Physical Sciences and Mathematics Commons^™

A Study Of Vector And Matrix Norms, Alvena Weiskircher

Theses & Honors Papers

A vector or matrix can be associated with a single nonnegative scalar . Basically this is the concept of a vector or matrix norm. While the study of these norms may be classified as numerical analysis , a limited background in linear algebra , matrix theory , and advanced calculus is sufficient to pursue the study of norms.

In this paper many of the properties and theorems concerning norms have been proven . It is thought that the most important results deal with the use of vector and matrix norms in testing for convergence of sequences and series of matrices …

An Analytic Study Of A System Of Nonlinear Ordinary Differential Equations At An Irregular Type Singularity, James M. Lamb

Masters Theses

No abstract provided.

Decompositions Of Modules And Matrices, Thomas Shores, Roger Wiegand

Department of Mathematics: Faculty Publications

A canonical form for a module M over a commutative ring R is a decomposition M ≈ R/I₁ Ο … Ο R/I_n, where the I_j are ideals of R and 1₁ ≤ . . . ≤ I_n. A complete structure theory is developed for those rings for which every finitely generated module has a canonical form. The (possibly larger) class of rings, for which every finitely generated module is a direct sum of cyclics, is also considered, and partial results are obtained for rings with fewer than 2^{c …}

On Hamiltonian - Connected Graphs, James E. Williamson

Dissertations

No abstract provided.

Linear Operators Between Nonarchimedean Banach Spaces, Krishnamachari S. Nadathur

Dissertations

I Preliminaries

The purpose of this dissertation is to extend some classical results on compact and Fredholm operators to the case in which the linear spaces involved are non-archimedean normed linear spaces over a valued field.

In Section I are listed some definitions and basic concepts that are needed for a study of non-archimedean valuation theory. The concepts of tensor products of nonarchimedean Banach spaces over a spherically complete field F, and of the tensor product of operators, are also dealt with in this section.

The proofs of most of the results in Section II are based on the known …

Study Of Dynamic Programming And Gambling Systems., N. D. Prabhakar Dr.

Doctoral Theses

The body of methods known as Dynamic Programming (d.p.) was developed by Bellman and was successfully applied by him to solve practical problems in diverse fields (see 12] and the pa pers cited there.). These methods revolved around an intuitively appealing principle which Bellman called the principle of optimatity. A general formulation of d.p. problem was given by Blackwell (3, s] which is narrower in scope than Bollman's but includes many important applications i12) and offers a proper framework for asking the many inte- resting and mathematically sophisticated questions that arise in d.p.. Strauch, Brown, Maitra, Furukawa, Dantas, Hinderer etc., …

S-Algebras On Sets In C To The Power Of N, Donald R. Chalice

Mathematics Faculty Publications

We give conditions which are necessary and sufficient for polynomial approximation of any continuous function on a compact subset of Cⁿ.

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 …

Nonlinear Stochastic Integral-Equation Of Hammerstein Type, William J. Padgett

Faculty Publications

No abstract provided.

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.

Loss Probabilities In Queueing Processes, R. P. Singh

Masters Theses

No abstract provided.

Severance Classes And Multiplicative Arithmetic Functions, Timothy B. Carroll

Dissertations

No abstract provided.

Local Connectivity In Graphs, Donald W. Vanderjagt

Dissertations

No abstract provided.

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 …

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 …

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.

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 …

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.

Radiation Problem, Gerald L. Fuller

Honors Theses

A sphere of radius 'a' which is radioactive and which has an average range 'b' in the sphere. What fraction of total radiation will escape the sphere?

Modern Art Through Geometric Eyes, Janice M. West

Honors Theses

When tourists--even homefolks--go through a modern art museum, many opinions are accumulated. Some people may have chills when they see a certain painting, while others get a sick feeling of dizziness when they see the same one. In fact, if there were an opinion box at the exit of an art show, I imagine you could almost accurately count the different opinions by counting the total number of people who viewed the show. Yet, there is one opinion that most 'ole foggies' (and I use the term loosely) would agree upon, and that is this: "Why that's nothing but a …

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 …

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 …

On Generalized Matrix Functions, John Hawkins, Adi Ben-Israel

John B. Hawkins

No abstract provided.

Nonnegative And Alternating Expansions Of One Set Of Orthogonal Polynomials In Terms Of Another, William F. Trench

William F. Trench

No abstract provided.