Digital Commons Network^™

Imbedding Graphs In Pseudosurfaces, Wayne S. Petroelje

Masters Theses

No abstract provided.

A New Test For Normality, Richard Leroy Roller

All Master's Theses

This paper presents a new test for normality which is based on a complete characterization of the normal distribution. Motivation for the test is given in terms of a proof of this characterization. The test is derived and evaluated by computer-simulated sampling from alternative distributions. The empirical powers of the test generated from such samplings are tabled and compared to nine commonly used tests. Evaluation of the proposed test is discussed and further avenues of investigation are suggested.

The Constructive Theory Of Distributions, Elsie M. Gustafson

Masters Theses

No abstract provided.

Orthogonality In Normed Spaces, Martin R. Mccarthy

All Master's Theses

This paper presents three definitions of orthogonality in normed spaces. Each definition is shown equivalent to the inner product being zero when restricted to an inner product space. The definitions arise from such properties in two space as the diagonals of a rectangle being equal and the Pythagorean Theorem. The third definition shows that the idea of an inner product can be generalized under certain conditions.

A Comparative Investigation Of The Effects Of Frequent Testing Upon Achievement In Secondary Advanced Algebra, John Thomas Fullerton

All Master's Theses

Relatively speaking, few studies have concerned themselves with the problem of frequent testing, and as Keys pointed out, empirical evidence, uncomplicated by differences in the amount of testing material employed, on the effects of frequent testing is, at best, scarce (14:427). Also many studies used tests and test results for direct instruction, thus introducing additional variables. Furthermore, the choice of subjects and disciplines has been limited, the better part being taken from college psychology and sociology classes or high school science classes. This investigation was not an attempt to modify previous experiments, nor was it an attempt to identify which …

Lower Bounds In The Stekloff Problem, Shrikant Narayan Rao

Masters Theses

No abstract provided.

Relationships Between Reversible And Connected Automata, Robert Michael Johnson

All Master's Theses

The present investigation explores some of the relationships among special classes of automata defined by Bavel and Muller (1:231-240), Trauth (6:170-175), and Cutlip (2).

A New Confidence Interval For The Mean Of A Normal Distribution, David Lee Wallace

All Master's Theses

A typical problem in statistical inference is the following: An experimenter is confronted with a density function f(x; ϴ) which describes the underlying population of measurements. The form of f may or may not be known, and ϴ is a parameter (possibly vector-valued) which describes the population. The statistician's job is to estimate or to test hypotheses about the unknown parameter ϴ. In this paper, we shall consider interval estimation of the mean of the normal density function.

Convergence Rates For The Central Limit Theorem For Random Sums, Christopher E. Olson

Mathematics & Statistics ETDs

Let (X_i} be a sequence of independent, identically-distributed random variables with EX²_i < ꝏ and E(X_i - EX_i)² = 1.

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

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

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

Torus Knots, David S. Bradley

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

We have compiled here many interesting results concerning a particular collection of knots called torus knots. Torus knots are merely simple closed curves imbedded in an unknotted torus T² in E³. We show that the fundamental groups of T², π(T²), is the direct product of the additive group of integers with itself. The ordered pair (p, q) in Z x Z determines an equivalence class of loops on the torus, and we show in Section II that the class [(p, q)] contains a loop whose image is a simple closed curve if and …

Integral Representation Theorems, Leiko Hatta

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since F. Riesz showed in 1909 that the dual of C[0,1] is BV[0,1] (the functions of bounded variation on [0, 1] with || g ||_BV = V(g)) via the Stieltjes integral, obtaining representations for linear operators in various settings has been a problem of interest. This paper shows the historical manner of representations, the road map type theorems and representations obtained via the v-integral.

The Poincaré Conjecture, Joseph D. Peck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The central theme for this paper is provided by the following three statements:

(1) Every compact connected 1-manifold is S1.

(2) Every compact connected simply connected 2-manifold is S2.

(3) Every compact connected simply connected 3-manifold is S3.

We provide proofs of statements (1) and (2). The veracity of the third statement, the Poincaré Conjecture, has not been determined. It is known that should a counter-example exist it can be found by removing from S3 a finite collect ion of solid tori and sewing them back differently. We show that it is not possible to find a counterexample by removing …

A Theory Of Multiplicity For Multiplicative Filtrations, Wayne Wilson Bishop

Dissertations

No abstract provided.

The *S-Product Of Arithmetic Functions, Kathryn Diane Kopec

Masters Theses

No abstract provided.

Optimum Estimators And Strategies In Survey Sampling., M. K. Ramakrishnan Dr.

