Mathematics Commons^™

Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase

ACMS Conference Proceedings 1977

The purpose of this paper is to show that both sides of the predestination/free-will discussion are admissible in a way that is more profound than simply the wave-particle duality of light. In wave-particle duality there are two competing physical models of reality which are contradictory. This paper will show that not a contradiction but a difference in viewpoint is the fundamental issue in the discussion of predestination and free will. A discussion of Skolem’s paradox is helpful in this demonstration.

Introduction (1977), Robert Brabenec

ACMS Conference Proceedings 1977

No abstract provided.

Table Of Contents (1977), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1977

No abstract provided.

Epistemology To Ontology, Charles R. Hampton

ACMS Journal 2004

This paper argues for mathematicians thinking about the philosophy of math, especially Christians. It briefly sketches the limitations of formalism, intuitionism, and logicism and uses Christian concept of creation to argue that one can take the best of each of these philosophies and avoid the pitfalls. It also argues for the real existence of mathematical objects apart from the human mind.

Recent Problems In The Foundations Of Mathematics, Terence H. Perciante

ACMS Journal 2004

This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and …

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Journal 2004

Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …

Positive Perturbations Of Unbounded Operators, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.

A Proof Of Convergence For The Tridiagonal Ql Algorithm In Floating-Point Arithmetic, James George Sanderson

Mathematics & Statistics ETDs

Numerous routines are available to find the eigenvalues of a real symmetric tridiagonal matrix. Since it is known to converge in exact arithmetic, the tridiagonal QL algorithm with origin shift is widely used. Here we analyze the algorithm in floating-point arithmetic. This analysis suggests two modifications to the EISPACK implementation TQLl that enable one to prove correctness and hence convergence of the routine.

Also, it is known that the implicit and explicit versions of the QL algorithm produce the same results in exact arithmetic. A counter-example to the floating-point analog of this theorem is presented.

The Use Of Prior Observations In Constructing Prediction Intervals For The Normal Distribution, Charles B. Davis

Mathematics & Statistics ETDs

A prediction interval procedure uses information contained in a sample together with other relevant information to produce an interval which will contain the next observation to be taken from the population with confidence no less than a pre-determined /J. One prediction inter­val procedure renders another "inadmissible" at the fJ level if (1) both procedures maintain the B confidence level and (2) the former produces intervals which are at least as "short" as, and sometimes "shorter" than, those produced by the latter; "short" is defined in a natural fashion in terms of expected length or expected upper (lower) limit. as is …

An Abstract Matrix Model: The Column Model, Tomas Eufracio Salazar

Mathematics & Statistics ETDs

In this dissertation we introduce an abstract model for matrix theory, The Column Model. We investigate some properties of the special class of partially ordered linear algebras that satisfy the conditions of the Model. We use the order structure of the Model to obtain some results on: idempotents in the Model, nonnegative elements of the Model having nonnegative generalized inverses, factor theorems in the Model and concepts in the Model that are related to the usual notion of eigenvalues of an m-by-m matrix. Since the set of m-by-m matrices belongs to the special class of partially ordered linear algebras satisfying …

A Metric Graph Structure For Information Retrieval, Karl Jerry Melendez

Mathematics & Statistics ETDs

Document retrieval systems accept a user request for information and respond with a list of documents which contain information relevant to the request. When the documents (or abstracts of the documents) are stored in a computer memory, a function can be defined which estimates the semantic distance between documents. If this function together with the set of documents forms a metric space, a graph, which I call a progressive graph, can be constructed to aid the search for the documents with relevant information.

Progressive graphs are studied and the search algorithms which use this graph structure are presented. The search …

Estimation Of Growth Curves By Least Square Splines, Dorothy Rybaczyk Pathak

Mathematics & Statistics ETDs

The primary object of this dissertation is to present some con­tributions to the theory of estimation of growth curves by least square splines in the presence of unknown unequal variances. The theoretical developments rest heavily on the standard least square theory and the theory of polynomial spline functions. A modifica­tion of the Aitken procedure of weighted least squares is used to estimate regression parameters. It is shown that this modification of the Aitken procedure does not unduly influence the nice least square properties of estimators so obtained; the estimators re­ main unbiased, consistent and asymptotically efficient.

