Mathematics Commons^™

Solvability Of Differential Systems Near Singular Points, Leon M. Hall

Doctoral Dissertations

"Functional analysis techniques are used to prove a theorem, analogous to the Harris-Sibuya-Weinberg theorem for ordinary differential equations, which yields as corollaries a number of existence theorems for holomorphic solutions of linear functional differential systems of the form z^Dy'(z) = A(z)y(z) + B(z)y(αz) + C(z)y'(αz) in the neighborhood of the singularity at z = 0"--Abstract, page 2.

On Interaction In The Two-Way Aov Model Without Replication Including Power Comparisons Of Two Tests For Non-Additivity, Victor John Hegemann

Doctoral Dissertations

"Data analysts have long been concerned with the problem of giving a complete analysis of the two-way crossed classification design with one observation per cell when interaction is present in the data. Conventional tests of hypotheses and statistical inferences are not applicable in this case since an estimate of the error variance is not available. Transformation of the data to additive data has been one solution to this problem; however, interpretation of the physical units of the transformed data is difficult. Recent contributions to the analysis of this design include a test for interaction, a test for testing differences in …

Methods And Applications Of The Mean-Variance Portfolio Selection Model, John W. Marsh

Doctoral Dissertations

"The Mean-Variance portfolio selection model, or Efficient Market model, is examined in terms of the small investor. The performance is first tested on the small sample space of the thirty Dow Jones Industrials. The results show that it is possible to outperform the market by investing in the minimum-variance, or safest, portfolio. The Critical-Line algorithm as developed by Markowitz and modified by Sharpe is used in this analysis.

Since the Critical-Line algorithm is very time-consuming and does not always converge to a solution, an alternate algorithm is developed. This algorithm, referred to as the “Simplified Algorithm”, is designed to find …

The Completions Of Local Rings And Their Modules., Christopher Scott Taber

Masters Theses

"This paper gives a generally self-contained introduction to the completions of local rings and their modules. The '.Fbrmal Power Series, the Ideal-adic, and the Projective Limit completions are established, and the conditions under which they are equivalent are also given. In addition, two methods of obtaining the completion of an R-module from the completion of the ring Rare supplied. As an ideal of R may also be taken as an R-module, a discussion of obtaining its completion from the completed ring is also provided. Two well-known examples are furnished in this paper"--- Abstract, p. ii

Linear Geometry, Phyllis L. Thomas

Masters Theses

"This paper contains material suitable for a one semester course in linear geometry where the student has had a one semester course in linear algebra previously. It compiles information in the areas of affine sets, affine geometry, convex sets, and a few applications. Also included are Caratheodory's theorem and the well-known theorem by Helly as proved by Radon"--Abstract, page ii.

Quasi-Unmixed Local Rings And Quasi-Subspaces, Peter G. Sawtelle

Mathematics and Statistics Faculty Research & Creative Works

The concept of a quasi-subspace is defined so that it plays a role relative to quasi-unmixedness analogous to that of subspace to unmixedness. This definition is used to characterize quasi-unmixed local rings. © 1973 American Mathematical Society.

A First Order Method For Differential Equations Of Neutral Type, R. N. Castleton, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

A first order method is presented for solution of the initial-value problem for a differential equation of neutral type with implicit delay in the critical case where the time-lag is zero and the method of stepwise integration does not apply. A convergence theorem is proved, and numerical examples are given. © 1973, American Mathematical Society.

Some Results On Quasi-Uniform Spaces, Karen Sylvia Carter

Doctoral Dissertations

"An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T₁ space does not necessarily have a T₁ strong completion.

The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.

Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is …

Tchebycheff Approximation On A Discrete Point Set: Algorithms Old And New, William Edward Mcbride

Doctoral Dissertations

"Several linear and nonlinear algorithms for solving the discrete Tchebycheff problem are compared in this study. The Lawson algorithm is compared with two more well-known methods of linear Tchebycheff approximation. A new acceleration scheme for the Lawson algorithm is introduced and its performance is tested with an already existing acceleration technique. The new version is found to be better than the previous one but not as effective as the traditional Exchange method.