Doctoral Theses

This thesis consists of nine chapters. In the first chapter we give the basic concepts and definitions and also a broad review of the literature related to the problems considered in this thesis. The second and third chapters are devoted to a detailed modified comparison of sampling with and without replacement, for the case of equal and unequal probability sampling respectively. In the fourth and fifth chapters we discuss the criteria of hyper-admissibility and linear suf2iciency for the choice of an optimum estimator for a given sampling design. The succeeding three chapters have as their main objective the central problem …

Statistical Study Of Tongue Pigmentation In Man., Dabeeru Chandrasekhara Rao Dr.

Doctoral Theses

Tongue pigmentation in man:The 'partioular' type of dark apots and patohes on the surface of the tongue, as investigated in the prosent thesis, wae first not ioed in human populations by Davis [5], who called it 'tongue piementation'. It is to be emphasized that not all colour piements come under this 'particular' type. There are some pathological conditione giving rise to transient discolouration of the tongue. This aspeot will be disouesed a little later. Such tongue pigmentation does not seem to have been reported for any population, human or otherwise.Tongue pigmentation be usually found on the upper surface or borders …

Contributions To The Theory Of Directed And Undirected Graphs., Siddani Bhaskara Rao Dr.

Doctoral Theses

Graph thoory has becone such a well Imown and widely applicd subject with nuncrous applications in operations rescarch, coding thoory, gone thoory, physical and so oial sciences (to montion only a few), that it is not neccasary to give a goneral introduction to 1t. Instead wo give below a Burnary of the reaults containod in thia thosis chapterwisc.This thesis contains five chapters which are, morc or loss, indopendent of cach. other. In Chaptcr 1, we study the existence of locally restricted graphs, that is graphs having a proscribod property with given dogrecs. In Section 1.1, wc obtain necossary and sufficient …

Some Statistical Considerations On Population Structure, Genetic Correlation And Human Multiple Births., Ranajit Chakraborty Dr.

Doctoral Theses

Siree the reiiecovery of Mentel'a works tamsrds tha beglaning of this contury the mnetiolete did not confine their atudies only at fanilial level. The atudy of penetie entities at poyulation level also bocune equally important for understending the mol.ani an of inharitanec. Thda branch of urderotanding the neoahantes of herodity, knowa sa Population Geneties, has by noe bacane no eli incm that a discunoion of say part of it drea not nead ny geneeal introtuetion. In view of shia faot, we irstead speni sone time to get into the problans diseussus in this thesia.Bastcally wa atudy theeo problene in this …

Random Evolutions On Diffusion Processes, Donald Quiring

Mathematics & Statistics ETDs

Let {V(t,ω), t ≥ O, ω ε Ω} be a diffusion process on the real line with infinitesimal operator 1/2σ²(⋅)D² + m(⋅)D. Markov processes {V_n, n = 1,2,....} on the real line are constructed in such a way that the paths of V_n are step functions with jump size n^-1/2 and

P_O [lim sup |V_n(s)-V(s)| = 0] =1

n∞ 0≤s≤t,

where P_O assigns probability one to paths starting at the origin at t = 0.

Let {T_V(t), t≥0, vε R} be a family of linear contraction operators …

The History And Nature Of Pi, Karen A. Rand

Honors Theses

No abstract provided.

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 …

Comparison Of Three Schools Of Thought In The Foundations Of Mathematics, Carolyn Rhodes

Honors Theses

Some of the most memorable events of the twentieth century took place as a result of conflict. Out of the numerous conflicts staged during this period, only one was resolved not on a common everyday piece of writing paper. The proponents of the conflict--E. V. Huntington, Oswald Veblen, Bertrand Russell, A. N. Whitehead, and David Hilbert--did not use weapons, but they used basic mathematical structure to wage the most extensive and critical investigation into the foundations of mathematics. As a result three schools of thought which are of special prominence and interest were brought to light. These are the postulational …

Bayesian Statistics: The Fundamental Theorem, Carolyn Rhodes

Honors Theses

The problem of the foundation of statistics is to state a set of principles which entail the validity of all correct statistical inference, and which do not imply that any fallacious inferences is valid. This sentence describes the purpose of much writing on statistical inferences, in general, and Bayesian statistics, in particular. Bayesian statistics was first introduced in a publication by Thomas Bayes in The London Philosophical Transactions, volumes 53 and 54 for the years 1763 and 1764, after Bayes' death in 1761. However, since the entire statistical research of Bayes' involves enormous study, this paper will limit itself to …

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.

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, …

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 …

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 …