A variational principle for cyclic polygons with prescribed edge lengths

We provide a new proof of the elementary geometric theorem on the existence and uniqueness of cyclic polygons with prescribed side lengths. The proof is based on a variational principle involving the central angles of the polygon as variables. The uniqueness follows from the concavity of the target function. The existence proof relies on a fundamental inequality of information theory. We also provide proofs for the corresponding theorems of spherical and hyperbolic geometry (and, as a byproduct, in $1+1$ spacetime). The spherical theorem is reduced to the euclidean one. The proof of the hyperbolic theorem treats three cases separately: Only the case of polygons inscribed in compact circles can be reduced to the euclidean theorem. For the other two cases, polygons inscribed in horocycles and hypercycles, we provide separate arguments. The hypercycle case also proves the theorem for "cyclic" polygons in $1+1$ spacetime.Comment: 18 pages, 6 figures. v2: typos corrected, final versio

Disorder Effects in the Bipolaron System Ti4_{4}O7_{7} Studied by Photoemission Spectroscopy

We have performed a photoemission study of Ti$_{4}$O$_{7}$ around its two transition temperatures so as to cover the metallic, high-temperature insulating (bipolaron-liquid), and low-temperature insulating (bipolaron-crystal) phases. While the spectra of the low-temperature insulating phase show a finite gap at the Fermi level, the spectra of the high-temperature insulating phase are gapless, which is interpreted as a soft Coulomb gap due to dynamical disorder. We suggest that the spectra of the high-temperature disordered phase of Fe$_{3}$O$_{4}$, which exhibits a charge order-disorder transition (Verwey transition), can be interpreted in terms of a Coulomb gap.Comment: 4 pages, 3 epsf figures embedde

A flexible framework for evaluating the socio-cultural impacts of a small festival

The increasing popularity of festivals and events, coupled with their positive and negative impacts on host communities, has led to a growing body of research on the impacts of festivals and events. As a substantial amount of this research has focused on assessing the economic impacts of festivals, there is growing demand for the measurement of the socio-cultural impacts of these festivals and events. To address this issue a study was conducted that developed a framework for the social impact evaluation of festivals and piloted a tool that measured the community perceptions of socio-cultural impacts

VPI-7: The First Zincosilicate Molecular Sieve Containing Three-membered T-Atom Rings

VPI-7: the first microporous zincosilicate to contain 3-membered rings (3MR) is reported

Frequency Domain Simulations of Charge-Density-Wave Strains: Comparison with Electro-Optic Measurements

We have studied changes in charge-density-wave strain under application of square-wave currents of variable amplitude and frequency by numerically solving the phase-slip augmented diffusion model introduced by Adelman et al (Phys. Rev. B 53, 1833 (1996)). The frequency dependence of the strain, at each position and amplitude, was fit to a modified harmonic oscillator expression, and the position and current dependence of the fitting parameters determined. In particular, the delay time (1/resonant frequency) vanishes adjacent to the contact and grows with distance from the contact, and both the delay time and relaxation time decrease rapidly with increasing current (and phase-slip rate), as experimentally observed in the electro-optic response of blue bronze. We have also found that pinning the phase at the contacts causes more rapid changes in strain between the contacts than allowing the phase to flow outside the contacts.Comment: 12 pages, 4 figures, submitted to Phys. Rev.

Non-fermi-liquid single particle lineshape of the quasi-one-dimensional non-CDW metal Li_{0.9}Mo_{6}O_{17} : comparison to the Luttinger liquid

We report the detailed non-Fermi liquid (NFL) lineshape of the dispersing excitation which defines the Fermi surface (FS) for quasi-one-dimensional Li_{0.9}Mo_{6}O_{17}. The properties of Li_{0.9}Mo_{6}O_{17} strongly suggest that the NFL behavior has a purely electronic origin. Relative to the theoretical Luttinger liquid lineshape, we identify significant similarities, but also important differences.Comment: 5 pages, 3 eps figure

Two-dimensional Hubbard-Holstein bipolaron

We present a diagrammatic Monte Carlo study of the properties of the Hubbard-Holstein bipolaron on a two-dimensional square lattice. With a small Coulomb repulsion, U, and with increasing electron-phonon interaction, and when reaching a value about two times smaller than the one corresponding to the transition of light polaron to heavy polaron, the system suffers a sharp transition from a state formed by two weakly bound light polarons to a heavy, strongly bound on-site bipolaron. Aside from this rather conventional bipolaron a new bipolaron state is found for large U at intermediate and large electron-phonon coupling, corresponding to two polarons bound on nearest-neighbor sites. We discuss both the properties of the different bipolaron states and the transition from one state to another. We present a phase diagram in parameter space defined by the electron-phonon coupling and U. Our numerical method does not use any artificial approximation and can be easily modified to other bipolaron models with longer range electron-phonon and/or electron-electron interaction.Comment: 14 pages, 12 figure

Non-Fermi liquid angle resolved photoemission lineshapes of Li0.9Mo6O17

A recent letter by Xue et al. (PRL v.83, 1235 ('99)) reports a Fermi-Liquid (FL) angle resolved photoemission (ARPES) lineshape for quasi one-dimensional Li0.9Mo6O17, contradicting our report (PRL v.82, 2540 ('99)) of a non-FL lineshape in this material. Xue et al. attributed the difference to the improved angle resolution. In this comment, we point out that this reasoning is flawed. Rather, we find that their data have fundamental differences from other ARPES results and also band theory.Comment: To be published as a PRL Commen