The Star Catalogue of Hevelius

The catalogue by Johannes Hevelius with the positions and magnitudes of 1564 entries was published by his wife Elisabeth Koopman in 1690. We provide a machine-readable version of the catalogue, and briefly discuss its accuracy on the basis of comparison with data from the modern Hipparcos Catalogue. We compare our results with an earlier analysis by Rybka (1984), finding good overall agreement. The magnitudes given by Hevelius correlate well with modern values. The accuracy of his position measurements is similar to that of Brahe, with sigma=2 arcmin for with more errors larger than 5 arcmin than expected for a Gaussian distribution. The position accuracy decreases slowly with magnitude. The fraction of stars with position errors larger than a degree is 1.5 per cent, rather smaller than the fraction of 5 per cent in the star catalogue of Brahe.Comment: Accepted by Astronomy and Astrophysics; 23 pages; 62 figures; 1 table made accessible via CD

The Impact of Market Rules and Market Structure on the Price Determination Process in the England and Wales Electricity Market

This paper argues that the market rules governing the operation of the England and Wales electricity market in combination with the structure of this market presents the two major generators National Power and PowerGen with opportunities to earn revenues substantially in excess of their costs of production for short periods of time. Generators competing to serve this market have two strategic weapons at their disposal: (1) the price bid for each generation set and (2) the capacity of each generation set made available to supply the market each half-hour period during the day. We argue that because of the rules governing the price determination process in this market, by the strategic use of capacity availability declarations, when conditions exogenous to the behavior of the two major generators favor it, these two generators are able to obtain prices for their output substantially in excess of their marginal costs of generation. The paper establishes these points in the following manner. First, we provide a description of the market structure and rules governing the operation of the England and Wales electricity market, emphasizing those aspects that are important to the success of the strategy we believe the two generators use to exercise market power. We then summarize the time series properties of the price of electricity emerging from this market structure and price-setting process. By analyzing four fiscal years of actual market prices, quantities and generator bids into the market, we provide various pieces of evidence in favor of the strategic use of the market rules by the two major participants. The paper closes with a discussion of the lessons that the England and Wales experience can provide for the design of competitive power markets in the US, particularly California, and other countries.

Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators

We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C │x│^(-2) is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and, in particular, for relativistic Schrödinger operators. We also allow for the inclusion of magnetic vector potentials. As an application, we extend, for the first time, the proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zɑ = 2/π, for ɑ less than some critical value