Digital Commons Network^™

Selection Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

An upper bound asymptotic to $2n\log _e n$ is established for the number of comparators required in a network that classifies $n$ values into two classes, each containing $n / 2$ values, with each value in one class less than or equal to each value in the other. (The best lower bound known for this problem is asymptotic to $(n / 2)\log _2 n$.)

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.

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 …

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 …

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 …

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) …

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.

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 …

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

Mathematics 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.

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.

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.

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.

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.

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

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.

A Comparison Of Ancient Mathematical And Calendrical Systems, Karen Schlauch

Masters Theses

No abstract provided.

Some Remarks On Reproducing Kernel Krein Spaces, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

The one-to-one correspondence between positive functions and reproducing kernel Hilbert spaces was extended by L. Schwartz to a (onto, but not one-to-one) correspondence between difference of positive functions and reproducing kernel Krein spaces. After discussing this result, we prove that matrix value function K(z,ω) symmetric and jointly analytic in z and ω in a neighborhood of the origin is the reproducing kernel of a reproducing kernel Krein space. We conclude with an example showing that such a function can be the reproducing kernel of two different Krein spaces.

Foundations Of Fuzzy Sets, Lawrence Stout, Ulrich Höhle

Lawrence N. Stout

This paper gives an overview of the origins of fuzzy set theory and the problems for the foundations of fuzzy sets arising from those origins and current practice. It then gives detailed accounts of categorical approaches using a closed structure to capture the fuzzy AND connective. Within these categories weak forms of subobject representations provide an internal second order logic. An approach to fuzzy real numbers and fuzzy topology is included to illustrate the use of this internal; second order theory.

A Symmetric Porosity Conjecture Of Zajícek, Karen Saxe, P. Humke, M. Evans

Karen Saxe

No abstract provided.

Reductions Of Graphs And Spanning Eulerian Subgraphs, Zhi-Hong Chen

Zhi-Hong Chen

A Survey Of Fuzzy Set And Topos Theory, Lawrence Stout

Lawrence N. Stout

This paper is a comparison and contrast of approaches to many-valued mathematics offered by Fuzzy Set theory and topos theory. It gives a survey of the categorical foundations of Fuzzy Set theory and related topoi. Topoi are not a basis for Fuzzy Set theory but they do suggest appropriate directions to go and questions to ask for a synthesis which does provide a foundation. One possible structure which has a topos-like internal logic and the, rich variety of logical connectives used in fuzzy sets is included.

Asymptotic Behavior Of Solutions Of Functionally Perturbed Nonoscillatory Second Order Differential Equations, William F. Trench

William F. Trench

No abstract provided.