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

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

The Oral Administration of Antitoxins for Prevention of Diphtheria, Tetanus, and Possibly Sepsis, with Some Observations on the Influence of Certain Drugs in Preventing Digestion and Promoting Absorption from the Alimentary Canal

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On character generators for simple Lie algebras

We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is first reviewed. A new general formula is then found. It makes clear the distinct roles of ``outside'' and ``inside'' elements of the integrity basis, and helps determine their quadratic incompatibilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We find that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure

The connection between the 15 GHz radio and gamma-ray emission in blazars

Since mid-2007 we have carried out a dedicated long-term monitoring programme at 15 GHz using the Owens Valley Radio Observatory 40 meter telescope. One of the main goals of this programme is to study the relation between the radio and gamma-ray emission in blazars and to use it as a tool to locate the site of high energy emission. Using this large sample of objects we are able to characterize the radio variability, and study the significance of correlations between the radio and gamma-ray bands. We find that the radio variability of many sources can be described using a simple power law power spectral density, and that when taking into account the red-noise characteristics of the light curves, cases with significant correlation are rare. We note that while significant correlations are found in few individual objects, radio variations are most often delayed with respect to the gamma-ray variations. This suggests that the gamma-ray emission originates upstream of the radio emission. Because strong flares in most known gamma-ray-loud blazars are infrequent, longer light curves are required to settle the issue of the strength of radio-gamma cross-correlations and establish confidently possible delays between the two. For this reason continuous multiwavelength monitoring over a longer time period is essential for statistical tests of jet emission models.Comment: To appear in the Proceedings of the IAU Symposium No. 313: "Extragalactic jets from every angle," Galapagos, Ecuador, 15-19 September 2014, F. Massaro, C. C. Cheung, E. Lopez, and A. Siemiginowska (Eds.), Cambridge University Pres

A quasi-periodic oscillation in the blazar J1359+4011

The OVRO 40-m telescope has been monitoring the 15 GHz radio flux density of over 1200 blazars since 2008. The 15 GHz light curve of the flat spectrum radio quasar J1359+4011 shows a strong and persistent quasi-periodic oscillation. The time-scale of the oscillation varies between 120 and 150 days over a $\sim4$ year time span. We interpret this as the active galactic nucleus mass-scaled analog of low-frequency quasi-periodic oscillations from Galactic microquasars, or as evidence of modulation of the accretion flow by thermal instabilites in the "inner" accretion disc.Comment: 4 pages, 2 figures, 1 table. Accepted for publication in MNRAS Letter