A nonlinear version of Lawson's algorithm is proposed for the solution of problems having approximating functions which are varisolvent. Some linear theorems of Lawson are extended to the …

Some Quasi-Uniform Space Examples, Troy L. Hicks, J. W. Carlson

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

An Acceleration Technique For A Conjugate Direction Algorithm For Nonlinear Regression, Larry Wilmer Cornwell

Doctoral Dissertations

"A linear acceleration technique, LAT, is developed which is applied to three conjugate direction algorithms: (1) Fletcher-Reeves algorithm, (2) Davidon-Fletcher-Powell algorithm and (3) Grey's Orthonormal Optimization Procedure (GOOP). Eight problems are solved by the three algorithms mentioned above and the Levenberg-Marquardt algorithm. The addition of the LAT algorithm improves the rate of convergence for the GOOP algorithm in all problems attempted and for some problems using the Fletcher-Reeves algorithm and the Davidon-Fletcher-Powell algorithm. Using the number of operations to perform function and derivative evaluations, the algorithms mentioned above are compared. Although the GOOP algorithm is relatively unknown outside of the …

Mathematical Modeling Of River Water Temperatures, Leland Lovell Long

Doctoral Dissertations

"The applicability of power spectral density techniques, Fourier series analysis, and linear regression to the mathematical modeling of river water temperature is demonstrated. Consideration is also given to the problem of estimating thermal inputs to rivers from man-made sources such as electrical power plants. First, power spectral density techniques are used in the time-series analysis of water temperature records which were taken from the Missouri River. Two spectral ranges are then studied from the standpoint of their applicability to (1) mathematical model building and (2) detection and identification of cyclic thermal inputs. Next, a Fourier regression fit to the time-series …

Structure Of Zero Divisors, And Other Algebraic Structures, In Higher Dimensional Real Cayley-Dickson Algebras, Harmon Caril Brown

Doctoral Dissertations

"Real Cayley-Dickson algebras are a class of 2ⁿ-dimensional real algebras containing the real numbers, complex numbers, quaternions, and the octonions (Cayley numbers) as special cases. Each real Cayley-Dickson algebra of dimension greater than eight (a higher dimensional real Cayley-Dickson algebra) is a real normed algebra containing a multiplicative identity and an inverse for each nonzero element. In addition, each element a in the algebra has defined for it a conjugate element ā analogous to the conjugate in the complex numbers. These algebras are not alternative, but are flexible and satisfy the noncommutative Jordan identity. Each element in these algebras can …

Quasi-Pseudometrics Over Tikhonov Semifields And Fixed Point Theorems, Ronald Evans Satterwhite

Doctoral Dissertations

"It has been shown that topological spaces are characterized as quasi-pseudometric spaces over some Tikhonov semifield.

Sufficient conditions are given for a T₁ space to be metrizable over some Tikhonov semifield.

Completely regular (uniform) spaces are characterized as pseudornetric spaces over some Tikhonov semifield.

Certain metric, pseudornetric, quasi-metric, quasipseudometric spaces over a Tikhonov semifield are shown to be respectively metric, pseudometric, quasi-metric, quasipseudometric spaces in the usual sense.

Several results from fixed point theory in the metric space setting are generalized to the setting of completely regular (uniform) Hausdorff spaces."--Abstract, page ii.

Statistical Studies Of Various Time-To-Fail Distributions, James Addison Eastman

Doctoral Dissertations

"Three models are considered that have U-shaped hazard functions, and a fourth model is considered that has a linear hazard function. Several methods for estimating the parameters are given for each of these models. Also, various tests of hypotheses are considered in the case of the model with the linear hazard function. One of the models with a U-shaped hazard function has a location and a scale parameter, and it is proved in general that any other parameters in a distribution of this type are distributed independently of the location and scale parameters.

