Digital Commons Network^™

Absolute Minimization By Supercomputer Computation, Donald Greenspan

Mathematics Technical Papers - Archive

Numerical methodology is developed for approximating the absolute minimum of a function or a functional. Only simplistic numerical techniques are introduced and explored. CRAY X—MP/24 computer examples are described and discussed.

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQ_n(x) = z_n^-1 exp[ -H_n(x)]Π dP(x_j), where x = (x₁,..., x_n) ∈ Rⁿ, where H_n is the Hamiltonian, z_n is …

Programs For Vortex Street Generation, Donald Greenspan

Mathematics Technical Papers - Archive

No abstract provided.

Programs And Data Sets For Quasimolecular Modeling Of Cavity Flow, Donald Greenspan

Mathematics Technical Papers - Archive

No abstract provided.

Computer Files For Drop Formation, Donald Greenspan

Mathematics Technical Papers - Archive

No abstract provided.

Cray X-Mp/24 Fortran Programs For Capillarity, Donald Greenspan

Mathematics Technical Papers - Archive

This technical report contains the FORTRAN programs used in generating capillary action. They are provided so that the computations described elsewhere can be reproduced by the interested reader. Without this availability, computer calculations and experiments could not be duplicated exactly, and related results and conclusions might be suspect.

Zeros Of Bouligand-Nagumo Fields, Flow-Invariance And The Bouwer Fixed Point Theorem, Nicolae H. Pavel

Mathematics Technical Papers - Archive

Mainly, in this paper we prove that if D is a convex compact of Rn, then the Brouwer fixed point property of D is equivalent to the fact that every Bouligand-Nagums vector field on D, has a zero in D. Using a version of this result on a normed space, as well as the Day [9] and Dugundji [10] theorems, we give a new proof to the fact that in every infinite dimensional Banach space X, there exists a continuous function from the closed unit ball B (of X) into B, without fixed points in B. We also show that …

Supercomputer Simulation Of Sessile And Pendent Drops, Donald Greenspan

Mathematics Technical Papers - Archive

A intermolecular approach is developed for the modeling of sessile and pendent drops. Fundamental mechanisms of drop formation are formulated in terms of gravity and classical intermolecular type forces. CRAY X-MP/24 computer examples illustrate standing and falling drops, free surface motions, and convergence to equilibrium. The role of temperature in drop configuration modeling is shown to be significant.

On A Multi-Channel Transportation Loss System With Controlled Input And Controlled Service, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

A multi-channel loss queueing system is investigated. The input stream is a controlled point process. The service in each of m parallel channels depends on the state of the system at certain moments of time when input and service may be controlled. To obtain explicitly the limiting distribution of the main process (Zt) (the number of busy channels) in equilibrium, an auxiliary three dimensional process with two additional components (one of them is a semi-Markov process) is treated as semi-regenerative process. An optimization problem is discussed. Simple expressions for an objective function are derived.

Statistical Analysis Of A Compound Power-Law Model For Repairable Systems, Max Engelhardt, Lee J. Bain

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

Conclusions - A compound (mixed) Poisson distribution is sometimes used as an alternative to the Poisson distribution for count data. Such a compound distribution, which has a negative binomial form, occurs when the population consists of Poisson distributed individuals, but with intensities which have a gamma distribution. A similar situation can occur with a repairable system when failure intensities of each system are different. A more general situation is considered where the system failures are distributed according to nonhomogeneous Poisson processes having Power Law intensity functions with gamma distributed intensity parameter. If the failures of each system in a population …

Unitary Weighted Composition Operators, Valentin Matache

Mathematics Faculty Publications

A necessary and sufficient condition for a weighted composition operator to be unitary is given in terms of the weight-function and of the composition function.

Class Groups Of Quadratic Fields Ii, Duncan A. Buell

Faculty Publications

A computation has been made of the noncyclic class groups of imaginary quadratic fields Q(√-D) for even and odd discriminants - D from 0 to - 25000000. Among the results are that 95% of the class groups are cyclic, and that -11203620 and -18397407 are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.

Maps Which Preserve Graphs, Van C. Nall

Department of Math & Statistics Faculty Publications

In 1976 Eberhart, Fúgate, and Gordh proved that the weakly confluent image of a graph is a graph. A much weaker condition on the map is introduced called partial confluence, and it is shown that the image of a graph is a graph if and only if the map is partially confluent.

In addition, it is shown that certain properties of one-dimensional continua are preserved by partially confluent maps, generalizing theorems of Cook and Lelek, Tymchatyn and Lelek, and Grace and Vought. Also, some continua in addition to graphs are shown to be the images of partially confluent maps only.

Expectation Inequalities Associated With Prophet Problems, Theodore P. Hill

Research Scholars in Residence

Applications of the original prophet inequalities of Krengel and Sucheston are made to problems of order selection, non-measurable stop rules, look-ahead stop rules, and iterated maps of random variables. Also, proofs are given of two results of Hill and Hordijk concerning optimal orderings of uniform and exponential distributions

Christianity And Mathematics, Calvin Jongsma

Faculty Work Comprehensive List

Recent decades have witnessed the growth of a rather remarkable phenomenon: Christian mathematicians discussing the integration of their Christian faith with their mathematical work. This cannot be a totally new turn of events; Christian mathematicians have probably always reflected on this issue to some extent. But the increased number of articles and talks dealing with this matter in the past two decades indicates a new current of thought at work, particularly among Evangelical Protestant Christians. Actually, it would be more accurate to put this observation in the plural, for the trend toward relating Christianity and mathematics is not a unified …

Martin's Axiom And A Regular Topological Space With Uncountable Net Weight Whose Countable Product Is Hereditarily Separable And Hereditarily Lindelöf, Krzysztof Ciesielski

Faculty & Staff Scholarship

n the paper it is proved that if set theory ZFC is consistent then so is the following

ZFC + Martin's Axiom + negation of the Continuum Hypothesis + there exists a 0-dimensional Hausrorff topological space X such that X has net weight nw(X) equal to continuum, but nw(Y)=\omega for every subspace Y of X of cardinality less than continuum. In particular, the countable product X^\omega of X is hereditarily separable and hereditarily Lindelof, while X does not have countable net weight. This solves a problem of Arhangel'skii.

