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Infinite Product Spaces Under The Tychonoff And Goofynoff Topologies, James A. Capps

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

The only topology considered for the infinite product of topological spaces in most current topology texts and research papers is the Tychonoff topology. Yet there is another topology which seems to be a much more topologically natural generalization of the usual "box" topology of finite products. We call this natural generalization the Goofynoff topology and exploit its properties. The use of the word "Goofynoff" (pronounced Goof'-n-off) is not universal and does not refer to any person of that name. In the few references to this topology that can be found, it is usually called simply the Box Topology. None of …

A General Lr(K) Parser Building Algorithm, Thomas Joshua Sager

Mathematics & Statistics ETDs

The problem is to find an efficient algorithm that, given the productions of a context-free grammar G, will discover whether G is LR(k) for given k and if it is build an efficient parser for G . The algorithm is given in Section 8. It is essentially a synthesis of the best parts of Knuth's and DeRemer's algorithms. On simple LR(k) grarranars it yields a result equivalent to DeRemer's algorithm, and like Knuth's algorithm it will work on all LR(k) grammars.

Convergence Lattices, Armando Rosario Gingras

Mathematics & Statistics ETDs

This study is concerned with complete lattices in which order convergence coincides with topological convergence with respect to the order topology. Such lattices are termed convergence lattices. After a brief discussion of topology on lattices (Introduction), some preliminary results concerning order convergence and the order topology are presented (Section 1). Several theorems characterizing convergence lattices are presented in Section 2. There it is shown that every neighborhood of a point of a convergence lattice contains an interval that is also a neighborhood of the point. It is also shown that each complete chain, each arbitrary product of convergence lattices, and …

The Solution Of Equations By Radicals, Stephen Davis

Student Scholarship

This paper investigates the algebraic conjecture that the general equation of degree n is not solvable by radicals if n is greater than four. While the author does not intend to provide a new rigorous proof, the work serves to organize and present the fundamental mathematical concepts necessary to understand the proof for an undergraduate audience. The historical context of the problem is explored, noting the early achievements in solving cubic and quartic equations during the sixteenth century and the later contributions of mathematicians like Lagrange, who attempted to find a general reduction method for the quintic. The ultimate solution …

Severance Classes And Multiplicative Arithmetic Functions, Timothy B. Carroll

Dissertations

No abstract provided.

Loss Probabilities In Queueing Processes, R. P. Singh

Masters Theses

No abstract provided.

Local Connectivity In Graphs, Donald W. Vanderjagt

Dissertations

No abstract provided.

Backward And Forward Equations For Random Evolutions., Manuel Keepler

Mathematics & Statistics ETDs

Let V= [v(t),t>=0] be a separable right continuous Markov hain with state space [1,…,N], stationary transition probabilities Pij(t) and infinitesimal matrix Q=(Qij). Let [Ti(t),t>=0, i=1,…,N] be a family of strongly continuous uniformly bounded semigroups of bounded linear operators on a Banach space B. Ai is the infinitesimal generator of T1.

Contributions To Methodology Of Construction Of Consistent Index Number., Dodla Sai Prasada Rao Dr.

Doctoral Theses

International variation in national product is a subject of considerable interest, and any meaningful comparison of national product or per capita national income has to be in termo of a common currency. An intertemporal comparison for the same country at two points of time is mote meaningful in real terms, or in other words when the currency unit is adjusted for change in the general price level between the two points of time. In the same manner, the level of output or of consumption of a group of persons belonging to a region or to a particular socio-economio group can …

Maximal And Minimal Topologies., Asit Baran Raha Dr.

Doctoral Theses

Given a topological property Ï€ and a pon-void set X, let Ï€(X) denote the set of topologies on X with property Ï€. 7 (X) is obviously partially ordered by inclusion, A topologi- cal space (X,T) is minimal if T is a minimal element in T (X). (X, T) is said to be maximal Ï€ if T1 1s a maximalelement in Ï€(X), The study of maximal and minimal topological space is, as a matter of fact, a study of maximal Ï€ and minimal Ï€ spaces. Topological spaces closely related to minimal T sp aces are T-closed and KatetoV T spaces, (X,T) …

Studies In Boolean Algebras And Measure Theory., K. P. S. Bhaskara Rao Dr.

Doctoral Theses

This Thesis is divided into six chapters the first three chapters constituting studies in Boolean algebras and the last three chapters constituting studies in measure theory. We give below a sketch of the main problems treated in this Thesis.A De composition theorem due to Sobczyk and Hammer (28] implies that strongly continuous charges on Boolean algebras play a role similar to that of nonatomic measures on Boolean g-algebras. CHAPTER 1. Rudin [25] and Knowles [14] gave necessary and sufficient conditions for the Boral o-ficld of a compact Hausdorff space to admit a nonatomic measure. But there are no necessary and …

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.

Brief Theory Of Coherent Processor, Richard C. Heyser

Unpublished Writings

The particular coherent data processor which is to be discussed relies heavily upon several basic concepts. These concepts represent a departure from conventional practice and hence the theoretical description must await their presentation in order to gain some continuity. We will accordingly present the underlying assumptions and signal physics prior to description of the processor itself.

