Classification of finite groups generated by reflections and rotations

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete classification. These groups naturally arise in the study of the quotient of a Euclidean space by a finite orthogonal group and hence in the theory of orbifolds.Comment: 38 pages, accepted by Transformation Group

The Density of Titanium(IV) Oxide Liquid

The density of TiO2 liquid in equilibrium with air has been measured at 1875° to 1925°C using an Ir double bob Archimedean method. The melt density data have been combined with data extrapolated from the CaSiO3─TiO2 join at 1600°C. A combined fit to these density data yields the following description of the density of liquid TiO2: ρ= 3.7611 - 0.00028T(°C), in the temperature range of 1600° to 1925°C. This expansivity value is consistent with those obtained on TiO2-rich melts using a Pt-based system at lower temperature and with multicomponent oxide data. The similarity between the volume of liquid TiO2 and that of crystalline rutile implies a dominantly octahedral coordination of Ti in the liquid state

Graphics Processing Units and High-Dimensional Optimization

This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many statistical algorithms. To exploit these devices fully, optimization algorithms should reduce to multiple parallel tasks, each accessing a limited amount of data. These criteria favor EM and MM algorithms that separate parameters and data. To a lesser extent block relaxation and coordinate descent and ascent also qualify. We demonstrate the utility of GPUs in nonnegative matrix factorization, PET image reconstruction, and multidimensional scaling. Speedups of 100 fold can easily be attained. Over the next decade, GPUs will fundamentally alter the landscape of computational statistics. It is time for more statisticians to get on-board

An investigation of the suitability of white rats for sub-orbital studies of behavior in a gravity field

Suitability of white rats for suborbital studies of behavior in gravity field

A Galois-theoretic approach to Kanev's correspondence

Let $G$ be a finite group, $\Lambda$ an absolutely irreducible $\Z[G]$-module and $w$ a weight of $\Lambda$. To any Galois covering with group $G$ we associate two correspondences, the Schur and the Kanev correspondence. We work out their relation and compute their invariants. Using this, we give some new examples of Prym-Tyurin varieties.Comment: 15 page

Infrared heterodyne radiometer for airborne atmospheric transmittance measurements

An infrared heterodyne radiometer (IHR) was used to measure atmospheric transmittance at selected hydrogen fluoride (2.7 micrometer) and deuterium fluoride (3.8 micrometer) laser transitions. The IHR was installed aboard a KC-135 aircraft for an airborne atmospheric measurements program that used the sun as a backlighting source for the transmission measurements. The critical components are: a wideband indium antimonide (1nSb) photomixer, a CW HF/DF laser L0, a radiometric processor, and a 1900 K blackbody reference source. The measured heterodyne receiver sensitivity (NEP) is 1.3 x 10 to the -19th power W/Hz, which yields a calculated IHR temperature resolution accuracy of delta I sub S/-3 sub S = 0.005 for a source temperature of 1000 K and a total transmittance of 0.5. Measured atmospheric transmittance at several wavelengths and aircraft altitudes from 9.14 km (30,000 ft) to 13.72 km (45,000 ft) were obtained during the measurements program and have been compared with values predicted by the AFGL Atmospheric Line Parameter Compilation