of a gamma distribution. For the case that both parameters in the ganuna distribution are unknown, approximate tests for the mean are derived and tables are provided for their implementation. The power of the tests are compared to the power of the uniformly most powerful tests on the mean when the shape parameter is known. In addition, some limiting results are derived. The second article compares conditional and unconditional methods of constructing confidence intervals for the location parameter in the two-parameter …

Some Selection And Ranking Procedures For The Two Parameter Weibull Distribution, Joseph Victor Kingston

Doctoral Dissertations

"This dissertation investigates some selection and ranking procedures for two or more Weibull populations. In particular it studies a restricted subset selection procedure when the populations have a common shape parameter, a 'pick the one best ' procedure for different shapes, classification procedures for both cases, simultaneous and 'best population' confidence intervals for both cases, and, finally, the problem of selecting the one population with largest or smallest shape. Except for the last problem named, the populations are ranked by their reliability. All procedures employ estimates of the parameters of interest based on either uncensored or Type II censored samples. …

Convex Cones And Dentability, J. C. Hankins, R. (Roy) M. Rakestraw

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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 $L^ * f = 0$ …

Characterizations Of Inner Product Spaces., John Lee Roy Williams

Masters Theses

"The parallelogram law and several extensions and generalizations which characterize inner product spaces among normed linear spaces are given. The characterization problem is motivated by its usefulness in foundations of general quantum theories and examples are given.

The technique of proving that a normed linear space is an inner product space by showing that its unit sphere is an ellipsoid is emphasized. Using this technique, a new integral characterization is obtained"-- Abstract, p. ii

Strict Convexity In Locally Convex Spaces And Fixed Point Theorems In Generalized Hilbert Spaces, Ed Wilburn Huffman

Doctoral Dissertations

"A new definition of strict convexity is introduced for locally convex spaces. Examples are given and several characterizations of strict convexity are established for locally convex spaces whose generating family of semi norms satisfies the parallelogram law.

Some fundamental fixed-point theorems are proved for locally convex spaces whose generating family of semi norms satisfies the parallelogram law. Other fixed-point theorems are proved for strictly convex locally convex spaces which are also F-spaces"-- Abstract, p. ii

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.

Extremal Structure Of Convex Sets, J. C. Hankins

Doctoral Dissertations

"Let X be a locally compact closed convex subset of a locally convex Haus Dorff topological linear space E. It is shown that every exposed point, respectively, ray of Xis a strongly exposed point, respectively, ray of X. Also, every extreme point, respectively, ray of Xis a denting point, respectively, ray of X. When the above results are combined one can restate two well-known Krein Milman type theorems due to Klee. There exists a closed convex set that has an extreme point that is neither a denting point nor an exposed point.

In Banach spaces, necessary and sufficient conditions are …

On Estimating Functionals Of Probability Densities And Applications To Parameter Estimation, Dolores Marie Halper Tichenor

Doctoral Dissertations

"Estimating the reciprocal of a scale parameter by means of frequency moments is investigated. An investigation of the bias and mean squared error is carried out and practical methods for implementing the method of frequency moments in the case of the Cauchy distribution are considered. A two-step estimation procedure is proposed, and a comparison of a one-step and two-step procedure is made. Uniform and normal distributions are considered as prior distributions for the interval width in the frequency moments method and mean squared error is tabulated.

A method to estimate I lxl ^j f ^k (x) dx is proposed where …

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.

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.