Digital Commons Network^™

When Is Every Order Ideal A Ring Ideal?, Melvin Henriksen, Suzanne Larson, Frank A. Smith

All HMC Faculty Publications and Research

A lattice-ordered ring ℝ is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f-rings ℝ such that ℝ/I is contained in an f-ring with an identity element that is a strong order unit for some nil l-ideal I of ℝ. In particular, if P(ℝ) denotes the set of nilpotent elements of the f-ring ℝ, then ℝ is an OIRI-ring if and only if ℝ/P(ℝ) is contained in an f-ring with an identity element that is a strong order unit.

The Probabilities Associated With The Game Jai-Alai, Robert Hesse

Honors Theses, 1963-2015

This paper studies the probabilities within the game Jai-alai. Before explaining the probabilities, one first needs to understand the game itself. Jai-alai is a racquetball-like game where eight ordered players compete against one another in the following manner: Player 1 plays Player 2. The winner of this game plays Player 3, while the loser goes to the end of the line behind Player 8. In the first seven games, 1 versus 2," versus 3,"""? versus 8, the winner is awarded one point, and in every game after that two points. A player wins the match when he is the first …

The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz

Physics - All Scholarship

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P; Q \Gamma ] = 1, with P and Q \Gamma 2 \Theta 2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations …

Supereuleriaun Graphs And The Petersen Graph, Zhi-Hong Chen

Scholarship and Professional Work - LAS

Using a contraction method, we find some best-possible sufficient condi­tions for 3-edge-connected simple graphs such that either the graphs have spanning eulerian subgraphs or the graphs are contractible to the Petersen graph.

On Attractive Force Between Electrons In The Same Molecular Orbital, Donald Greenspan

Mathematics Technical Papers - Archive

Is is assumed, on the basis of recent studies in particle theory, that two electrons in the same molecular orbital attract, rather than repel, and the consequences are explored by means of three dimensional, supercomputer, molecular mechanics type simulations of ground state H2 and D2. Using spectroscopic data, it is shown that, in every case, the resulting vibrational frequency and molecular diameter are entirely in agreement with experiment.

The Expected Capacity Of Concentrators, Nicholas Pippenger

All HMC Faculty Publications and Research

The expected capacity of a class of sparse concentrators called modular concentrators is determined. In these concentrators, each input is connected to exactly two outputs, each output is connected to exactly three inputs, and the girth (the length of the shortest cycle in the connexion graph) is large. Two definitions of expected capacity are considered. For the first (which is due to Masson and Morris), it is assumed that a batch of customers arrive at a random set of inputs and that a maximum matching of these customers to servers at the outputs is found. The number of unsatisfied requests …

Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff

All HMC Faculty Publications and Research

Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by …

Testing Exponentiality Against Idmrl Distributions With Unknown Change Point, D. L. Hawkins, Clive Loader, Subhash Kochar

Mathematics Technical Papers - Archive

Guess, Hollander and Proschan (1986) proposed tests for exponentiality versus IDMRL (increasing initially and then decreasing mean residual life) distributions when the change point, or corresponding quantile, is known. In this paper we propose two tests which do not require such knowledge of the change point. The tests are based on estimates of functionals of the cdf which discriminate between the exponential and IDMRL families.

On Electron Attraction In The Diatomic Bond, Donald Greenspan

Mathematics Technical Papers - Archive

Previously, it was shown that classical simulation of the ground state diatomic hydrogen, deuterium and tritium molecules yielded the correct vibrational frequencies and average molecular diameters under the assumption that the bonding electrons attracted, rather than repelled. It is shown here that the assumption of electron attraction also yields the correct vibrational frequencies and average molecular diameters for [see pdf for notation].

A Single-Server Queue With Random Accumulation Level, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The author studies the queueing process in a single-server bulk queueing system. Upon completion of a previous service, the server can take a group of random size from customers that are available. Or, the server can wait until the queue attains a desired level. The author establishes an ergodicity criterion for both the queueing process with continuous time parameter and the imbedded process. Under this criterion, the author obtains explicit formulas for the stationary distributions of both processes by using semi-regenerative techniques.

A Comparison Of Ancient Mathematical And Calendrical Systems, Karen Schlauch

Masters Theses

No abstract provided.

