Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

An odd perfect number, N, is shown to have at least nine distinct prime factors. If 3 does not divide N, then N must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.Comment: 17 page

Identification of the age-period-cohort model and the extended chain ladder model

In this paper, we consider the identification problem arising in the age-period-cohort models, as well as in the extended chain ladder model. We propose a canonical parametrization based on the accelerations of the trends in the three factors. This parametrization is exactly identified. It eases interpretation, estimation and forecasting. The canonical parametrization is shown to apply for a class of index sets which have trapezoid shapes, including various Lexis diagrams and the insurance reserving triangles.

A sharp-interface model of electrodeposition and ramified growth

We present a sharp-interface model of two-dimensional ramified growth during quasi-steady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and nonlinear electrode reactions. The model is validated by comparing its behavior in the initial stage with the predictions of a linear stability analysis.Comment: RevTex, 14 pages, 12 eps figure

Concentration polarization, surface currents, and bulk advection in a microchannel

We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behaviour of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction.Comment: 15 pages, 11 figures, Revtex 4.

Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that is: (a) ultralocal, (b) respects symmetries of hypercubic lattice, (c) corresponding kernel satisfies D gamma5 + gamma5 D = D gamma5 D (Ginsparg-Wilson relation), (d) describes single species of massless Dirac fermions in the continuum limit.Comment: 4 pages, REVTEX; few minor change

Instanton constraints and renormalization

The renormalization is investigated of one-loop quantum fluctuations around a constrained instanton in $\phi ^4$-theory with negative coupling. It is found that the constraint should be renormalized also. This indicates that in general only renormalizable constraints are permitted.Comment: 29 page

A Melanic Pieris Rapae from Michigan (Lepidoptera: Pierdae)

The Arthur J. Yates collection of Michigan Lepidoptera, recently donated to Michigan State University (see Fischer, 1967), contained a striking melanic male cabbage butterfly [Pieris rapae (Linnaeus)] (Figs. 1, 2) now incorporated into the MSU series. Yates collected the specimen on 29 May 1934 in Roseville, Macomb County, near the western shore of Lake St. Clair in southeastern Michigan. An examination of the androconia and genitalia, using the characters described by Chang (1963), assured proper identification of the specimen. Although we have found no record of a similar rapae taken in North America, there are some named European forms of various species of Pieris that resemble our specimen

The WIYN Open Cluster Study Photometric Binary Survey: Initial Findings for NGC 188

The WIYN open cluster study (WOCS) has been working to yield precise magnitudes in the Johnson-Kron-Cousins UBVRI system for all stars in the field of a selection of ``prototypical'' open clusters. Additionally, WOCS is using radial velocities to obtain orbit solutions for all cluster binary stars with periods of less than 1000 days. Recently, WOCS is being expanded to include the near-infrared JHK_s (deep ground-based plus 2MASS) and mid-infrared ([3.6], [4.5], [5.8], [8.0]) photometry from Spitzer/IRAC observations. This multi-wavelength data (0.3--8.0 microns) allows us photometrically to identify binaries, with mass ratios from 1.0--0.3, across a wide range of primary masses. The spectral energy distribution (SED) fitter by Robitaille et al. (2007) is used to fit the fluxes of 10--12 bands, converted from the observed magnitudes, to Kurucz stellar models. Using this photometric technique, we find that NGC 188 has a binary fraction of 36--49% and provide a star-by-star comparison to the WOCS radial velocity-based binary study.Comment: 2 pages, 2 figures, Conference Proceedings from "Dynamical Evolution of Dense Stellar Systems'', IAU Symposium 246, Eds. E. Vesperini, M. Giersz, & A. Sill

A double main sequence turn-off in the rich star cluster NGC 1846 in the Large Magellanic Cloud

We report on HST/ACS photometry of the rich intermediate-age star cluster NGC 1846 in the Large Magellanic Cloud, which clearly reveals the presence of a double main sequence turn-off in this object. Despite this, the main sequence, sub-giant branch, and red giant branch are all narrow and well-defined, and the red clump is compact. We examine the spatial distribution of turn-off stars and demonstrate that all belong to NGC 1846 rather than to any field star population. In addition, the spatial distributions of the two sets of turn-off stars may exhibit different central concentrations and some asymmetries. By fitting isochrones, we show that the properties of the colour-magnitude diagram can be explained if there are two stellar populations of equivalent metal abundance in NGC 1846, differing in age by approximately 300 Myr. The absolute ages of the two populations are ~1.9 and ~2.2 Gyr, although there may be a systematic error of up to +/-0.4 Gyr in these values. The metal abundance inferred from isochrone fitting is [M/H] ~ -0.40, consistent with spectroscopic measurements of [Fe/H]. We propose that the observed properties of NGC 1846 can be explained if this object originated via the tidal capture of two star clusters formed separately in a star cluster group in a single giant molecular cloud. This scenario accounts naturally for the age difference and uniform metallicity of the two member populations, as well as the differences in their spatial distributions.Comment: 9 pages, 8 figures, accepted for publication in MNRAS. A version with full resolution figures may be obtained at http://www.roe.ac.uk/~dmy/papers/MN-07-0441-MJ_rv.ps.gz (postscript) or at http://www.roe.ac.uk/~dmy/papers/MN-07-0441-MJ_rv.pdf (PDF