A planet transits an 11 th magnitude, G1V star in the constellation Corona Borealis. We designate the planet XO-1b, and the star, XO-1, also known as GSC 02041-01657. XO-1 lacks a trigonometric distance; we estimate it to be 200±20 pc. Of the ten stars currently known to host extrasolar transiting planets, the star XO-1 is the most similar to the Sun in its physical characteristics: its radius is 1.0±0.08 R ⊙ , its mass is 1.0±0.03 M ⊙ , V sini < 3 km s −1 , and its metallicity [Fe/H] is 0.015±0.04. The orbital period of the planet XO-1b is 3.941534±0.000027 days, one of the longer ones known. The planetary mass is 0.90±0.07 M J , which is marginally larger than that of other transiting planets with periods between 3 and 4 days. Both the planetary radius and the inclination are functions of the spectroscopically determined stellar radius. If the stellar radius is 1.0±0.08 R ⊙ , then the planetary radius is 1.30±0.11 R J and the inclination of the orbit is 87.7±1.2 • . We have demonstrated a productive international

We prove a new symplectic analogue of Kashiwara's equivalence from D -module theory. As a consequence, we establish a structure theory for module categories over deformation-quantizations that mirrors, at a higher categorical level, the Białynicki-Birula stratification of a variety with an action of the multiplicative group G m . The resulting categorical cell decomposition provides an algebrogeometric parallel to the structure of Fukaya categories of Weinstein manifolds. From it, we derive concrete consequences for invariants such as K -theory and Hochschild homology of module categories of interest in geometric representation theory. 53D55; 14F05

We give conditions for determining the extremal behavior for the (graded) Betti numbers of squarefree monomial ideals. For the case of non-unique minima, we give several conditions which we use to produce infinite families, exponentially growing with dimension, of Hilbert functions which have no smallest (graded) Betti numbers among squarefree monomial ideals and all ideals. For the case of unique minima, we give two families of Hilbert functions, one with exponential and one with linear growth as dimension grows, that have unique minimal Betti numbers among squarefree monomial ideals.

We study a certain cycle map defined on finite dimensional modules for the W-algebra with regular integral central character. Via comparison with the theory in postive characteristic, we show that this map injects into the top Borel-Moore homology group of a Springer fibre. This is the first result in a larger program to completely desribe the finite dimensional modules for the W algebras.

The setting of a process mean for a manufacturing process which frequently produces scrap and rework, can significantly affect profitability. Optimal mean setting is a methodology by which the process mean is adjusted to maximise profit. This paper studies the dynamics of the problem and investigates the possibility of applying different process means to each rework iteration, to further maximise profit. A proof is given confirming there is only one optimal mean that applies over all rework iterations in the single feature case. However, applying similar reasoning to a dual feature case led to the development of a new optimal mean setting methodology which outperformed the existing approach in terms of the maximum expected profit.