Modern Algebra And Discrete Structures, R. F. Lax

E-Textbooks

This text is intended for either an applied algebra course or a modern algebra course that includes more applications than has been traditional. It is at an advanced undergraduate (junior-senior) level and is suitable for a one-semester or two-quarter course. We assume that students have already had a course in linear algebra (although we briefly review concepts from linear algebra when they are needed in the sections on fields and linear codes).

Our treatment is fairly rigorous, with almost every proof supplied. However, we have tried to concentrate on examples and applications. In an applied algebra course, which usually consists …

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

Intelligent Structural Operators For The K-Way Graph Partitioning Problem, Gregor Von Laszewski

Northeast Parallel Architecture Center

A parallel genetic algorithm for the graph partitioning problem is presented, which combines general heuristic algorithms with techniques that are described in evolution theory. In the parallel genetic algorithm the selection of a mate is restricted to a local neighborhood. In addition, the parallel genetic algorithm executes an adaptation step after an individual is generated, with the genetic operators crossover and mutation. During the adaptation step the solution is improved by a common algorithm. Another selection step decides if the adapted descendant should replace the parent individual. Instead of using a uniform crossover operator a more intelligent crossover operator, which …

Analytic Continuation In Bergman Spaces And The Compression Of Certain Toeplitz Operators, William T. Ross

Department of Math & Statistics Faculty Publications

Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A² (G\K) and A²(G) be the Bergman spaces on G\K, respectively G and define N = A²(G\K) Ɵ A² (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of aG that do not intersect K. This result will be used to discuss the Fredholm theory of the operator C_f = P_NT_f│N, where f ϵ C(G) …

A Study Of The Survival Rate Of The Hepatitis B Virus, James Abraham Houck Iii

UNF Graduate Theses and Dissertations

Hepatitis B virus (HBV) is one of many viruses transmitted through the blood or body fluids. This paper concentrates on a mathematical study of the survival rate of HBV. Using data which includes the survival time for individuals who were diagnosed as being affected by HBV and those who died from HBV, we fit non-linear models to study the survival time for people affected by the virus. Survival probabilities suggest an exponential curve for the survival time. We also consider a pure death process which is a stochastic model for the survival time of the individuals affected. Our results show …

An Analysis Of The Monitored Electronic Alarm Activations In The Perth Metropolitan Area, Lynnette M. Bloom, James M. Cross, David Mcdougall

Research outputs pre 2011

This study as indicated in [7] was carried out under the auspices of Edith Cowan University's Institute of Security and Applied Technology and had the support of the Western Australian Police and the Perth-based Central Monitoring Agencies. The data analysed was obtained essentially from Police records, backed up by data from two of Perth's larger security companies, and consists of all the monitored alarms in the Perth Metropolitan Area which were attended by the police in the months of May and September 1989.In our consideration of the frequency of alarms by time of day and day of week, and the …

Nonlinear-Interaction Of A Detonation Vorticity Wave, D. G. Lasseigne, T. L. Jackson, M. Y. Hussaini

Mathematics & Statistics Faculty Publications

The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multidomain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results whenever obtained in this study agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient …

Activator-Inhibitor Control Of Tissue Growth, John A. Adam

Mathematics & Statistics Faculty Publications

This note develops a simple model for the competition between activator and inhibitor control mechanisms in one-dimensional tissue growth. The pedagogic usefulness of such a model is that it is easily accessible to undergraduate applied mathematicians and is suggestive of behavior known to occur in more realistic biological systems (e.g., some types of cancer). The limitations of the model are obvious and can provide a basis for discussion of the applicability of complementary levels of description in mathematical modeling.

A New Model Of The Molecular Bond, Donald Greenspan

Mathematics Technical Papers - Archive

It is assumed, on the basis of recent supercomputer calculations, that electrons attract, rather than repel. The consequences are explored by means of three dimensional, molecular mechanics type simulations of ground state [see pdf for notation]. Using spectroscopic data, it is shown that, in every case, the resulting vibrational frequencies and molecular diameters are entirely in agreement with experiment.

A Fixed Point Property For The Lorentz Space Lp,1(Μ), N L. Carothers, S J. Dilworth, C J. Lennard, D A. Trautman

Faculty Publications

No abstract provided.