The techniques developed in …

The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke

Mathematics and Statistics Faculty Publications

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.

Levi Structures For Polynomial Ideals., Richard Michael Grassl

Mathematics & Statistics ETDs

Let R be the ring of polynomials in a denumerable set of independent indeterminates over a field F and let I be an ideal (Xo,x1,x2, ... ) in R. A Levi structure for I provides bases for I and R as vector spaces over F and an associated algorithm for determining whether an element of R is in I.

Such structures have been developed previously for certain principal differential ideals [i.e., ideals (Xc),x1 , ... ) with xj the j-th derivative of Xol in which the generator is homogeneous and isobaric and for a family of related ordinary ideals. The …

Branching Processes With Cataclysmic Environmental Changes., Juan F. Corona-BurgueñO

Mathematics & Statistics ETDs

In this dissertation we consider a continuous time branching process with a random environment in which the environment changes according to a continuous time Markov chain. The extinction problem for this model is posed and solved by two distinct methods: by the method of random evolutions of Griego and Hersh and by the results of Athreya and Karlin on branching processes with random environments. Limit theorems for the population size as well as a system of partial differential equations for the expected number of particles (as functions of time) are obtained.

The Numerical Solution Of The Generalized Eigenvalue Problem For Rectangular Matrices, Charles Henry Burris Jr.

Mathematics & Statistics ETDs

This paper studies the Generalized Eigenvalue Problem Ax=λBx for real, rectangular matrices A and B. Several current algorithms for solving this problem are examined, most of which involve a determination of the rank of B, or one of its submatrices. An example is given in which such a decision cannot be made without introducing unnecessary error into the problem. The QZR Algorithm is then introduced as an algorithm which uses unitary transformations to reduce the matrices to a prescribed canonical form. This canonical form provides the information necessary for making decisions about rank. Since A and B can be non …

Independence, Essential Independence And Zero Correlation Of Two Random Variables Conditioned On A Third., Chester Raymond Crain Jr.

Mathematics & Statistics ETDs

In a recent paper Stoughton Bell and William J. Zimmer defined three distinct types of conditional independence; which they call pointwise, intervalwise and strong; of two random variables given a third. They considered these and four closely related independence properties, and they examined the relationships among the 128 (=23+4) Boolean combinations. Bell and Zimmer also considered the kinds of assumptions in applied research that would give rise to each type of conditional independence.

I have searched published texts and papers in probabil­ity and statistics for the three types of conditional inde­pendence. The type considered by Alfred Renyi [Foundations of Probability …

Symmetric Groups And Their Automorphism Groups, Harold Lyle Madison

All Master's Theses

This paper presents an account of the relationship between the symmetric group on n symbols, S_n, and its automorphism group for each natural number n. For n ≠ 2, S_n is isomorphic to its inner automorphism group. S₂ has only the identity automorphism. For n ≥ 3, n ≠ 6, each automorphism of S_n is an inner automorphism. An illustration shows where this proof fails when n = 6. S₆ has outer automorphism. An example of an outer automorphism for S₆ is given.

A Method Of Moments Applied To An Invariant Imbedding Solution Of A Certain Class Of Fredholm Integral Equations., Grenfell Paul Boicourt

Mathematics & Statistics ETDs

This dissertation first develops a method for solving the integral equation when y(z') is a constant and then extends it to the case where y(z') is a step function. The solution of the integral equation is achieved by solving the integro differential invariant imbedding equations derived from the integral equation by varying the limits of integration. The imbedding equations are solved using a moment method which reduces the calculation to an initial value problem. Proofs of the existence and convergence of the method are given. In the case where y(z') is a constant, the solution of the integral equation is …

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.

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 …

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. …