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Articles 2371 - 2400 of 2640

Full-Text Articles in Physical Sciences and Mathematics

Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91 Jan 1993

Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91

All HMC Faculty Publications and Research

In the casino game blackjack or "21," mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a "blackjack"). However, many casinos offer the player "lucky bucks" that pay the player either 3-to-2 or 2-to-1. In the usual game, the player's expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet.

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What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen Dec 1992

What They Didn’T Tell Me About Calculus And The Computer, Melvin Henriksen

All HMC Faculty Publications and Research

My first attempt at using computers as an aid to teaching calculus began in 1966 and culminated with the publication in 1971 of Single Variahle Calculus, written jointly with Milton Lees. Everyone used a mainframe and punched cards and few knew how to program. Computer use was limited to supplementary exercises that could be done today with a hand-held programmable calculator. A constructive sequential approach to limits and elementary numerical analysis were emphasized. The absence of programming displeased computer scientists, but it was too avant garde for all but a tiny minority of teachers of calculus. Attempts by others …

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Direct Picosecond Measurement Of Photoinduced Cooper Pair Breaking In Lead, John F. Federici, Benjamin I. Greene, Peter N. Saeta, Douglas R. Dykaar, F. Sharifi, R. C. Dynes Nov 1992

Direct Picosecond Measurement Of Photoinduced Cooper Pair Breaking In Lead, John F. Federici, Benjamin I. Greene, Peter N. Saeta, Douglas R. Dykaar, F. Sharifi, R. C. Dynes

All HMC Faculty Publications and Research

We report on a direct kinetic measurement of Cooper-pair breaking in superconducting lead. A 100-fs pulse of visible light was used to excite a thin-film lead sample, while the Cooper-pair density was optically probed using an ultrashort pulse of broadband far-infrared radiation. Subsequent to the absorption of the visible light, a rapid (ps) change in the far-infrared optical transmission was observed, corresponding to the breaking of Cooper pairs and the collapse of the superconducting gap.

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Geometrical Phases And Symmetries In Dissipative Systems, Adam S. Landsberg Aug 1992

Geometrical Phases And Symmetries In Dissipative Systems, Adam S. Landsberg

WM Keck Science Faculty Papers

A geometrical phase is constructed for dissipative dynamical systems possessing continuous symmetries. It emerges as the natural analog of the holonomy associated with the adiabatic variation of parameters in quantum-mechanical and classical Hamiltonian systems. In continuous media, the physical manifestation of this phase is a spatial shift of a wave pattern, typically a translation or rotation. An illustration associated with pattern formation in fluids is provided.

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Another Way Of Counting Nᴺ, Arthur T. Benjamin, Fritz Juhnke Aug 1992

Another Way Of Counting Nᴺ, Arthur T. Benjamin, Fritz Juhnke

All HMC Faculty Publications and Research

An original combinatorial proof of a combinatorial identity is presented.

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From The Editor, Issue 7, 1992, Alvin White Apr 1992

From The Editor, Issue 7, 1992, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

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Three Comments On Ethics, Saunders Maclane Apr 1992

Three Comments On Ethics, Saunders Maclane

Humanistic Mathematics Network Journal

No abstract provided.

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Toward A Definition Of 'Humanistic Mathematics', Sherman K. Stein Apr 1992

Toward A Definition Of 'Humanistic Mathematics', Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

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Letter To Professor Joanne S. Growney, John S. Lew Apr 1992

Letter To Professor Joanne S. Growney, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

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Poems Taken From "An Evening Of Mathematical Poetry" Apr 1992

Poems Taken From "An Evening Of Mathematical Poetry"

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics As A Humanistic Discipline, Elena Anne Corie Marchisotto Apr 1992

Mathematics As A Humanistic Discipline, Elena Anne Corie Marchisotto

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematical References In Literature, John S. Lew Apr 1992

Mathematical References In Literature, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

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Epistemological Pluralism: Styles And Voices Within The Computer Culture, Sherry Turkle, Seymour Papert Apr 1992

Epistemological Pluralism: Styles And Voices Within The Computer Culture, Sherry Turkle, Seymour Papert

Humanistic Mathematics Network Journal

No abstract provided.

