On the rooted Tutte polynomial

The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph. The connection with the Potts model is also reviewed.Comment: plain latex, 14 pages, 2 figs., to appear in Annales de l'Institut Fourier (1999

A simple theory of dipole antennas

Simple and quantitatively accurate representation of current distribution in dipole antenna

Origin of the X-ray Quasi-Periodic Oscillations and Identification of a Transient Ultraluminous X-Ray Source in M82

The starburst galaxy M82 contains two ultraluminous X-ray sources (ULXs), CXOM82 J095550.2+694047 (=X41.4+60) and CXOM82 J095551.1+694045 (=X42.3+59), which are unresolved by XMM-Newton. We revisited the two XMM-Newton observations of M82 and analyzed the surface brightness profiles using the known Chandra source positions. We show that the quasi-periodic oscillations (QPOs) detected with XMM-Newton originate from X41.4+60, the brightest X-ray source in M82. Correcting for the contributions of the unresolved sources, the QPO at a frequency of 55.8+/-1.3 mHz on 2001 May 06 had a fractional rms amplitude of 32%, and the QPO at 112.9+/-1.3 mHz on 2004 April 21 had an amplitude of 21%. The QPO frequency may possibly be correlated with the source flux, similar to the type C QPOs in XTE 1550-564 and GRS 1915+105, but at luminosities two orders of magnitude higher. X42.3+59, the second brightest source in M82, displayed a strikingly high flux of 1.4E-11 ergs/cm^2/s in the 2-10 keV band on 2001 May 6. A seven-year light curve of X42.3+59 shows extreme variability over a factor of 1000; the source is not detected in several Chandra observations. This transient behavior suggests accretion from an unstable disk. If the companion star is massive, as might be expected in the young stellar environment, then the compact object would likely be an IMBH.Comment: 9 pages, 6 figures, submitted to ApJ on May 08, 200

The Semiclassical Limit for SU(2)SU(2) and SO(3)SO(3) Gauge Theory on the Torus

We prove that for $SU(2)$ and $SO(3)$ quantum gauge theory on a torus, holonomy expectation values with respect to the Yang-Mills measure d\mu_T(\o) =N_T^{-1}e^{-S_{YM}(\o)/T}[{\cal D}\o] converge, as $T\downarrow 0$, to integrals with respect to a symplectic volume measure $\mu_0$ on the moduli space of flat connections on the bundle. These moduli spaces and the symplectic structures are described explicitly.Comment: 18 page