On The Bordism Ring Of Complex Projective Space, Claude Schochet

Mathematics Faculty Research Publications

The bordism ring MU∗(CP^∞) is central to the theory of formal groups as applied by D. Quillen, J. F. Adams, and others recently to complex cobordism. In the present paper, rings E∗(CP^∞) are considered, where E is an oriented ring spectrum, R=π∗(E), and pR=0 for a prime p. It is known that E∗(CP^∞) is freely generated as an R-module by elements {β_τ|r≧0}. The ring structure, however, is not known. It is shown that the elements {β …

Lower Bound Confidence Intervals, Julia Leigh Peck

All Master's Theses

Consider the onefold nested, equal numbers model

y_ij= μ + a_i + b_ij

where the a_i and b_ij are normally and independently distributed with zero expectations and variances o²_a and o²_b, respectively. This thesis derives a confidence interval for the external component of variance o²_a with a prescribed lower bound on the confidence coefficient. This method is compared with various approximations and with Williams' procedure [12], the only other bounded approximation. The actual confidence coefficient associated with the interval is then evaluated numerically and compared to the …

Imbedding Problems In Graph Theory, William Goodwin

Honors Theses

For some years there has been interest among mathematicians in determining the different ways in which certain graphs can be imbedded in given surfaces. M.P. VanStraten in 1948, determined that it is possible to imbed the graph K_3,3 (which is the graph representing the famous three houses, three utilities problem) in the torus in only two ways. She then used this fact to show that the graph representing the configuration of Desargues (containing K_3,3 as a subgraph) has genus two. One major source of motivation for the work on imbedding problems has been their relation to coloring problems …

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 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 …

Motions In Three-Space, Lovemore F. Mareya

All Graduate Theses, Dissertations, and Other Capstone Projects

The objective of this paper is to determine and verify formulae for finding images of points in three-dimensional space, for the following motions:

1. Translation
2. Reflection
3. Rotation

The transformation in two-dimensional space were reviewed and those methods, with appropriate refinements, extended to three-dimensional space.

Biometrics Of Bilateral Symmetry In Plants., T. Davis Dr.

Doctoral Theses

During the past ten deendes, observation rolating to ayune try, asymmatry, dis-oyame try, radlal symmetry, rotatiÉ”nal Bymne try, bilateral aymme try and ambidextry in the fields of bo tany, Boology, geology, chemiatry, eryatellography, physics, astronomy, engineering, mathematics, sunio, poetry and art vere recorded by various scientists. The prevent treatise is a sua- mary of an elaborato study on bilaterai syame try or microrinage symse try occurring in vari us plant organs. Unlike moet of the earlior reports, the problem here has been takled unified on a quantitative basis, thereby ereating situations where sophisti-cated techniques of statietios could be effectively employed. …

Stochastic Integro-Differential Equations Of Volterra Type, William J. Padgett, Chris P. Tsokos

Faculty Publications

No abstract provided.

Nonnegative Matrices Whose Inverses Are M-Matrices, Thomas L. Markham

Faculty Publications

A characterization of a class of totally nonnegative matrices whose inverses are M-matrices is given. It is then shown that if A is nonnegative of order n and A^-1 is an M-matrix, then the almost principal minors of A of all orders are nonnegative.

Adaptive Prediction Of Stationary Time Series By Modified Conjugate Direction Methods, James Otto Friel

Mathematics & Statistics ETDs

We consider the problem of obtaining finite memory linear one-step predictors for a non-deterministic weakly stationary stochastic process {u_t : t = 0, ± 1, ± 2, ± ···} which have minimum mean square error. If φ(k) = Ɛ u_t u_t+k is the (unknown) covariance function for the process this problem reduces to solving the system of linear equations φ x = φ where φ = (φ(1), φ(2), ..., φ(d)), φ = (φ(i - j)) i, j = 1, 2, ..., d. Two iterative procedures are developed for producing a sequence of estimators {x_n}_{n=1 …}

Linear Estimation: The Kalman-Bucy Filter, William Douglas Schindel

Graduate Theses - Mathematics

The problem of linear dynamic estimation, its solution as developed by Kalman and Bucy, and interpretations, properties and illustrations of that solution are discussed. The central problem considered is the estimation of the system state vector X, describing a linear dynamic system governed by

dx/dt = F(t)X(t) + G(t)U(t)

Y(t) = H(t)X(t) + V(t)

for observations of Y (system output), where V is a random observation-corrupting process, and U is a random system driving process.

An extension of the Kalman-Bucy filter to estimation in the absence of priori knowledge of the random process U and V is developed and illustrated.

Flexible Algebras Of Degree Two, Joseph H. Mayne

Mathematics and Statistics: Faculty Publications and Other Works

All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra. We then investigate the multiplicative structure of those algebras which are partially stable over an algebraically closed field of characteristic p A 2, 3, 5. The results obtained are then used to develop conditions under which such algebras must be commutative.

On The Genus Of Hamiltonian Groups, Paul E. Himelwright

Masters Theses

No abstract provided.

Completions Of Lattices With Semicomplementation, Alan A. Bishop

Dissertations

No abstract provided.

Reducing Uncertainty, Richard C. Heyser

Unpublished Writings

Intended for audio engineers, Richard C. Heyser meant for this paper to bring attention to the misapplication of the theoretical concept, the Uncertainty Principle. Heyser argues that this concept has been "freely applied without regard to the errors which may result due to lack of understanding of its derivation."

Uniform Convergence Of Lacunary Fourier Series, Julio Edgardo Barety

Mathematics & Statistics ETDs

Let G be a compact group and its dual group which we suppose to be countable. We suppose that S = {_n}_n≥0 is a non-decreasing sequence of finite subsets of having the property that = . If F is the topological dual of a homogeneous Banach space B provided with its norm topology, one can then define in a natural way convergence in norm in F with respect to the sequence S. With F one can associate two Banach spaces F_b and F_c consisting of those elements of F whose Fourier series has bounded …