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

ACMS Conference Proceedings 1977

No abstract provided.

Scs 35: Dedekind Complete Posets And Scott Topologies, Oswald Wyler

Seminar on Continuity in Semilattices

No abstract provided.

Scs 34: On Complete Lattices L For Which O(L) Is Continuous - A Lattice Theoretical Characterization Of Cs., Gerhard Gierz, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

With inputs from J.D. Lawson and M. Mislove.

Theoretical Input-Output Analysis : Three Generalization., Sajal Lahiri Dr.

Doctoral Theses

This atudy "generalisost. inmit-output (10) malynde in the nensa of developing its baste theme and oentral idea in aome apeaifie ddreotions, Three brond direetions cre explored, undar the titlar of Rpaaio-dependenooof 10-mettiolenta, etrustural brenk, and *investment and growth coneietenay, In ecoh ecse the anlyada keepa to the Logie of I0 analynde in the sense of ita approaoh, concepts od methoda. Thie inaludes fn partimlar the edaptation of a cartain banla method of 10 nhelysia to analyse the struoture of reintione obtained in enah onse,The study is divided into five parto where the first providea a detolled introduotion to, and thn …

Scs 33: Complement To "The Spectral Theory Of Distributive Continuous Lattices", Karl Heinrich Hofmann, Jimmie D. Lawson

Seminar on Continuity in Semilattices

No abstract provided.

Existence Of Solutions Of Boundary Value Problems For Nonlinear Second Order Systems In A Banach Space, A. Richard Mitchell, V. Chandra

Mathematics Technical Papers - Archive

This paper is concerned with the existence of solutions of boundary value problems (BVP, for short) for nonlinear second order ordinary differential equations of the type (1.1) [see pdf for notation] (1.2) [see pdf for notation] where [see pdf for notation] is a real Banach space. In case [see pdf for notation], existence was proved by first obtaining a priori bounds for [see pdf for notation] of a solution of (1.1) and (1.2) and then employing a theorem of Scorza-Dragoni [3,7,16]. The methods involve assuming inequalities in terms of the second derivative of Lyapunov-like functions relative to H, using comparison …

On The Existence Of Weak Solutions Of Differential Equations In Nonreflexive Banach Spaces, V. Lakshmikantham, Evin Bronson, A. Richard Mitchell

Mathematics Technical Papers - Archive

The study of the Cauchy problem for differential equations in a Banach space relative to the strong topology has attracted much attention in recent years [2,4,5,7]. This study has taken two different directions. One direction is to impose compactness type conditions that guarantee only existence and the corresponding results are extensions of the classical Peano's Theorem. The other approach is to utilize dissipative type conditions that assure existence and uniqueness of solutions, and the corresponding results are extensions of the classical Picard's Theorem. However, a similar study of the Cauchy problem in a Banach space relative to the weak topology …

A Random Differential-Equation Approach To Probability Distribution Of Bod And Do In Streams, William J. Padgett, G Schultz, Chris P. Tsokos

Faculty Publications

No abstract provided.

An Improved Approach For "Optimization" Of Multiple Policy Objectives, Perihan Soliman Tawfik

Dissertations and Theses

This thesis involved three categories of activity; development and testing of an expanded version of ELECTRE II, also the development of a computer software program for ELECTRE II.

The expanded version of ELECTRE II took the form of an input aiding questionnaire along with a tailored structure to suit a particular problem. The contents of the questionnaire were based on geueral problem solving concepts (techniques, strategies) gleaned from the systems science literature. This questionnaire assumed a programmed instruction format in contrast to that of an interactive computer software package, so that it would not be prohibitive in terms of expenses …

Scs 32: The Spectral Theory Of Distributive Continuous Lattices, Karl Heinrich Hofmann, Jimmie D. Lawson

Seminar on Continuity in Semilattices

No abstract provided.

Mathematical Analysis Of Stress Relaxation In Articular Cartilage During Compression, Jerome Eisenfeld, Harold Lipshitz, Van C. Mow

Mathematics Technical Papers - Archive

Articular cartilage is the avascular bearing material covering the articulating ends of the mating bony segments of synovial joints. Functionally articular cartilage provides a near frictionless surface, whose coefficient of friction 0.002, which is tough and wear resistant. These biomechanical functions of the tissue are preserved so long as the tissue is maintained in a normal physiological state. The destruction and subsequent loss of articular cartilage as a result of degenerative joint diseases would lead to joint stiffness, pain and deformities. An abnormal state of mechanical stress exerted upon the tissue is an initiating factor or at least a precursor …

Interval Estimation Of Reliability Characteristics Of A K-Identical Unit Standby Redundant System, Danny D. Dyer

Mathematics Technical Papers - Archive

Standby redundancy is a method for increasing the reliability of a system through the use of additional "backup" units. Assuming perfect failure-sensing and switch-over, we consider such a system when the units are identical, non-repairable, and their lifetimes follow a two-parameter exponential distrubution. Based on unit Type II censored data, interval estimates of the system threshold parameter, mean time to failure, and reliability at time [see pdf for notation], are made through structural inference (a group theoretic approach to fiducial theory). A discussion of n-content structural tolerance intervals for the distribution of the lifetime of the system is also given. …

Scs 31: The Lattice Of Ideals Of A C*-Algebra, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 30: Continuous Semilattices And Duality, Jimmie D. Lawson

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Convex Cones And Dentability, J. C. Hankins, R. (Roy) M. Rakestraw

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

On The Mann Iteration Process In A Hilbert Space, Troy L. Hicks, John D. Kubicek

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Class Of Singular Neutral-Differential Systems, W. J. Fitzpatrick, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

Noetherian operator theory is used to prove an existence theorem for a singular functional-differential system. An analogue of the standard existence and uniqueness results at an ordinary point follows as a corollary. © 1977 American Mathematical Society.

