A closer look at semistability for singular principal bundles

We substantially refine the theory of singular principal bundles introduced in a former paper. In particular, we show that we need only honest singular principal bundles in our compactification. These are objects which carry the structure of a rational principal bundle in the sense of Ramanathan. Moreover, we arrive at a much simpler semistability condition. In the case of a semisimple group, this is just the Gieseker-version of Ramanathan's semistability condition for the corresponding rational principal $G$-bundle.Comment: To appear in the International Mathematics Research Notices. V2: Minor correction

Control of a free-flying robot manipulator system

The development of and test control strategies for self-contained, autonomous free flying space robots are discussed. Such a robot would perform operations in space similar to those currently handled by astronauts during extravehicular activity (EVA). Use of robots should reduce the expense and danger attending EVA both by providing assistance to astronauts and in many cases by eliminating altogether the need for human EVA, thus greatly enhancing the scope and flexibility of space assembly and repair activities. The focus of the work is to develop and carry out a program of research with a series of physical Satellite Robot Simulator Vehicles (SRSV's), two-dimensionally freely mobile laboratory models of autonomous free-flying space robots such as might perform extravehicular functions associated with operation of a space station or repair of orbiting satellites. It is planned, in a later phase, to extend the research to three dimensions by carrying out experiments in the Space Shuttle cargo bay

Global Boundedness for Decorated Sheaves

An important classification problem in Algebraic Geometry deals with pairs (\E,\phi), consisting of a torsion free sheaf \E and a non-trivial homomorphism \phi\colon (\E^{\otimes a})^{\oplus b}\lra\det(\E)^{\otimes c}\otimes \L on a polarized complex projective manifold (X,\O_X(1)), the input data $a$, $b$, $c$, \L as well as the Hilbert polynomial of \E being fixed. The solution to the classification problem consists of a family of moduli spaces ${\cal M}^\delta:={\cal M}^{\delta-\rm ss}_{a/b/c/L/P}$ for the $\delta$-semistable objects, where \delta\in\Q[x] can be any positive polynomial of degree at most $\dim X-1$. In this note we show that there are only finitely many distinct moduli spaces among the ${\cal M}^\delta$ and that they sit in a chain of "GIT-flips". This property has been known and proved by ad hoc arguments in several special cases. In our paper, we apply refined information on the instability flag to solve this problem. This strategy is inspired by the fundamental paper of Ramanan and Ramanathan on the instability flag.Comment: To appear in the International Mathematics Research Notices. V2: A few typos corrected (notably in the definition of semistability in the introduction); Expanded Introductio

A high resolution semiconductor detector for applications in space

Nuclear radiation detectors with volumes of approximately 1 cu cm was fabricated from single crystals of germanium-silicon alloy containing as much as 20 weight percent germanium. The properties of these detectors were investigated and will be discussed. Tests reveal that the gamma ray photoelectric peak efficiency of an alloy detector with only 12 weight percent germanium is approximately 4 times that of a silicon detector of equal volume. The room temperature roomure appears to be a good possibility. Storage for long periods at room temperature does not seem to adversely affect these devices. The results of preliminary radiation damage experiments suggest that the alloy detectors possess a radiation damage resistance far greater than that of silicon