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What Is Mathematics And Why Don't They Know That?, Harald M. Ness Apr 1992

What Is Mathematics And Why Don't They Know That?, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

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Writing Humanistic Mathematics, Ruth Hubbard Apr 1992

Writing Humanistic Mathematics, Ruth Hubbard

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics From An English Major's Point Of View, Elizabeth Miller, Kathleen M. Shannon Apr 1992

Mathematics From An English Major's Point Of View, Elizabeth Miller, Kathleen M. Shannon

Humanistic Mathematics Network Journal

No abstract provided.

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The Profit Motive: The Bane Of Mathematics Education, Neal Koblitz Apr 1992

The Profit Motive: The Bane Of Mathematics Education, Neal Koblitz

Humanistic Mathematics Network Journal

No abstract provided.

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Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92 Apr 1992

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

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A Theoretical Investigation Of The Ground And Low‐Lying Excited States Of Butadiene Radical Cation, Robert J. Cave, Michael G. Perrott '90 Mar 1992

A Theoretical Investigation Of The Ground And Low‐Lying Excited States Of Butadiene Radical Cation, Robert J. Cave, Michael G. Perrott '90

All HMC Faculty Publications and Research

Results are presented from ab initio calculations on the ground and several low‐lying excited states of the butadiene radical cation. In particular, we have calculated geometries for the ground and several excited states at the multiconfiguration self‐consistent field level and characterized the planar stationary points. The vertical ionization potentials from the neutral molecule ground state and vertical excitation energies at the computed equilibrium geometry of the cation were also examined. A variety of methods were tested for the calculation of ionization potentials and excitation energies, including multiconfiguration self‐consistent field, multireference singles and doubles configuration interaction (with and without size‐consistency correction), …

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Intervalley Scattering In Gaas And Inp Probed By Pulsed Far‐Infrared Transmission Spectroscopy, Peter N. Saeta, John F. Federici, Benjamin I. Greene, Douglas R. Dykaar Mar 1992

Intervalley Scattering In Gaas And Inp Probed By Pulsed Far‐Infrared Transmission Spectroscopy, Peter N. Saeta, John F. Federici, Benjamin I. Greene, Douglas R. Dykaar

All HMC Faculty Publications and Research

The dynamics of photoexcited electrons in GaAs and InP were studied using the transmission of 200‐fs pulses of far‐infrared radiation in the spectral range 15–100 cm−1. Kinetic traces of the infrared transmission as a function of delay between optical excitation and infrared probe show a probe‐limited decrease in transmission followed by a more gradual (0.7–2 ps) drop to a steady value, consistent with the slow return of electrons from high‐mass satellite valleys. Infrared transmission spectra, analyzed in the context of a Drude model, reveal density‐dependent electron mobilities 3–4 times below equilibrium n‐doped values. Electron‐hole collisions likely account …

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Carbon And Nitrogen Isotopic Signatures Of Bat Guanos As A Record Of Past Environments, Hiroshi Mizutani, Donald A. Mcfarlane, Yuko Kabaya Feb 1992

Carbon And Nitrogen Isotopic Signatures Of Bat Guanos As A Record Of Past Environments, Hiroshi Mizutani, Donald A. Mcfarlane, Yuko Kabaya

WM Keck Science Faculty Papers

Carbon and nitrogen isotope ratios were measured for various ecogeochemical samples relevant to bat guano ecosystems. In particular, ca. 800-year-old subfossil guano from Jackson's Bay Cave Compex, Jamaica, yielded ratios similar to the modern guano from other Jamaican bat caves but quite different from modern guano of the same area. Diagenetic change and differences in bat food habits were unlikely explanations for the observation. Instead, insects that feed on C4 and CAM plants were the main prey for the bats in present Jackson's Bay area, while the ultimate source of organic matter for bats in other Jamaican caves and for …

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Nitrogen And Carbon Isotope Studies Of A Bat Guano Core From Eagle Creek Cave, Arizona, Usa, Hiroshi Mizutani, Donald A. Mcfarlane, Yuko Kabaya Feb 1992

Nitrogen And Carbon Isotope Studies Of A Bat Guano Core From Eagle Creek Cave, Arizona, Usa, Hiroshi Mizutani, Donald A. Mcfarlane, Yuko Kabaya

