Symmetric bilinear forms and vertices in characteristic 2

Let $G$ be a finite group and let $k$ be an algebraically closed field of characteristic $2$ and let $M$ be an indecomposable $kG$-module which affords a non-degenerate $G$-invariant symmetric bilinear form. We introduce the symmetric vertices of $M$. Each of these is a $2$-subgroup of $G$ which contains a Green vertex of $M$ with index at most $2$. If $M$ is irreducible then its symmetric vertices are determined up to $G$-conjugacy. If $B$ is the real $2$-block of $G$ containing $M$, we show that each symmetric vertex of $M$ is contained in an extended defect group of $B$. Moreover, we characterise the extended defect groups in terms of symmetric vertices. In order to prove these results, we develop the theory of involutary $G$-algebras. This allows us to translate questions about symmetric $kG$-modules into questions about projective modules of quadratic type.Comment: Changes from v2: erroneous Lemma 2.3 (on lifting idempotents) corrected. Consequent minor changes made to the rest of the paper. Table of contents remove

Spacecraft studies of Phobos and Mars

Utilizing the Termoskan data set of the Phobos '88 mission we have recognized a new feature on Mars: Ejecta blanket Distinct In the THermal infrared (EDITH). Virtually all of the more than one hundred of these features discovered in the Termoskan data are located on the plains near Valles Manneris. EDITH's have a startlingly clear dependence upon terrains of Hesperian age, implying a spatial or temporal dependence on Hesperian terrains. Almost no thermally distinct ejecta blankets are associated with any of the thousands of craters within the data set that occur on the older Noachian units. EDITH's also do not appear on the portions of the younger Tharsis Amazonian units seen in the data. The Hesperian terrain dependence cannot be explained by either atmospheric or impactor variations; Noachian and Hesperian terrains must have experienced identical atmospheric and impactor conditions during Hesperian times. Thermally distinct eject a blankets therefore reflect target material differences and/or secondary modification processes. A further discussion of EIDTH's is presented

Disk heating by more than one spiral density wave

We consider a differentially rotating, 2D stellar disk perturbed by two steady state spiral density waves moving at different patterns speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time dependent gravitational field can be heated (their random motions increased).This is particularly noticeable in the simultaneous propagation of a 2-armed spiral density wave near the corotation resonance (CR), and a weak 4-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with 2 spiral waves moving at different pattern speeds we find: (1) the variance of the radial velocity, sigma_R^2, exceeds the sum of the variances measured from simulations with each individual pattern; (2) sigma_R^2 can grow with time throughout the entire simulation; (3) sigma_R^2 is increased over a wider range of radii compared to that seen with one spiral pattern; (4) particles diffuse radially in real space whereas they don't when only one spiral density wave is present. Near the CR with the stronger, 2-armed pattern, test particles are observed to migrate radially. These effects take place at or near resonances of both spirals so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic disks. If multiple spiral patterns are present in the Galaxy we predict that there should be large variations in the stellar velocity dispersion as a function of radius.Comment: 20 pages, 13 figures. Submitted to MNRA

Space photography and the exploration of Mars

A general exposition of the scientific potentialities and analytic framework of space photography is presented using the photography of Mars from flybys and orbiters as the principal example. Space photography is treated here as a communication process in which planetary scene information is communicated to the eye-brain receiver of earth-based interpreters. The salient parameters of this process are: (1) total information returned, (2) surface resolution, and (3) a priori knowledge regarding the planetary surface observed

Ten Micron Photometry of 25 Stars from B8 To M7

A photometer employing a liquid hydrogen-cooled mercury-doped germanium photoconductor whose spectral response is limited to the 8 - 14 µ region by a low pass interference filter and a BaF_2 window coupled with the cell's threshold wavelength has been placed at the east arm Cassegrain focus of the 200 inch Hale telescope. Twenty-five stars have been measured. The earliest star for which two measurements have been obtained is the B8Ia star β Orionis. The latest star is the M7e star X Cygni. The brightest star, L37 X 10^(-14) watts/cm^2, is α Orionis. The carbon star DS Peg was also measured. In a two-color diagram formed with B and V there is an intrinsic increase in dispersion going to later type stars and a systematic trend away from the blackbody relation. The ratios of the stellar fluxes to those expected from blackbodies at the published stellar effective-temperatures and angular diameters are not far from one. A systematic trend exhibited may not be real because of the assumptions involved in inteferometric diameter determinations. DS Peg does not appear overly peculiar in the two-color plots, but X,Cygni falls on the opposite side of the blackbody curve ("blue excess") compared with most of the late type stars. The fluxes presented here have not been corrected for presently uncertain telescope transmission losses which may be important

Bayesian model comparison and model averaging for small-area estimation

This paper considers small-area estimation with lung cancer mortality data, and discusses the choice of upper-level model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We give a general methodology for both evaluating the data evidence for different models and averaging over plausible models to give robust area effect distributions. We reanalyze the data of Tsutakawa [Biometrics 41 (1985) 69--79] on lung cancer mortality rates in Missouri cities, and show the differences in conclusions about the city rates from this methodology.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS205 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org