Digital Commons Network^™

A Logic Programming Model Of The Game Of Sprouts, Ralph M. Butler, Selden Y. Trimble, Ralph W. Wilkerson

Computer Science Faculty Research & Creative Works

The Game of Sprouts Has Intrigued Mathematicians for Nearly Twenty Years. This Paper Describes a Representation Scheme Which Simplifies Much of the Geometry of the Game. using This Representation, We Develop a Prolog Program Which Will Play Sprouts. It is Hoped that the Program Will Prove to Be a Useful Research Tool in Finding the Key to a Winning Strategy for Sprouts and that the Representation Will Serve as a Useful Model for Studying Planar Graphs.

A Logic Programming Model Of The Game Of Sprouts, Ralph M. Butler, Selden Y. Trimble, Ralph W. Wilkerson

Computer Science Faculty Research & Creative Works

The Game of Sprouts Has Intrigued Mathematicians for Nearly Twenty Years. This Paper Describes a Representation Scheme Which Simplifies Much of the Geometry of the Game. using This Representation, We Develop a Prolog Program Which Will Play Sprouts. It is Hoped that the Program Will Prove to Be a Useful Research Tool in Finding the Key to a Winning Strategy for Sprouts and that the Representation Will Serve as a Useful Model for Studying Planar Graphs. © 1987, ACM. All Rights Reserved.

Generalizations Of The Sidon-Telyakovskii Theorem, Caslav V. Stanojevic, Vera B. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

The well-known Sidon-Telyakovskii integrability condition is considerably lightened as follows. © 1987 American Mathematical Society.

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.

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.

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.

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.

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

Mathematics

No abstract provided.

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.

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.

Ua66/10/2 Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

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 …

Proof And Intuition, Michael Detlefsen

ACMS Journal 2004

This paper aims to give a clear exposition of two critiques of logicism. The intuitionist, Brouwer, is best known for rejecting the law of the excluded middle (his "special critique.") The paper argues that Brouwer's "general critique" is deeper and more extensive than this. That is, Brouwer is arguing that mathematical knowledge requires a kind of direct mathematical experience, analogous to sensory experience and this cannot be attained simply by linguistic operations independently of experience. It also discusses Poincare's critiques - that there is a huge difference between genuine mathematical insight and an ability to logically manipulate mathematical truths and …

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 …

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