WM Keck Science Faculty Papers

Nitrogen and carbon isotope ratios were studied in a stratified deposit of guano of Mexican Free-tailed bats in Eagle Creek Cave, Arizona, U.S.A. Little diagenetic change was observed over the 25-year time span of the guano deposit. High aridity and reduced circulation of air in the cave are hypothesized to have slowed the normally rapid decomposition of the excreta and the subsequent escape of resultant ammonia. The results suggest the high dependency of the speed of diagenetic change on specific physical and other conditions of the caves and indicate that great care need be exercised in the interpretation of the …

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Optical Rectification At Semiconductor Surfaces, Shun Lien Chuang, Stefan Schmitt-Rink, Benjamin I. Greene, Peter N. Saeta, Anthony F. J. Levi Jan 1992

Optical Rectification At Semiconductor Surfaces, Shun Lien Chuang, Stefan Schmitt-Rink, Benjamin I. Greene, Peter N. Saeta, Anthony F. J. Levi

All HMC Faculty Publications and Research

We show that far-infrared radiation can be generated in the depletion field near semiconductor surfaces via the inverse Franz-Keldysh effect or electric-field-induced optical rectification. This mechanism is conceptually different from those previously proposed and accounts for many recent experimental observations.

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A Casscf Study Of Various Rotamers Of The Hexatriene Radical Cation, Robert J. Cave, Jenifer L. Johnson Jan 1992

A Casscf Study Of Various Rotamers Of The Hexatriene Radical Cation, Robert J. Cave, Jenifer L. Johnson

All HMC Faculty Publications and Research

Results are presented from ab initio calculations on the ground and two low-lying excited states of the hexatriene radical cation in a variety of stable conformations of the electronic ground state of the molecule. We have performed Hartree-Fock geometry optimizations using the STO-3G and 6-31g basis sets and have performed vibrational analyses for all stable conformers in the 6-31G basis. In addition, we have performed geometry optimizations in both basis sets using CASSCF wave functions where the five π electrons are correlated. No new geometrical information is obtained at this level of treatment. Excitation energies to the two lowest-lying doublet …

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Intrinsic Chirality Of Complete Graphs, Erica Flapan, Nikolai Weaver Jan 1992

Intrinsic Chirality Of Complete Graphs, Erica Flapan, Nikolai Weaver

Pomona Faculty Publications and Research

A graph is said to be intrinsically chiral if no embedding of the graph in 3-space is respected by any ambient orientation-reversing homeomorphism. In this note, we characterize those complete graphs that are intrinsically chiral.

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Ultrafast Electronic Disordering During Femtosecond Laser Melting Of Gaas, Peter N. Saeta, J.-K. Wang, Y. Siegal, N. Bloembergen, E. Mazur Aug 1991

Ultrafast Electronic Disordering During Femtosecond Laser Melting Of Gaas, Peter N. Saeta, J.-K. Wang, Y. Siegal, N. Bloembergen, E. Mazur

All HMC Faculty Publications and Research

We have observed an ultrarapid electronic phase transformation to a centrosymmetric electronic state during laser excitation of GaAs with intense femtosecond pulses. Reflection second-harmonic intensity from the upper 90 atomic layers vanishes within 100 fs; reflectivity rises within 0.5 ps to a steady value characteristic of a metallic molten phase, long before phonon emission can heat the lattice to the melting temperature.

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The Calculus Virgin, Louis Leithold May 1991

The Calculus Virgin, Louis Leithold

Humanistic Mathematics Network Journal

No abstract provided.

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Leibniz — Beyond The Calculus, Hardy Grant May 1991

Leibniz — Beyond The Calculus, Hardy Grant

Humanistic Mathematics Network Journal

No abstract provided.

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Student Seminars On "Famous Equations", Richard G. Montgomery May 1991

Student Seminars On "Famous Equations", Richard G. Montgomery

Humanistic Mathematics Network Journal

No abstract provided.

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The Human/Computer Interface: Their Side Or Ours?, R. S.D. Thomas May 1991

The Human/Computer Interface: Their Side Or Ours?, R. S.D. Thomas

Humanistic Mathematics Network Journal

No abstract provided.

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