Power sums of Coxeter exponents

Consider an irreducible finite Coxeter system. We show that for any nonnegative integer n the sum of the nth powers of the Coxeter exponents can be written uniformly as a polynomial in four parameters: h (the Coxeter number), r (the rank), and two further parameters.Comment: 14 page

Yellow Supergiants and Post-Red Supergiant Evolution in the Large Magellanic Cloud

The empirical evidence for an upper mass limit for the red supergiant (RSG) progenitors of the Type II-P SNe at about 18 Msun, raises questions about the fate of the most luminous, most massive RSGs. These stars may evolve back to warmer temperatures to end their lives as hotter stars or collapse directly to black holes. The yellow hypergiants, many with extensive circumstellar dust and high mass loss, are excellent candidates for post-RSG evolution. We have identified six high luminosity yellow supergiants (YSGs) in the LMC with circumstellar dust including two of the FYPS (Dorn et al, 2022). We discuss their SEDs, mass lost and mass loss rates. Together with three additional FYPS, these nine stars are about 1/3 of the YSGs above 10^5 Lsun. We conclude that the high luminosity YSGs with surface pulsations and circumstellar dust, distinct from other YSGs, are candidates for post-RSG evolution in the LMC.Comment: To appear in the Astronomical Journa

Mid-Cycle Changes in Eta Carinae

In late 2006, ground-based photometry of $\eta$ Car plus the Homunculus showed an unexpected decrease in its integrated apparent brightness, an apparent reversal of its long-term brightening. Subsequent HST/WFPC2 photometry of the central star in the near-UV showed that this was not a simple reversal. This multi-wavelength photometry did not support increased extinction by dust as the explanation for the decrease in brightness. A spectrum obtained with GMOS on the Gemini-South telescope, revealed subtle changes mid-way in $\eta$ Car's 5.5 yr spectroscopic cycle 0when compared with HST/STIS spectra at the same phase in the cycle. At mid-cycle the secondary star is 20--30 AU from the primary. We suggest that the spectroscopic changes are consistent with fluctuations in the density and velocity of the primary star's wind, unrelated to the 5.5 yr cycle but possibly related to its latitude-dependent morphology. We also discuss subtle effects that must be taken into account when comparing ground-based and HST/STIS spectra.Comment: 34 pages, 9 Figure

Contributions from cognitive neuroscience to understanding functional mechanisms of visual search.

We argue that cognitive neuroscience can contribute not only information about the neural localization of processes underlying visual search, but also information about the functional nature of these processes. First we present an overview of recent work on whether search for form - colour conjunctions is constrained by processes involved in binding across the two dimensions. Patients with parietal lesions show a selective problem with form - colour conjunctive search relative to a more difficult search task not requiring cross-dimensional binding. This is consistent with an additional process - cross-dimensional binding - being involved in the conjunctive search task. We then review evidence from preview search using electrophysiological, brain imaging, and neuropsychological techniques suggesting preview benefits in search are not simply due to onset capture. Taken together the results highlight the value of using converging evidence from behavioural studies of normal observers and studies using neuroscientific methods. © 2006 Psychology Press Ltd