412 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Billiards are dynamical systems. In the simplest case, a “billiard table” is a compact domain Q ⊂ Rd with a piecewise smooth boundary. For a large part of the theory the class of smoothness plays no role. The reader is invited to think about components of the boundary ∂Q as subsets of C∞-submanifolds of codimension 1. The phase space M of the billiard ...

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

Bristol et al. (1) recently introduced and summarized 17 sets of predictions of the carcino-genicity of 30 chemicals currently undergoing long-term rodent cancer bioassay in the National Toxicology Program (NTP). These predictions will eventually be compared with the bioassay outcomes. To aid that process, a summary table was provided by Bristol et al. (1). In the legend to that summary table, ...

A compact, high-resolution Fourier-transform spectrometer for atmospheric near-ultraviolet spectroscopy has been installed at the Jet Propulsion Laboratory's Table Mountain Facility (34.4 degrees N, 117.7 degrees W, elevation 2290 m). This instrument is designed with an unapodized resolving power near 500,000 at 300 nm to provide high-resolution spectra from 290 to 675 nm for the quantification...

In this paper the authors present a hierarchical Automatic Test Pattern Generation (ATPG) system, which searches for a compact set of test patterns, in an otherwise large search-space. A Genetic Algorithm (GA) is employed by the system, and the search for test patterns is guided by dynamically evolving a global record table (GRT), which is the prime component for directing the search towards an...

We have constructed a scanning soft-x-ray microscope that uses a laser-produced plasma as the soft-x-ray source and normal-incidence multilayer-coated mirrors in a Schwarzschild configuration as the focusing optics. The microscope operates at a wavelength of 14 nm, has a spatial resolution of 0.5 microm, and has a soft-x-ray photon flux through the focus of 10(4)-10(5) sec(-1) when operated wit...

We demonstrate sub-100 nm resolution water-window soft X-ray full-field transmission microscopy with a compact system. The microscope operates at lambda = 3.37 nm and is based on a 100 Hz table-top regenerative debris-free droplet-target laser-plasma X-ray source in combination with normal-incidence multilayer condenser optics for sample illumination. High-spatial-resolution imaging is performe...

This is a continuation of [16] where the complete diagram of metric normalizers of the fundamental groupG= ⊗ in Isom H will be determined (Table 2). Thus we completely classify the symmetry groups N/G of the 3− surface, i.e. the connected sum of 3 projective planes, into 12 normalizer classes, up to topological equivariance, by the algorithm for fundamental domains, developed in [9], [10], [11]...