Statistics and Probability Commons^™

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 …

A Fortran List Processor (Flip), Karl A. Fugal

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A series of Basic Assembler Language subroutines were developed and made available to the FORTRAN IV language processor which makes list processing possible in a flexible and easily understood way.

The subroutine will create and maintain list structures in the computer's core storage. The subroutines are sufficiently general to permit FORTRAN programmers to tailor list processing routines to their own individual requirements. List structure sizes are limited only by the amount of core storage available.

Bayesian Estimate Of System Reliability, Naresh Shah

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

A Bayesian estimate of reliability for each component in the system of n-components, each exponentially distributed, is developed which utilizes the basic notion of loss in estimation theory. Here we assume that each component is independently dis­tributed. In reliability estimation, the loss associated with over­estimation is usually greater than the loss associated with under­estimation; and hence loss function can be a very useful tool. The prior distribution and loss function of reliability considered in this paper are flexible to be compatible with other situations in which reliability estimates are required. When the loss function is symmetric and no prior information …

The Ideal And New Interval Topologies On Lattice Ordered Groups., Frieda Koster Holley

Mathematics & Statistics ETDs

In his 1967 edition of Lattice Theory, G. Birkhoff posed the question: "When is a directed group a topological group and a topological lattice in its new interval topology?'. This problem and the similar problem involving the ideal topology are investigated.

A New Characterization Of Besicovitch Almost Periodic Functions., Abdallah N. Dabboucy

Mathematics & Statistics ETDs

Besicovitch and Bohr have given an internal description or Besicovitch almost periodic functions which involves the notion of “satisfactory uniformity” and is somewhat complicated. Raouf Doss has given an alternative simpler internal description, which, however, involves an infinity of independent conditions. Theorem. Let f E Lp(a,b) for all real numbers a,b. Then ff (BP-AP}

if end only if (1) the functions fn obtained by truncating f atn=l,2, … !·ll-converge to f; (2) lim)C+{) x llf-fl! BP =O; (3a) for every f: > 0 the set (x: l!f x -fl' P < eJ is relatively dense; and (3b) for every E: > 0

for all sufficiently large T, where E = {x: l\fx-fllB < e). Here fx(y) = f(x+y), XE denotes the characteristic function of E and 1 :Sp< oo. The theorem extends to LC connected groups, compactly generated Abelian groups and a somewhat stronger version of it extends to discrete countable Abelian groups.

Right Baer Semigroups., William Christopher Hardy

Mathematics & Statistics ETDs

In his paper, "A Semigroup Approach to Lattices, 11 (Canad . Jour. Math., Vol. 18 (1966)), M. F. Janowitz showed that every lattice with 0 and 1 is isomorphic to the lattice formed by the left annihilators of a suitably chosen Baer semigroup when they are ordered under set inclusion. A Baer semigroup, s~ was then said to coordinatize a lattice, L, if Lis isomorphic to the lattice of left annihilators of S. This dissertation presents a similar semigroup approach to lattices by showing that a poset, P, with O and 1 forms a meet semilattice if and only if …

Analysis Of Heat Transfer In A Two-Layer Circular Cylinder:Constant Flux On Outer Surface And Zero Flux On Inner Surface, Mary Elena Franklin

Mathematics & Statistics ETDs

The one-dimensional time-dependent equation of heat conduction is solved analytically for an infinite two-layer circular cylinder whose core may be either hollow or solid. On the outer surface of the cylinder, which has no heat loss due to convection, a constant heat flux from an external source of heating is applied uniformly. The layers are in perfect thermal contact, and there is no heat loss at their interface. At the smaller radius of the inner layer is a perfect insulator so that the heat flux on the inner surface of the two-layer cylinder is zero. The temperature is uniform initially …