Physical Sciences and Mathematics Commons^™

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

Mathematics Technical Papers

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. …

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

Mathematics Technical Papers

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 …

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.

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.

Dickey-Lincoln School Lakes, Maine, U.S.A. And Quebec, Canada: Design Memorandum No. 5: Water Quality, New England Division, United States Army Corps Of Engineers

Dickey-Lincoln School Lakes Project

This design memorandum presents the results of several studies undertaken to provide an understanding of present and potential future water quality conditions within and downstream from Dickey and Lincoln School Lakes in accordance with the requirements of ETL 1110-2-1402, dated 12 November 1976. Included are an examination of baseline water quality conditions and the findings of qualitative and quantitative predictive analyses performed to evaluate water quality conditions during all phases of the project's lifetime. This document will also serve as a reference for the water quality portions of the project Environmental Impact Statement.

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 $L^ * f = 0$ …

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.

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.

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.

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.

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 …

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.

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.

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) …

Asymptotic Properties Of A Nonlinear Diffusion Process Arising In Articular Cartilage, Van C. Mow, Jerome Eisenfeld

Mathematics Technical Papers

There has been considerable effort put forth to analyse degenerative Joint diseases in terms of the principles of mechanics and hydrodynamics [8]. This effort has led to mathematical models which are systems of nonlinear partial differential equations (see e.g., [6] and [7]). The mathematical models are based on assumptions concerning the nature of the physical system which are not a priori known. Therefore laboratory experiments are performed with an eye towards validating the mathematical models. This paper deals with a particular mathematical model, a nonlinear diffusion equation, which has been proposed by Mow and Monsour [4], [5] to describe the …

Existence Of Solutions In A Closed Set For Delay Differential Equations In Banach Spaces, V. Moauro, S. Leela

Mathematics Technical Papers

The study of the Cauchy problem for ordinary differential equations in a Banach space has been extensive [1,3-7,9-12]. The two main directions that are followed in such a study are (i) finding monotonicity type conditions which guarantee the existence as well as uniqueness of solutions and (ii) finding compactness type conditions which assure only the existence of solutions [3,4]. It is also known [10,12] that in order to prove the existence of solutions in a closed subset F of the Banach space, a boundary condition of the type [see pdf for notation] is required.

General Moment Methods For A Class Of Nonlinear Models, Stephen W. Cheng, Jerome Eisenfeld

Mathematics Technical Papers

This paper deals with the following problems: (i) the development of a general theory which incorporates several methods as special cases; (ii) the applicability of moment methods to a class of nonlinear problems, (iii) the specification of the class of admissible weighting functions; (iv) the estimation of the number of parameters; (v) the elimination of the cut-off error in the analysis of fluorescence decay data.

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

Mathematics Technical Papers

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 …

Stochastic Integration, Diane Knipfer

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

Differential equations have been used to model physical systems, but in many processes this has not been sufficient due to the presence of random occurrences in the system. One method of dealing with this problem is to model the system as a stochastic or random process.

A stochastic process, x, is a function mapping the product of a probability space, Ω, and a subset of the real numbers, TcR, into the real numbers, x: Ω*T→R. In many physical situations, T can be thought of as representing time and Ω as all possible outcomes of the process. For a fixed t …

A Topological Structure On The Structure Sheaf,, Lawrence Stout

Scholarship

No abstract provided.

Stability Of Differential Systems With Impulsive Perturbations In Terms Of Two Measures, S. Leela

Mathematics Technical Papers

The study of differential systems of the form (1.1) [see pdf for notation] where [see pdf for notation] denotes the distributional derivative of [see pdf for notation], a function of bounded variation (that is, differential systems with impulsive perturbations, also called measure differential equations), is both interesting and important because most models for biological neural nets,pulse frequency modulation systems, automatic control problems with impulsive inputs and many physical processes are best described by such equations [1-3,8,10,12,13]. Since the solutions of (1.1) are discontinuous (that is, functions of bounded variation), the investigation of the stability properties of (1.1) by the usual …

A Topological Structure On The Structure Sheaf,, Lawrence Stout

Lawrence N. Stout

No abstract provided.

Scs 29: On The Closedness Of The Set Of Primes In Continuous Lattices, Karl Heinrich Hofmann, Oswald Wyler

Seminar on Continuity in Semilattices

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

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.

Scs 28: The Lattice Of Open Subsets Of A Topological Space, Klaus Keimel, Michael Mislove

Seminar on Continuity in Semilattices

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

Scs 27: Closure Operators And Kernel Operators In Cl, Michael Mislove

Seminar on Continuity in Semilattices

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