Mathematics Commons^™

Line Critical Point Determining And Point Distinguishing Graphs.Geodetic Orientations Of Complete K-Partite Graphs., Larry Dean Gassman

Mathematics & Statistics ETDs

I. Sumner defined a graph to be point determining if and only if distinct points have distinct neighborhoods and he has characterized connected line-critical point determining graphs. Here a short alternate proof of his characterization is provided and arbitrary line-critical point determining graphs are then characterized. Next line-critical point distinguishing graphs are considered; a graph is point distinguishing if and only if it is the complement of a point determining graph. Finally line-critical graphs that are both point determining and point distinguishing are characterized.

II. Ore defined a graph to be geodetic if and only if there is a unique …

Estimation Of Probability Functions Using Splines., Douglas Wade Hill

Mathematics & Statistics ETDs

In this paper, three classes of spline functions are applied to the problem of estimating probability distribution and density functions. In each case, it is shown that the spline function approximating the sample cumulative distribution function converges almost surely to the unknown distribution, F, given that F has at least two continuous derivatives. If F has three or more continuous derivatives, the derivative of the spline converges to the density function. For polynomial splines of sufficiently high degree if F has k continuous derivative, the rate of convergence for the j-th derivative is shown to be 0(hk-j-1/2) where h is …

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 …

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.

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.

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

Faculty Publications

No abstract provided.

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 …}

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 …

Patricia-Ii Two Level Overlayed Indexes For Large Libraries., James Leon Clark

Mathematics & Statistics ETDs

PATRICIA is a Practical Algorithm To Retrieve Informa­tion Coded In Alphanumeric. The library index built by PATRICIA is entirely core resident. PATRICIA-II extends PATRICIA by building both a lower index and an upper index. This allows for the indexing of a much larger library. The lower index is core resident and the upper index is divided into upper pages which are stored on disk. At any given time only the lower index and one upper page are in core. Upper pages reference only themselves, not each other. In addition to these innovations, PATRICIA-II retains all of the features of its …

Application Of Fast Poisson Solvers To The Numerical Approzimation Of Parabolic Problems., Billy Lewis Buzbee

Mathematics & Statistics ETDs

Let T be a positive constant, let D^n be the interior of the unit hypercube in R^n with boundary ∂D^n, let a(t;x1,x2,…,xn) be a strictly positive funtion, and consider the parabolic problem ut= ∇*a ∇u + s(t;x1,x2,…,xn) in D^nx[0,T]

Where

U(t)=0 on ∂D^nx[0,T]

And

U(0)=f

This report compares three A-stable marching procedures for approximating this problem by finite differences. The procedures considered are the pure explicit procedure (APX) with 6t sufficiently restricted to insure A-stability, the pure implicit procedure (PM) or backwards difference equation, and a recently developed pure implicit procedure (SOC) which is second order correct in time and …

Branches And Completions For Real Algebraic Curves, Arthur E. Bukowski

Mathematics & Statistics ETDs

Let Q be a real ideal in a commutative ring A over an ordered field k. Do the classical results of cummutative rings hold for the ideal Q, the realradical of Q, and the real primes of A? We deal with these questions in Section 1. We prove that the minimal realprimes of Q are the minimal primes of Hence the minimal real primes of A are the minimal primes of some a_iϵ A}. A finitely generated realsimple ring isin fact a field and so any maximal realideal in a finitely generated ring A|k is a maximal ideal. …

Some Problems In Combinatorial Number Theory., Frank Ernest Higgins

Mathematics & Statistics ETDs

In this paper we consider three unrelated problems in combinational number theory. The first of these pertains to minimal residual polynomials, the second to certain group factorizations and the third to the addition of positive integers in their Zeckendorf representations.

In section II We show that for any given positive integer m there exists a unique integer monic polynomial P of least degree and whose coefficients satisfy certain inequalities with the property that m divides P(x) for every integer x. This polynomial is called the minimal residual polynomial modulo m. We then show that this polynomial assumes various forms which …

A Maximum Principle For Time-Lag Control Problems With Bounded States, Gary R. Bunce

Mathematics & Statistics ETDs

A maximum principle is obtained for control problems involving system equations with a constant time lag in the control and state variables. The arcs under consideration are subject to constraints of the form

The results are obtained using the method of M. R. Hestenes.