A new method used to estimate the …

Elementary Length Topologies Constructed Using Pseudo-Norms With Values In Tikhohov Semi-Fields, Jackie Ray Hamm

Doctoral Dissertations

"Elementary length topologies defined on normed and pseudo-normed linear spaces are studied. It is shown that elementary length topologies constructed with different pseudo-norms are never equivalent. Elementary length topologies are constructed on certain topological spaces and some of their properties are investigated. It is shown that certain "measuring devices" (i.e., norms, pseudo-norms, semi-norms, and pseudo-metrics) which take their values in Tikhonov semifields may be used to construct elementary length topologies on any topological linear space. Relationships between two elementary length topologies generated with different measuring devices are considered.

Let (X,t) be a topological linear space such that t is determined …

Nonrandom Characteristics Of Common Stock Prices, Donald Leroy Gaitros

Doctoral Dissertations

"This study presents an application of operations research techniques to the development of stock price generation and simulation models to aid in the understanding of price movement. Relationships between stock price and volume and stock price and market averages which follow descernible trends and patterns are discovered. Technical trading rules are developed based on these relationships which empirically have shed doubt on the random walk hypothesis of price movement. This in turn gives evidences that technical analysis can be an aid to price forecasting"--Abstract, page ii.

Existence And Uniqueness For Nonlinear Neutral-Differential Equations, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

Fixed point theorems are used to prove existence and uniqueness of the C1 solution of the initial-value problem for a functional-differential equation of neutral type. © 1971, American Mathematical Society. All Rights Reserved.

On Completeness In Quasi-Uniform Spaces, John W. Carlson, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Existence And Continuous Dependence For A Class Of Nonlinear Neutraldifferential Equations, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

This paper presents existence, uniqueness, and continuous dependence theorems for solutions of initial-value problems for neutral-differential equations of the form (equation omited), where f, g, and h are continuous functions with g(0, x0)=h(0, x0) = 0. The existence of a continuous solution of the functional equation z(t) =f(t, z(h(t))) is proved as a corollary. © 1971 American Mathematical Society.

Characterizing Topologies By Classes Of Functions And Multifunctions, Alexander Hamlin Cramer

Doctoral Dissertations

"Topological spaces are characterized by the algebraic and topological structures of their classes of continuous selfmaps. The problem of determining the topology of a set given certain classes of multifunctions or relations is considered. The algebraic structure of the upper semicontinuous multifunctions is shown to determine the topology of T₁ spaces. A partial order for classes of topologies for the real numbers is defined and relationships between various classes are established"--Abstract, page ii.

Modeling The Visual Pathway For Interactive Diagnosis Of Visual Fields, Chiam Geoffrey Goldbogen

Doctoral Dissertations

"Visual fields are an important tool for the ophthalmologist in the detection, diagnosis, and monitoring of certain diseases and maladies of the visual pathway. The aim of the present research is to build a computer system which utilizes a learning machine to develop a mathematical model of the visual pathway. It is hoped that this system may be used in the field of ophthalmology as a teaching aid, or may assist in various aspects of diagnosis. Faults corresponding to blind or impaired areas of visual fields are extracted from medical records of a patient's condition. The structure of the model …

Some Statistical Inferences For The Bivariate Exponential Distribution, Bruce Mohr Bemis

Doctoral Dissertations

"The bivariate exponential distribution is neither absolutely continuous nor discrete due to the property that there is a positive probability that the two random variables may be equal. Basic properties of the distribution are presented as well as methods of parameter estimation including maximum likelihood. The distribution is shown to satisfy the usual regularity conditions in spite of its possession of a singularity. The maximum likelihood estimates are asymptotically efficient. Two other methods of estimation are compared with the maximum likelihood method in terms of efficiency. Tests of the hypothesis that two random variables each have independent exponential distributions versus …