Refined Approximations Of The Solutions Of A Coupled System With Turning Points, W. A. Harris, S. Shao

Mathematics and Statistics Faculty Publications

We present in this paper the asymptotic behavior of solutions of a boundary value problem for a coupled system of differential equations u″ = ν, εν″ + f(u, u′)ν′ - g(x, u, u′)ν = 0 on a compact interval I, where f(u, u′) has turning points in I. We provide upper and lower solutions, β(x, ε) and α(x, ε), respectively, which bound solutions, exhibiting boundary layer and interior layer behavior, for which limε → 0+ {β(x, ε) - α(x, ε)} = 0 uniformly on I.

On Separable Torsion- Free Modules Of Countable Density Character, R. Gobel, Brendan Goldsmith

Articles

The endomorphism algebras of modules of large cardinalities have been extensively studied in recent years using the combinatorial set-theoretic techniques of Shelah-the so-called black-box methods (see, e.g., [4, 5, 151). Despite the spectacular success of these methods, they are not suitable for realization theorems at small carinalities. Of course at the level of countability (or rather more generally for cardinals ~2’~) there are in some cases the original dramatic results of A. L. S. Corner [ 1, 2, 31 and the more recent generalizations of Gobel and May [ 111. Very recently the study of realization problems at cardinalities

Analysis And Finite Element Approximation Of Optimal Control Problems For The Stationary Navier-Stokes Equations With Dirichlet Controls, M. D. Gunzburger, L. S. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. The n, finite …

A Note On Nonabelian (64, 28, 12) Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

The existence of difference sets in abelian 2-groups is a recently settled problem [5]; this note extends the abelian constructs of difference sets to nonabelian groups of order 64.

Minimax-Optimal Stop Rules And Distributions In Secretary Problems, Theodore P. Hill, Ulrich Krengel

Research Scholars in Residence

For the secretary (or best-choice) problem with an unknown number N of objects, minimax-optimal stop rules and (worst-case) distributions are derived, under the assumption that $N$ is a random variable with unknown distribution, but known upper bound n. Asymptotically, the probability of selecting the best object in this situation is of order of (log n)^-1. For example, even if the only information available is that there are somewhere between 1 and 100 objects, there is still a strategy which will select the best item about one time in five.

When Is Every Order Ideal A Ring Ideal?, Suzanne Larson

Mathematics, Statistics and Data Science Faculty Works

A lattice-ordered ring R is called an OIRI-ring if each of its order ideals is a ring ideal. Generalizing earlier work of Basly and Triki, OIRI-rings are characterized as those f-rings R such that R/I is contained in an f-ring with an identity element that is a strong order unit for some nil l-ideal I of R. In particular, if P(R) denotes the set of nilpotent elements of the f-ring R, then R is an OIRI-ring if and only if R/P(R) is contained in an f-ring with an identity element that is a strong order unit.

Ein Beitrag Zur Klassifikation Von Koppelkurven (A Contribution To The Classification Of Coupler Curves), Jorg Feldvoss, Wolfram Funk, Peter Tolle

University Faculty and Staff Publications

A study of the coupler curves of four-bar and Watt mechanisms is undertaken either theoretically or based on a computer program that is integrated in a CAD-System. This leads even in the case of four-far linkages to some new insights concerning the existence of nodes and cusps. The possible real singularities of non-degenerate coupler curves of the Watt mechanism are determined and by means of our computer program, we demonstrate their difficult structure.

The Impact Of Tourism On Block Island, Thomas Green

Marine Affairs Theses and Major Papers

This thesis examines the impacts of tourism on the residents of Block Island. More specifically the study seeks to identify the specific areas of concern, as perceived by the residents, in three major areas of impact: economic, social and environmental. It was hypothesized that the residents of Block Island, a mature tourist destination area, had formulated perceptions of the impacts of tourism and that these perceptions, if analyzed, would identify protection of the environment and threats to the Island's lifestyle as major concerns. Factor analysis was employed to analyze survey responses from residents on questions regarding tourism on Block Island. …

Best Lp Aapproximation With Multiple Constraints For 1 ⩽ P < ∞, J. J. Swetits, S. E. Weinstein, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The problem considered in this paper is best L_p approximation with multiple constraints for 1 ⩽ p < ∞. Characterizations of best L_p approximations from multiple n-convex splines and functions are established and the relationship between them is investigated. Applications to best monotone convex approximation are studied.