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Claremont Colleges

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Articles 1831 - 1860 of 1985

Full-Text Articles in Mathematics

On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger Jan 1991

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.

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Selection Networks, Nicholas Pippenger Jan 1991

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

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Stochastic Orderings Induced By Star-Shaped Functions, Henry A. Krieger Jan 1991

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.

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When Is Every Order Ideal A Ring Ideal?, Melvin Henriksen, Suzanne Larson, Frank A. Smith Jan 1991

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.

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The Expected Capacity Of Concentrators, Nicholas Pippenger Jan 1991

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 …

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Modulated, Frequency-Locked, And Chaotic Cross-Waves, William B. Underhill, Seth Lichter, Andrew J. Bernoff Jan 1991

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 …

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Editorial, Issue 5, 1990, Alvin White May 1990

Editorial, Issue 5, 1990, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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Advanced Displacement Exam, Robert Messer May 1990

Advanced Displacement Exam, Robert Messer

Humanistic Mathematics Network Journal

No abstract provided.

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Real Needs Of School Children, Hassler Whitney May 1990

Real Needs Of School Children, Hassler Whitney

Humanistic Mathematics Network Journal

No abstract provided.

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Teaching Global Issues Through Mathematics, Richard H. Schwartz May 1990

Teaching Global Issues Through Mathematics, Richard H. Schwartz

Humanistic Mathematics Network Journal

No abstract provided.

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What Has Mathematics Got To Do With Values?, Stephen Lerman May 1990

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

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics And Ethics, Reuben Hersh May 1990

Mathematics And Ethics, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

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A Social View Of Mathematics: Iimplications For Mathematics Education, Stephen Lerman May 1990

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

Humanistic Mathematics Network Journal

No abstract provided.

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The Humanistic Aspects Of Mathematics And Their Importance, Philip J. Davis May 1990

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

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics — A Significant Force In Our Culture, Harald M. Ness May 1990

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

Humanistic Mathematics Network Journal

No abstract provided.

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Heuristic Thinking And Mathematics, J. F. Lucas May 1990

Heuristic Thinking And Mathematics, J. F. Lucas

Humanistic Mathematics Network Journal

No abstract provided.

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Preparing Teachers To Teach Mathematics Within A Humanistic Perspective, Beatriz S. D'Ambrosio May 1990

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

Humanistic Mathematics Network Journal

No abstract provided.

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Graphs, Maneuvers, And Turnpikes, Arthur T. Benjamin Mar 1990

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 Zm 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.

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Ordered Ultraconnected Rings, Melvin Henriksen, Frank A. Smith Jan 1990

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 Zω into R, there is an i < ω such that ϕ(f) = f(i) • 1 for every f € Zω . 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 Zω/P for some free minimal prime ideal P of Zω.

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Faster Circuits And Shorter Formulas For Multiple Addition, Multiplication And Symmetric Boolean Functions, Michael Paterson, Uri Zwick, Nicholas Pippenger Jan 1990

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 …

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Pumps, Filters, And Lenses; Humanistic Issues In Calculus Reform, Dan Kalman Dec 1989

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

Humanistic Mathematics Network Journal

No abstract provided.

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Reflections On Attending Three Contributed Paper Sessions On Humanistic Mathematics In Phoenix 1989, Peter Flusser Dec 1989

Reflections On Attending Three Contributed Paper Sessions On Humanistic Mathematics In Phoenix 1989, Peter Flusser

Humanistic Mathematics Network Journal

No abstract provided.

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Hassler Whitney 1907-1989: Some Recollections, 1979·1989, Anneli Lax Dec 1989

Hassler Whitney 1907-1989: Some Recollections, 1979·1989, Anneli Lax

Humanistic Mathematics Network Journal

No abstract provided.

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Lessons From Cognitive Theory For Teaching Mathematical Modeling To Freshmen, Richard H. Elderkin Dec 1989

Lessons From Cognitive Theory For Teaching Mathematical Modeling To Freshmen, Richard H. Elderkin

Humanistic Mathematics Network Journal

No abstract provided.

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The Visits Of Hassler Whitney To Brazil: Hassler Whitney, In Memoriam, Ubiratan D'Ambrosio Dec 1989

The Visits Of Hassler Whitney To Brazil: Hassler Whitney, In Memoriam, Ubiratan D'Ambrosio

Humanistic Mathematics Network Journal

No abstract provided.

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Tapping Creativity And Ingenuity Of Liberal Arts Majors In A Math Course, Helen Christensen Dec 1989

Tapping Creativity And Ingenuity Of Liberal Arts Majors In A Math Course, Helen Christensen

Humanistic Mathematics Network Journal

No abstract provided.

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An Empowering, Participatory Research Model For Humanistic Mathematics Pedagogy, Arthur B. Powell, Dawud A. Jeffries, Aleshia E. Selby Dec 1989

An Empowering, Participatory Research Model For Humanistic Mathematics Pedagogy, Arthur B. Powell, Dawud A. Jeffries, Aleshia E. Selby

Humanistic Mathematics Network Journal

No abstract provided.

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Front Matter, Issue 4, 1989 Dec 1989

Front Matter, Issue 4, 1989

Humanistic Mathematics Network Journal

No abstract provided.

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Editorial, Issue 4, 1989, Alvin White Dec 1989

Editorial, Issue 4, 1989, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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Education Is For The Students' Future, Hassler Whitney Dec 1989

Education Is For The Students' Future, Hassler Whitney

Humanistic Mathematics Network Journal

No abstract provided.

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