Designing The Optimal Placement Of Spaces In A Parking Lot, R. Bingle, D. Meindertsma, W. Oostendorp, Gene A. Klaasen

University Faculty Publications and Creative Works

We develop a method for determining the optimal size and placement of parking spaces and approach aisles for an automobile parking lot. In particular, our solution concerns a parking lot of size 100' x 200' located at the corner of an intersection of two streets in a New England town. We begin by arguing the superiority of driver operation over attendant operation of vehicles to be parked. Then a statistical analysis is performed on a sampling of 160 1987 model automobiles to determine upper bounds and ideal values for the length and width of a parking space and for the …

Ce Equivalence And Shape Equivalence Of 1-Dimensional Compacta, R. J. Daverman, Gerard A. Venema

University Faculty Publications and Creative Works

In this paper the relationship between CE equivalence and shape equivalence for locally connected, 1-dimensional compacta is investigated. Two theorems are proved. The first asserts that every path connected planar continuum is CE equivalent either to a bouquet of circles or to the Hawaiian earring. The second asserts that for every locally connected, 1-dimensional continuum X there is a cell-like map of X onto a planar continuum. It follows that CE equivalence and shape equivalence are the same for the class of all locally connected, 1-dimensional compacta. In addition, an example of Ferry is generalized to show that for every …

[Introduction To] A Gentle Introduction To The Vax System, John R. Hubbard

Bookshelf

This book was written originally for students enrolled in computer science courses at the University of Richmond. Very few had worked on a large time-sharing system like the VAX.

The purpose of this book is to help the novice become comfortable using any of the Digital Equipment Corporations VAX computers, from the Micro-VAX to the powerful VAX 8000 system. The book is meant to be used as a tutorial.

On The Thermal Stresses Due To A Uniform Heat Flow Past A Circular Hole With A Radial Edge Crack, George F. Edmonds

Mathematics & Statistics Theses & Dissertations

The problem solved in this dissertation is that of finding the stresses in an isotropic, linear, thermoelastic solid when a uniform heat flow is disturbed by the presence of an insulated circular hole with a radial edge crack. By superimposing a Mellin transform solution of the equations of thermoelasticity on a Michell series solution the author reduces the problem to a pair of singular integral equations which are then solved numerically. The stress intensity factors and crack formation energies, quantities of interest to workers in fracture mechanics, are then calculated.

Programs And Data Sets For Quasimolecular Modeling Of Vortices, Donald Greenspan

Mathematics Technical Papers - Archive

No abstract provided.

Approximation By Rational Functions, Ronald A. Devore

Faculty Publications

Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f' is in L log L on a finite interval, then f can be approximated in the uniform norm by rational functions of degree n to an error 0(1/n) on that interval.

Alfred Tarski And Undecidable Theories, George F. Mcnulty

Faculty Publications

No abstract provided.

Design And Analysis Of Efficient Algorithms To Solve The Maximum Concurrent Flow Problem, Farhad Shahrokhi

Dissertations

The maximum concurrent flow (MCFP) is a generalized commodity flow problem, where every pair of entities can send and receive flow Ma85 , BM86 , MS86 . We develop efficient labeling algorithms to solve the MCFP. We explore the combinatorial structure of the MCFP and show that the problem of associating costs (distances) to the edges so as to maximize the minimum cost of routing the concurrent flow is the dual of the MCFP. This duality covers max-flow min-cut theorem as a special case. Applications in packet switched networks At81 and cluster analysis Ma86 are discussed.

On The Laplacian, Frank A. Farris, James Ward Brown

Mathematics and Computer Science

In various applied mathematics courses one appearance of the Laplacian operator is in the study of heat distributions.

Sequence Alignment With Matched Sections, Jerrold R. Griggs, Philip J. Hanlon, Michael S. Waterman

Faculty Publications

In molecular biology, two finite sequences are compared by displaying one sequence written over another in an alignment. The number of alignments of two sequences is related to the Stanton-Cowan numbers. This paper gives asymptotics for the number of alignments of two sequences of length n with matching sections of size at least b.

Keane Leads Us Olympiad Team To 1st Place Tie With Ussr, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

Prophet Inequalities For Averages Of Independent Non-Negative Random Variables, Theodore P. Hill

Research Scholars in Residence

No abstract provided.

George Boole: His Life And Work (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: George Boole: His Life and Work by Desmond MacHale. (Profiles of Genius Series, 2.) xiii + 304 pp., illus., bibls., index. Dublin: Boole Press, 1985.

Jacobi Moments In Applied Mathematics With Computer Applications, John A. Kapenga

Dissertations

This work provides solid asymptotic representations, sharp error bounds and stable recurrence methods (both three term and two dimensional) for the Jacobi moments. These moments are currently used in several areas of numerical analysis (numerical integration, integral equations and boundary value problems).

A powerful representation theorem, due to H. Gingold, which uses the Jacobi moments is extended and analyzed. Applications of this theorem to multi-turning point problems and several other areas are given.

For a number of important problems in mathematical physics it is not possible to prove that the currently employed methods of solution converge, or are valid in …