Physical Sciences and Mathematics Commons^™

An Historical Approach To Precalculus And Calculus, Victor J. Katz

Humanistic Mathematics Network Journal

No abstract provided.

Ethics In Mathematics: A Request For Information, Robert P. Webber

Humanistic Mathematics Network Journal

No abstract provided.

Augsburg's Humanistic Curriculum Project, Larry Copes, Beverly Stratton

Humanistic Mathematics Network Journal

No abstract provided.

An Alternative Approach To The History Of Mathematics, Claudia Henrion

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics: Contributions By Women, Jacqueline M. Dewar

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Philosophy: The Story Of A Misunderstanding, Gian-Carlo Rota

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Poetry : Isolated Or Integrated?, Joanne S. Growney

Humanistic Mathematics Network Journal

No abstract provided.

How Mathematics Teachers Use "Writing To Learn", Susan Hunter

Humanistic Mathematics Network Journal

No abstract provided.

The Hermeneutics Of Mathematical Modeling, David Tudor

Humanistic Mathematics Network Journal

No abstract provided.

On Teaching In The Mathematical Sciences, James M. Cargal

Humanistic Mathematics Network Journal

No abstract provided.

Ultimately, Mathematics Is Poetry, Alfred Warrinnier

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics For Life And Society, Miriam Lipschutz-Yevick

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics, Truth And Integrity, Peter Hilton, Jean Pedersen

Humanistic Mathematics Network Journal

No abstract provided.

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 …

On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger

All HMC Faculty Publications and Research

A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments.

Stochastic Orderings Induced By Star-Shaped Functions, Henry A. Krieger

All HMC Faculty Publications and Research

The non-decreasing functions whicl are star-shaped and supported above at each point of a non-empty closed proper subset of the real line induce an ordering, on the class of distribution functions with finite first moments, that is strictly weaker than first degree stochastic dominance and strictly stronger than second degree stochastic dominance. Several characterizations of this ordering are developed, both joint distribution criteria and those involving only marginals. The latter are deduced from a decomposition theorem, which reduces the problem to consideration of certain functions which are star-shaped on the complement of an open interval.

Disjoint Covers In Replicated Heterogeneous Arrays, P.K. Mckinley, N. Hasan, Ran Libeskind-Hadas, C.L. Liu

All HMC Faculty Publications and Research

Reconfigurable chips are fabricated with redundant elements that can be used to replace the faulty elements. The fault cover problem consists of finding an assignment of redundant elements to the faulty elements such that all of the faults are repaired. In reconfigurable chips that consist of arrays of elements, redundant elements are configured as spare rows and spare columns.

This paper considers the problem in which a chip contains several replicates of a heterogeneous array, one or more sets of spare rows, and one or more sets of spare columns. Each set of spare rows is identical to the set …

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 $(n / 2)\log _2 n$.)

Optical Property Measurements In Turbid Media Using Frequency Domain Photon Migration, Bruce J. Tromberg, Lars O. Svaasand, Tsong-Tseh Tsay, Richard C. Haskell, Michael W. Berns

All HMC Faculty Publications and Research

In frequency domain photon migration (FDPM), amplitude-modulated light is launched into a turbid medium, e.g. tissue, which results in the propagation of density waves of diffuse photons. Variations in the optical properties of the medium perturb the phase velocity and amplitude of the diffusing waves. These parameters can be determined by measuring the phase delay and demodulation amplitude of the waves with respect to the source. More specifically, the damped spherical wave solutions to the homogeneous form of the diffusion equation yield expressions for phase (φ) and demodulation (m) as a function of source distance, modulation frequency, absorption coefficient (β), …

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 …

Sunbelt Texas, Char Miller

Pomona Faculty Publications and Research

What then is the Sunbelt, and Texas' place within it? The region first had to be recognized as a region, of course, and that has taken some doing. The term was initially employed in the late 1960s and soon came to loom large in the popular imagination. Still, its boundaries were and are inexact. Where is the Sunbelt? Some commentators have adopted an all-inclusive definition which links together those states south of the thirty-seventh parallel; an even more expansive version includes Virginia and the Pacific Northwest. Others rely on more precise, but no less problematic descriptions which, depending on the …

Malaysian Deforestation Proceeds Apace, Paul Faulstich

Pitzer Faculty Publications and Research

A hunger fast, dubbed Fast Action, was staged in front of the Japanese Consulate General in Honolulu on July 20 to protest the destruction of the most ancient and biologically diverse ecosystem on Earth. Organized by Hawai'i Earth First! and the O'ahu Rainforest Action Group, Fast Action was designed to alert people to the destruction of tropical rainforests in Sarawak, Malaysia. Protesters demanded on immediate moratorium on the cutting of rainforests in,which the Penan and other-native peoples live.

Hawaii's Hottest Issue: Update On Geothermal Development, Paul Faulstich

Pitzer Faculty Publications and Research

Walking through Hawai'i's Wao Kele O Puna rainforest, you can hear the coarse volcanic soil crunch underfoot. A surrealistic calm lingers in the thick air while songbirds call out from the understory. Yet this is a forest under siege.

Geothermal developers want to tap the volcanic heat beneath the Wao Kele O Puna forest and use it to make electricity and profits.

Editorial, Issue 5, 1990, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

The Humanistic Aspects Of Mathematics And Their Importance, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics — A Significant Force In Our Culture, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Heuristic Thinking And Mathematics, J. F. Lucas

Humanistic Mathematics Network Journal

No abstract provided.

Advanced Displacement Exam, Robert Messer

Humanistic Mathematics Network Journal

No abstract provided.

Real Needs Of School Children, Hassler Whitney

Humanistic Mathematics Network Journal

No abstract provided.