Special Subrings Of Real, Continuous Functions, Paul Marlin Harms

Doctoral Dissertations

"Some lattice-ordered subrings of C(X) containing C*(X) are examined where X is a completely regular space. Each realcompact spaceY between [v]x and ßx is associated with a lattice-ordered subring of C(X) which is isomorphic to C(Y) and contains C*(X). The cardinal number of (ßX - [v]X) is a lower bound for the cardinal number of these subrings. Every prime ideal in each of these subrings is comparable with the intersection of the subring and a maximal ideal in C(X). The structure space of maximal ideals is studied for special subrings in C(X) containing C_K(X), the continuous functions of …

Inclusion Theorems For Boundary Value Problems For Delay Differential Equations, Leon M. Hall

Masters Theses

"In this thesis existence and uniqueness of solutions to certain second and third order boundary value problems for delay differential equations is established. Sequences of upper and lower solutions similar to those used by Kovač and Savčenko are defined by means of an integral operator, and conditions are given under which these sequences converge monotonically from above and below to the unique solution of the problem. Some numerical examples for the second order case are presented. Existence and uniqueness is also proved for the case where the delay is a function of the solution as well as the independent variable"--Abstract, …

Integrability Of The Sums Of The Trigonometric Series 1/2 Aₒ + ∞ [Over] Σ [Over] N=1 AN Cos Nθ And ∞ [Over] Σ [Over] N=1 AN Sin Nθ, John William Garrett

Masters Theses

"The trigonometric series C = 1/2 aₒ + ∞ [over] Σ [over] [n=1] a[subscript n] cos nΘ and S = ∞ [over] Σ [over] n=1 a[subscript n] sin nΘ, where {a[subscript n]} monotonically decreases to zero both converge almost everywhere to functions f and g respectively. f (or g) is L iff C (or S) is the Fourier series of f (or g) iff term-by-term integration of C (or S) is valid. There are three equivalent conditions, each of which implies that C is the Fourier series of f...."--Abstract, page ii.

Completeness And Related Topics In A Quasi-Uniform Space, John Warnock Carlson

Doctoral Dissertations

"Completions and a strong completion of a quasi-uniform space are constructed and examined. It is shown that the trivial completion of a T₀ space is T₀ . Examples are given to show that a T₁ space need not have a T₁ strong completion and a T₂ space need not have a T₂ completion. The nontrivial completion constructed is shown to be T₁ if the space is T₁ and the quasi-uniform structure is the Pervin structure. It is shown that a space can be uniformizable and admit a strongly complete quasi-uniform structure and not admit a complete uniform structure. Several counter-examples …

Extension Of Some Theorems Of Complex Functional Analysis To Linear Spaces Over The Quaternions And Cayley Numbers, James E. Jamison

Doctoral Dissertations

"In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert …

A Coordinate Oriented Algorithm For The Traveling Salesman Problem, Joseph Sidney Greene

Doctoral Dissertations

"The traveling salesman problem may be stated as follows: "A salesman is required to visit each of n given cities once and only once, starting from any city and returning to the original place of departure. What route should be chosen in order to minimize the total distance traveled?" A new algorithm is developed which gives a good approximation to the solution for a large number of cities using reasonable computer time and which will converge to the exact solution if allowed to continue. This algorithm is a branch and bound technique which utilizes the distance between cities in its …

A Heuristic Algorithm For Determining A Constructive Suboptimal Solution To The Combinatorial Problem Of Facility Allocation, Harry Kerry Edwards

Doctoral Dissertations

"The major problem in plant layout is to determine the most economical relative location of facilities. There are two distinct types of suboptimal solutions to this combinatorial problem: construction and improvement. The writer has developed Modular Allocation Technique (MAT) which is the first useful construction suboptimal technique. The MAT general algorithm, a theorem relating the MAT solution to the optimal solution and an example problem are given. A computer program has been written that will apply MAT to the allocation problem for a maximum of 40 facilities. Results are given to demonstrate how MAT solutions may be used as initial …