Physical Sciences and Mathematics Commons^™

Typically Real Functions And Typically Real Derivatives, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

Sufficient conditions, in terms of typically real derivatives, are given which force functions to be univalent. © 1987, Hindawi Publishing Corporation. All rights reserved.

Operations With Distribution Vectors, Brian Fisher, Todor D. Todorov

Mathematics

No abstract provided.

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

Three Partition Refinement Algorithms, Robert Paige L., Robert Endre Tarjan

Mathematics and Statistics Faculty Research & Creative Works

We present improved partition refinement algorithms for three problems: lexicographic sorting, relational coarsest partition, and double lexical ordering. Our double lexical ordering algorithm uses a new, efficient method for unmerging two sorted sets.

First Integrals For Equations With Nonlinearities Of The Emden-Fowler Type, William Trench, Leon Bahar

William F. Trench

No abstract provided.

Characteristic Polynomials Of Symmetric Rationally Generated Toeplitz Matrices, William Trench

William F. Trench

No abstract provided.

Automorphisms Of Normal Partial Transformation Semigroups, Inessa Levi

Faculty Bibliography

No abstract provided.

The Sharpness Of Some Cluster Set Results, D. Rung, Samih Obaid

Faculty Publications

We show that a recent cluster set theorem of Rung is sharp in a certain sense. This is accomplished through the construction of an interpolating sequence whose limit set is closed, totally disconnected and porous. The results also generalize some of Dolzenko's cluster set theorems.

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.

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.

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 …

The Complexity Of Computations By Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

We survey the current state of knowledge concerning the computation of Boolean functions by networks, with particular emphasis on the addition and multiplication of binary numbers.

Sorting And Selecting In Rounds, Nicholas Pippenger

All HMC Faculty Publications and Research

We present upper bounds for sorting and selecting the median in a fixed number of rounds. These bounds match the known lower bounds to within logarithmic factors. They also have the merit of being “explicit modulo expansion”; that is, probabilistic arguments are used only to obtain expanding graphs, and when explicit constructions for such graphs are found, explicit algorithms for sorting and selecting will follow. Using the best currently available explicit constructions for expanding graphs, we present the best currently known explicit algorithms for sorting and selecting in rounds.

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.

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 …

An Analysis Of The Massachusetts Inshore Lobster Fishery, Peter Robertson Hoar

Marine Affairs Theses and Major Papers

The purpose of this thesis was to explore the limited entry alternative of fishery management by examining the history of a particular limited entry scheme: the Massachusetts inshore commercial lobster fishery license limitation law. A review was made of existing limited entry theory, followed by a description of limited entry programs extant in U.S. fisheries. The legislative and political histories of the Massachusetts lobster fishery limited entry program was then examined. The limited entry law was then analyzed by comparing what actually occurred with what is supposed to occur according to limited entry theory. A quantitative analysis of changes in …

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

Mathematics Technical Papers

No abstract provided.

Computer Files For Drop Formation, Donald Greenspan

Mathematics Technical Papers

No abstract provided.

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 …

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.

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.

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

Mathematics Technical Papers

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

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

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.

Programs For Vortex Street Generation, Donald Greenspan

Mathematics Technical Papers

No abstract provided.

On Endomorphism And Automorphisms Of Some Torsion-Free Modules, Brendan Goldsmith

Articles

The relationship between the endomorphism ring and the automorphism group of an abelian p-group has been extensively investigated. It is known that theautomorphism group need not generate the full endomorphism ring. In this paper we investigate the analagous problem for torsion free modules over a complete discrete valuation ring obtaining similar results.

[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.

Rigid And Nonrigid Achirality, Erica Flapan

Pomona Faculty Publications and Research

In order to completely characterize a molecule it is useful to understand the symmetries of its molecular bond graph in 3-space. For many purposes the most important type of symmetry that a molecule can exhibit is mirror image symmetry. However, the question of whether a molecular graph is equivalent to its mirror image has different interpretations depending on what assumptions are made about the rigidity of the molecular structure. If there is a deformation of 3-space taking a molecular bond graph to its mirror image then the molecule is said to be topologically achiral. If a molecular graph can be …

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.

Absolute Minimization By Supercomputer Computation, Donald Greenspan

Mathematics Technical Papers

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.