Operators As Elements In A Partially Ordered Linear Algebra., Edward Wayne Davenport

Mathematics & Statistics ETDs

R. DeMarr {unpublished) has begun a study of linear operators as elements in a Dedekind O-complete partially ordered linear algebra {dsc-pola). The order structure necessary to produce elements in a dsc-pola which behave as specific operators on a specific space of functions is studied.

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

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Some Applications Of Decompositions Of The Identity To Ordered Vector Spaces., John Annulis

Mathematics & Statistics ETDs

We study decompositions of the identity (for definition see Vulikh [13]) in Dedekind a-complete vector lattices. In Chapter 1, we define and develop a notion of continuous elements with respect to a decomposition of the identity. We shall also develop a spectral theory for these elements. In Chapter 2, two Stieltjes-type type integrals are defined with respect to decompositions of the identity. The relationship of these integrals to the continuous elements is then explored. In Chapter 3, we prove two results in ordered vector spaces. The first result is that every infinite dimensional Dedekind complete vector lattice has a base …

A Maximum Principle For An Optimal Control Problem With Integral Constraints., Vernon Bakke

Mathematics & Statistics ETDs

In this problem necessary conditions are obtained for an optimal control problem ·whose state variables are given in terms of integral equations. The conditions are obtained separately for Volterra equations and Fredholm equations. The main result for each case is the maximum principle and multiplier rule. For the Volterra equations, transversality conditions are obtained.

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.

On Some Special Classes Of Partially Ordered Linear Algebras., Taen-Yu Dai

Mathematics & Statistics ETDs

R. DeMarr (unpublished) has begun a study of Banach algebras as subalgebras of partially ordered linear algebras which are Dedekind a -complete. In [3] he has shown that the real Banach algebra of norm-bounded linear operators (mapping a real Banach space into itself) can be made into a partially ordered linear algebra which is Dedekind a -complete. This leads us to study a more gen­eralized function algebra by using the order structure. In this paper from analytical point of view we will study some special classes of partially ordered linear algebras which are Dedekind a -complete. In chapter 1 we …

Stacking Methods And Mixing Properties Of Measure-Preserving Transformations., Sarah Lee Meyer Christiansen

Mathematics & Statistics ETDs

In this paper we study ergodic and mixing properties of transformations. Stacking methods are employed to construct the transformations used in this paper. Number theoretical methods are developed and used to study mixing properties. Two new mixing properties B-mixing and S-mixing are defined, and are shown to be between partial mixing and weak mixing. Finally a transformation is constructed which is weak mixing but not S-mixing, and hence not partially mixing. Several applications to additive number theory are given.

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.

I. Existence Of Eigenvalues For Integral Equations; Ii. A Collocation Method For Boundary Value Problems, Robert Dodd Russell

Mathematics & Statistics ETDs

I. The existence of eigenvalues is shown for certain classes of integral equations with continuous kernels. A number of interesting and useful results are thereby treated in a unified and relatively elementary way. The simplicity of these new proofs make the results accessible to introductory courses on the theory of integral equations.

II. Collocation with piecewise polynomial functions is developed as a method for solving two-point bour:rlary value problems. Convergence is shown for a general class of linear problems and a rather broad class of nonlinear problems. Some computational examples are presented to illustrate the wide applicability and efficiency of …

Goursat Problems For The Abstract Equation Urs = Lu, Walter J. Roth

Mathematics & Statistics ETDs

Transitive Subgraphs Of Undirected And Directed Graphs., Charles C. Harner

Mathematics & Statistics ETDs

A graph G is transitive if it is transitive when considered as a relation; i.e., if the edges ab and be are in G, so is ac. In this paper, several natural questions concerning transitivity and related concepts are investigated.

Because the terminology and notation of graph theory is not standard, a brief section of definitions and notation is included in Section II. Section III is a study of the transitive cut number of a graph, the minimum number of edges which must be removed from the graph so that the remaining subgraph is transitive. Undirected graphs on n points …