Physical Sciences and Mathematics Commons^™

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.

Hawaiians Fight For The Rainforest, Paul Faulstich

Pitzer Faculty Publications and Research

On March 25, 141 were arrested as part of the largest demonstration yet against the drilling of geothermal wells in the Wao Kele O Puna Rainforest on the Big Island of Hawaii. The geothermal project, undertaken by True Geothermal Company and endorsed by Hawaii's governor and other high-powered, short-sighted people, has already invaded the largest intact tropical lowland rainforest in the United States. The demonstration drew over 1500 protesters,

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.

Preparing Teachers To Teach Mathematics Within A Humanistic Perspective, Beatriz S. D'Ambrosio

Humanistic Mathematics Network Journal

No abstract provided.

Teaching Global Issues Through Mathematics, Richard H. Schwartz

Humanistic Mathematics Network Journal

No abstract provided.

What Has Mathematics Got To Do With Values?, Stephen Lerman

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Ethics, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

A Social View Of Mathematics: Iimplications For Mathematics Education, Stephen Lerman

Humanistic Mathematics Network Journal

No abstract provided.

Graphs, Maneuvers, And Turnpikes, Arthur T. Benjamin

All HMC Faculty Publications and Research

We address the problem of moving a collection of objects from one subset of Z^m to another at minimum cost. We show that underfairly natural rules for movement assumptions, if the origin and destination are far enough apart, then a near optimal solution with special structure exists: Our trajectory from the originto the destination accrues almost all of its cost repeatingat most m different patterns of movement. Directions for related research are identified.

Size‐Inconsistency Effects In Molecular Properties For States With Valence‐Rydberg Mixing: The Low‐Lying Π→Π∗ States Of Ethylene And Butadiene, Robert J. Cave

All HMC Faculty Publications and Research

Ab initio results for the low‐lying 1B1u states of ethylene are used to discuss size‐inconsistency effects on calculated molecular properties for states where valence‐Rydberg mixing is important. Results for the expectation value of x2, x being the coordinate perpendicular to the plane of the molecule, are presented from quasidegenerate variational perturbation theory and multireference configuration‐interaction calculations. These results are compared with values from previous studies. It is argued that size inconsistency in configuration‐interaction studies can have a significant effect on estimated molecular properties. Calculations on several low‐lying states of butadiene are also reported where similar size‐inconsistency effects are found.

Hawaii's Rainforest Crunch: Land, People, And Geothermal Development, Paul Faulstich

Pitzer Faculty Publications and Research

One hundred and forty-one people, led by Native Hawaiians, were arrested on 25 March 1990 as part of the largest demonstration yet against geothermal development in Hawaii. The gathering was intended to focus attention on Native Hawaiian rights and the ecological consequences of drilling geothermal wells in the near-pristine Wao Kele O Puna rain forest. The energy project, undertaken by True Geothermal Company and endorsed by Hawaii's governor and other imposing figures, has already invaded the largest intact tropical lowland rain forest in the United States.

Faster Circuits And Shorter Formulas For Multiple Addition, Multiplication And Symmetric Boolean Functions, Michael Paterson, Uri Zwick, Nicholas Pippenger

All HMC Faculty Publications and Research

A general theory is developed for constructing the shallowest possible circuits and the shortest possible formulas for the carry-save addition of n numbers using any given basic addition unit. More precisely, it is shown that if BA is a basic addition unit with occurrence matrix N, then the shortest multiple carry-save addition formulas that could be obtained by composing BA units are of size n1p+o(1)/, where p is the unique real number for which the Lp norm of the matrix N equals 1. An analogous result connects the delay matrix M of the basic addition unit BA and the minimal …

Ordered Ultraconnected Rings, Melvin Henriksen, Frank A. Smith

All HMC Faculty Publications and Research

A ring R with identity element 1 is called ultraconnected if for each unital homomorphism ϕ of Z^ω into R, there is an i < ω such that ϕ(f) = f(i) • 1 for every f € Z^ω . Our main result is that if no sum of nonzero squares in R is 0 and R has only trivial idempotents, then R fails to be ultraconnected iff R contains a subring isomorphic to Z^ω/P for some free minimal prime ideal P of Z^ω.

Olmos Park And The Creation Of A Suburban Bastion, Char Miller, Heywood T. Sanders

Pomona Faculty Publications and Research

An examination of this small Texas community will also cast light on the larger world of which it was a part. The development of Olmos Park, then, was inextricably bound up with and reflective of the political machinations and social problems that dominated San Antonio in the first decades of this century. As Mauerman understood, the suburb was a fragment of the urban whole, an observation that needs to be pushed one step farther. The forces that shaped Olmos Park and determined its relations with San Antonio were also part of a national pattern, of tensions generated by the explosive …

The Rise Of Urban Texas, Char Miller, David R. Johnson

Pomona Faculty Publications and Research

Texas contains three of the nation's ten largest cities, but their existence has not yet affected the hold that the state's rural heritage has on Texas' imagination--or so Texans' attachment to two nineteenth-century cultural landmarks, the Alamo and the Chisholm Trail, would suggest. As the shrine of Texas liberty, the Alamo continually generates elegies to the manly courage and bravery of the fallen heroes of 1836.

Editorial, Issue 4, 1989, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Front Matter, Issue 4, 1989

Humanistic Mathematics Network Journal

No abstract provided.

Pumps, Filters, And Lenses; Humanistic Issues In Calculus Reform, Dan Kalman

Humanistic Mathematics Network Journal

No abstract provided.