Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlev\'e Equations

To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima's quiver variety with no stability parameter/framing if the integers attached on the vertices are all equal to one. The construction of reflection functors for quiver varieties are generalized to our case, in which these relate to simple reflections in the Weyl group of some symmetrizable, possibly non-symmetric Kac-Moody algebra. The moduli spaces of meromorphic connections on the rank 2 trivial bundle over the Riemann sphere are described as our manifolds. In our picture, the list of Dynkin diagrams for Painlev\'e equations is slightly different from (but equivalent to) Okamoto's

Geometry of Multiplicative Preprojective Algebra

Crawley-Boevey and Shaw recently introduced a certain multiplicative analogue of the deformed preprojective algebra, which they called the multiplicative preprojective algebra. In this paper we study the moduli space of (semi)stable representations of such an algebra (the multiplicative quiver variety), which in fact has many similarities to the quiver variety. We show that there exists a complex analytic isomorphism between the nilpotent subvariety of the quiver variety and that of the multiplicative quiver variety (which can be extended to a symplectomorphism between these tubular neighborhoods). We also show that when the quiver is star-shaped, the multiplicative quiver variety parametrizes Simpson's (poly)stable filtered local systems on a punctured Riemann sphere with prescribed filtration type, weight and associated graded local system around each puncture.Comment: 51pages; corrected typos and references; changed font; v4 is the same as v3 except margi

Apparatus and method to keep the walls of a free-space reactor free from deposits of solid materials

An apparatus and method is disclosed for keeping interior walls of a reaction vessel free of undesirable deposits of solid materials in gas-to-solid reactions. The apparatus includes a movable cleaning head which is configured to be substantially complementary to the interior contour of the walls of the reaction vessel. The head ejects a stream of gas with a relatively high velocity into a narrow space between the head and the walls. The head is moved substantially continuously to at least intermittently blow the stream of gas to substantially the entire surface of the walls wherein undesirable solid deposition is likely to occur. The disclosed apparatus and process is particularly useful for keeping the walls of a free-space silane-gas-to-solid-silicon reactor free of undesirable silicon deposits

Radiation effects on three low-power microcircuits

Irradiation of several low power circuit elements by Co-60 gamma radiation, low and high energy electrons, and neutrons is discussed. The bipolar circuits were SE480 Q NAND gate, and a micropower frequency divider was used in electronic wrist watches. The MOS device was a dual p-channel MOSFET

The effects of impurities on the performance of silicon solar cells

The major factors that determine the tolerable concentrations of impurities in silicon feedstock for solar cells used in power generation are discussed in this report. It is concluded that a solar-grade silicon can be defined only for a specific manufacturing process. It is also concluded that it is the electrical effects, efficiency and resistivity, that are dominant in determining tolerable concentrations of impurities in the silicon feedstock. Crystal growth effects may become important when faster growth rates and larger crystal diameters are developed and used