Regular Singular Differential Equations Whose Conjugate Equation Has Polynomial Solutions, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

Consider the n -dimensional singular differential system defined by the operator $L:(Ly)(z) = z^p y'(z) + A(z)y(z)$, where z is a complex variable and p is a positive integer. The solvability of the nonhomogeneous system $Ly = g$ depends on the solutions of the homogeneous conjugate system, $L^ * f = 0$, where $L^ * $ is the operator conjugate to L. We show that $L^ * f = 0$ has polynomial solutions if the constant matrix in the series expansion of $A(z)$ has at least one nonpositive integer eigenvalue. Also, we show that if $L^ * f = 0$ …

Fifty Years Of Uncertainty, Richard C. Heyser

Unpublished Writings

Richard C. Heyser frequently explores ways to find a "mathematical basis for perception" in his writings. In this article, Heyser discusses implementing geometry elements to quantum physics.

Applying Mathematics Without A License, Melvin Henriksen

All HMC Faculty Publications and Research

A recent educational experience made me realize the extent to which the mathematical community has become fragmented and how this has served to inhibit communication both with others and ourselves.

An Algebraic Characterization Of The Freudenthal Compactification For A Class Of Rimcompact Spaces, Melvin Henriksen

All HMC Faculty Publications and Research

Throughout C(X) will denote the ring of all continuous real-valued functions on a Tychonoff space X, and C*(X) will denote the subring of bounded elements of C(X). The real line is denoted by R, and N denotes the (discrete) subspace of positive integers. A subset S of X such that the map f → f|_s is an epimorphism of C(X) (resp. C*(X)) is said to be C-embedded (resp. C*-embedded) in X. As is well-known, every f Є C*(X) has a unique continuous extension βf over its Stone-Čech compactification βX [GJ, Chapter 6]. That is, X is …

Some Sufficient Conditions For The Jacobson Radical Of A Commutative Ring With Identity To Contain A Prime Ideal, Melvin Henriksen

All HMC Faculty Publications and Research

Throughout, the word "ring" will abbreviate the phrase "commutative ring with identity element 1" unless the contrary is stated explicitly. An ideal I of a ring R is called pseudoprime if ab = 0 implies a or b is in I. This term was introduced by C. Kohls and L. Gillman who observed that if I contains a prime ideal, then I is pseudoprime, but, in general, the converse need not hold. In [9 p. 233], M. Larsen, W. Lewis, and R. Shores ask if whenever the Jacobson radical J(R) of an arithmetical ring is pseudoprime, it follows that J(R) …

Lipschitz Spaces Of Distributions On The Surface Of Unit Sphere In Euclidean N-Space, Harvey Greenwald

Mathematics

In this paper Lipschitz spaces of distributions are defined and various inclusion relations are shown. Certain properties such as completeness, separability, and the density of the testing space for appropriate Lipschitz spaces are proved. The Littlewood-Paley function is defined and used to prove inclusion relationships between Lipschitz and Lebesgue spaces.

Tychonoff Spaces That Have A Compactification With Countable Remainder, Melvin Henriksen

All HMC Faculty Publications and Research

In this paper, an attempt is made to characterize spaces that are Zippin or strongly Zippin. We succeed in this goal only in small part, but we do obtain a number of conditions on a space that are either necessary or sufficient for such compactifications to exist.

Mathematics In America: The First Hundred Years, Judith V. Grabiner

Pitzer Faculty Publications and Research

There are two main questions I shall discuss in this paper. First, why was American mathematics so weak from 1776 to 1876? Second, and much more important, how did what happened from 1776-1876 produce an American mathematics respectable by international standards by the end of the nineteenth century? We will see that the "weakness" -at least as measured by the paucity of great names- co-existed with the active building both of mathematics education and of a mathematical community which reached maturity in the 1890's.

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 …

K-Theory And Steenrod Homology: Applications To The Brown-Douglas-Fillmore Theory Of Operator Algebras, Jerome Kaminker, Claude Schochet

Mathematics Faculty Research Publications

The remarkable work of L. G. Brown, R. Douglas and P. Fillmore on operators with compact self-commutators once again ties together algebraic topology and operator theory. This paper gives a comprehensive treatment of certain aspects of that connection and some adjacent topics. In anticipation that both operator theorists and topologists may be interested in this work, additional background material is included to facilitate access.

Estimation Of The Guarantee Time In A Two-Parameter Exponential Failure Model, Danny D. Dyer

Mathematics Technical Papers - Archive

There are available several classical point estimators of the guarantee time (location parameter) in a two-parameter exponential failure model. For the purpose of making a pairwise comparison of the estimators, a two-fold technique is introduced which essentially examines (a) the "odds" in favor of an estimator being closer to the true value than is a competing estimator and (b) an estimator's average closeness given that it is closer to the true value as well as given that it is not. Closeness to the true value is measured through an absolute error loss function. Joint consideration of these concepts is discussed …