Physical Sciences and Mathematics Commons^™

Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su

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No abstract provided in this article.

Recounting Fibonacci And Lucas Identities, Arthur T. Benjamin, Jennifer J. Quinn

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No abstract provided in this article.

Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff

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Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”

Almost Periodic Factorization Of Certain Block Triangular Matrix Functions, Ilya M. Spitkovsky, Darryl H. Yong

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Let

where , and . For rational such matrices are periodic, and their Wiener-Hopf factorization with respect to the real line always exists and can be constructed explicitly. For irrational , a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible and commuting , was disposed of earlier-it was discovered that an almost periodic factorization of such matrices does not always exist, and a necessary and sufficient condition for its existence was found. This paper is devoted mostly to the situation when is not invertible but the commute pairwise (). The complete description is …

Black Holes And Five-Brane Thermodynamics, Emil Martinec, Vatche Sahakian

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The phase diagram for Dp-branes in M theory compactified on T⁴,T⁴/Z₂,T⁵, and T⁶ is constructed. As for the lower-dimensional tori considered in our previous work [E. Martinec and V. Sahakian, Phys. Rev. D 59, 124005 (1999)], the black brane phase at high entropy connects onto matrix theory at low entropy; we thus recover all known instances of matrix theory as consequences of the Maldacena conjecture. The difficulties that arise for T⁶ are reviewed. We also analyze the D1-D5 system on T⁵; we discuss its relation to matrix models …

Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00

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No abstract provided in this article.

Probing Nonequilibrium Electron Distributions In Gold By Use Of Second Harmonic Generation, K. L. Moore '99, Thomas D. Donnelly

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Second-harmonic radiation is generated at a gold surface by use of a laser pulse that is varied in duration from 14 to 29 fs and in intensity from 10⁹ to 10¹¹W/cm² . At laser intensities below 10¹⁰W/cm² , the second-harmonic signal has the expected quadratic dependence on pump-laser intensity; however, at higher intensities, the dependence is supraquadratic. This difference arises because the leading edge of the laser pulse interacts significantly with the gold electrons to create a nonequilibrium, photoexcited distribution. The second-harmonic generation process occurs before electron–electron or electron–phonon collisions can equilibrate the …

Black Holes And The Sym Diagram. Ii, Emil Martinec, Vatche Sahakian

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The complete phase diagram of objects in M theory compactified on tori T^p,p=1,2,3, is elaborated. Phase transitions occur when the object localizes on cycle(s) (the Gregory-Laflamme transition), or when the area of the localized part of the horizon becomes one in string units (the Horowitz-Polchinski correspondence point). The low-energy, near-horizon geometry that governs a given phase can match onto a variety of asymptotic regimes. The analysis makes it clear that the matrix conjecture is a special case of the Maldacena conjecture.

Unevening The Odds Of "Even Up", Arthur T. Benjamin, Jennifer J. Quinn

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No abstract provided in this article.

The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99

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"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.

Magic "Squares" Indeed, Arthur T. Benjamin, Kan Yasuda '97

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No abstract provided in this article.

Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99

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In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …

On The Number Of Radially Symmetric Solutions To Dirichlet Problems With Jumping Nonlinearities Of Superlinear Order, Alfonso Castro, Hendrik J. Kuiper

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This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem

Δu+f(u)=h(x)+cφ(x)

on the unit ball Ω⊂R^N with boundary condition u=0 on ∂Ω. Here φ(x) is a positive function and f(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f'(u)<μ, where μ is the smallest positive eigenvalue for Δψ+μψ=0 in Ω with ψ=0 on ∂Ω. It is shown that, given any integer k≥0, the value c may be chosen so large that there are 2k+1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c.

Model Updating By Adding Known Masses And Stiffnesses, Philip D. Cha, Lisette G. De Pillis

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New approaches are developed to update the analytical mass and stiffness matrices of a system. By adding known masses to the structure of interest, measuring the modes of vibration of this mass-modified system, and finally using this set of new data in conjunction with the initial modal survey, the mass matrix of the structure can be corrected. A similar approach can also be used to update the stiffness matrix of the system by attaching known stiffnesses. Manipulating the mass and stiffness correction matrices into vector forms, the connectivity information can be enforced, thereby preserving the physical configuration of the system, …

An Inverse Function Theorem, Alfonso Castro, J. W. Neuberger

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In this note we present a local surjectivity result which is applicable to differential equations for which full boundary conditions may not be known. Our method uses continuous steepest descent and Sobolev gradients.

Black Holes And The Sym Phase Diagram, Miao Li, Emil Martinec, Vatche Sahakian

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Making combined use of the matrix and Maldacena conjectures, the relation between various thermodynamic transitions in super Yang-Mills (SYM) theory and supergravity is clarified. The thermodynamic phase diagram of an object in DLCQ M theory in four and five non-compact space dimensions is constructed; matrix strings, matrix black holes, and black p-branes are among the various phases. Critical manifolds are characterized by the principles of correspondence and longitudinal localization, and a triple point is identified. The microscopic dynamics of the matrix string near two of the transitions is studied; we identify a signature of black hole formation from SYM physics.

A Theoretical Study Of The Electronic Coupling Element For Electron Transfer In Water, Newt E. Miller '99, Matthew C. Wander '97, Robert J. Cave

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The electronic coupling element for electron transfer between a donor and acceptor in water is examined using simulations combining molecular dynamics and semiempirical quantum mechanics. In the first phase of the simulations a model donor and acceptor are solvated in water, using realistic potentials. Following equilbration, molecular dynamics simulations are performed with the donor, acceptor, and water at approximately 300 K, under periodic boundary conditions. In the second phase of the simulation, the electronic coupling element between the donor and acceptor is calculated for a number of time slices, in the presence of the intervening water molecules (those having a …

The Bordalo Order On A Commutative Ring, Melvin Henriksen, Frank A. Smith

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If R is a commutative ring with identity and ≤ is defined by letting a ≤ b mean ab = a or a = b, then (R,≤) is a partially ordered ring. Necessary and sufficient conditions on R are given for (R,≤) to be a lattice, and conditions are given for it to be modular or distributive. The results are applied to the rings Z_n of integers mod n for n ≥ 2. In particular, if R is reduced, then (R,≤) is a lattice iff R is a weak Baer ring, and (R,≤) is a distributive lattice iff R …