External Shear in Quadruply Imaged Lens Systems

We use publicly available N-body simulations and semi-analytic models of galaxy formation to estimate the levels of external shear due to structure near the lens in gravitational lens systems. We also describe two selection effects, specific to four-image systems, that enhance the probability of observing systems to have higher external shear. Ignoring additional contributions from "cosmic shear" and assuming that lens galaxies are not significantly flattened, we find that the mean shear at the position of a quadruple lens galaxy is 0.11, the rms shear is roughly 0.15, and there is roughly a 45% likelihood of external shear greater than 0.1. This is much larger than previous estimates and in good agreement with typical measured external shear. The higher shear primarily stems from the tendency of early-type galaxies, which are the majority of lenses, to reside in overdense regions.Comment: 5 pages, 2 figures, ApJ in press, minor revision

Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

ISO far-infrared observations of rich galaxy clusters II. Sersic 159-03

The far-infrared emission from rich galaxy clusters is investigated. Maps have been obtained by ISO at 60, 100, 135, and 200 microns using the PHT-C camera. Ground based imaging and spectroscopy were also acquired. Here we present the results for the cooling flow cluster Sersic 159-03. An infrared source coincident with the dominant cD galaxy is found. Some off-center sources are also present, but without any obvious counterparts.Comment: 6 pages, 4 postscript figures, accepted for publication in `Astronomy and Astrophysics

Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two