Super stellar clusters with a bimodal hydrodynamic solution: an Approximate Analytic Approach

We look for a simple analytic model to distinguish between stellar clusters undergoing a bimodal hydrodynamic solution from those able to drive only a stationary wind. Clusters in the bimodal regime undergo strong radiative cooling within their densest inner regions, which results in the accumulation of the matter injected by supernovae and stellar winds and eventually in the formation of further stellar generations, while their outer regions sustain a stationary wind. The analytic formulae are derived from the basic hydrodynamic equations. Our main assumption, that the density at the star cluster surface scales almost linearly with that at the stagnation radius, is based on results from semi-analytic and full numerical calculations. The analytic formulation allows for the determination of the threshold mechanical luminosity that separates clusters evolving in either of the two solutions. It is possible to fix the stagnation radius by simple analytic expressions and thus to determine the fractions of the deposited matter that clusters evolving in the bimodal regime blow out as a wind or recycle into further stellar generations.Comment: 5 pages, 4 figures, accepted by A&

Indispensable binomials in semigroup ideals

In this paper, we deal with the problem of uniqueness of minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for uniqueness of such minimal system of generators. These conditions come from the study and combinatorial description of the so-called indispensable binomials in the semigroup ideal.Comment: 11 pages. This paper was initially presented at the II Iberian Mathematical Meeting (http://imm2.unex.es). To appear in the Proc. Amer. Math. So

The short resolution of a semigroup algebra

This work generalizes the short resolution given in Proc. Amer. Math. Soc. \textbf{131}, 4, (2003), 1081--1091, to any affine semigroup. Moreover, a characterization of Ap\'{e}ry sets is given. This characterization lets compute Ap\'{e}ry sets of affine semigroups and the Frobenius number of a numerical semigroup in a simple way. We also exhibit a new characterization of the Cohen-Macaulay property for simplicial affine semigroups.Comment: 12 pages. In this new version, some proofs have been detailed, the references on the computatation of the Frobenius number of a numerical semigroup have been updated and some typpos have been correcte

On Optimal Detection of Point Sources in CMB Maps

Point-source contamination in high-precision Cosmic Microwave Background (CMB) maps severely affects the precision of cosmological parameter estimates. Among the methods that have been proposed for source detection, wavelet techniques based on ``optimal'' filters have been proposed.In this paper we show that these filters are in fact only restrictive cases of a more general class of matched filters that optimize signal-to-noise ratio and that have, in general, better source detection capabilities, especially for lower amplitude sources. These conclusions are confirmed by some numerical experiments. \keywords{Methods: data analysis -- Methods: statisticalComment: 6 pages, 3 figure

Chandra view of Kes 79: a nearly isothermal SNR with rich spatial structure

A 30 ks \chandra ACIS-I observation of Kes 79 reveals rich spatial structures, including many filaments, three partial shells, a loop and a ``protrusion''. Most of them have corresponding radio features. Regardless of the different results from two non-equilibrium ionization (NEI) codes, temperatures of different parts of the remnant are all around 0.7 keV, which is surprisingly constant for a remnant with such rich structure. If thermal conduction is responsible for smoothing the temperature gradient, a lower limit on the thermal conductivity of $\sim$ 1/10 of the Spitzer value can be derived. Thus, thermal conduction may play an important role in the evolution of at least some SNRs. No spectral signature of the ejecta is found, which suggests the ejecta material has been well mixed with the ambient medium. From the morphology and the spectral properties, we suggest the bright inner shell is a wind-driven shell (WDS) overtaken by the blast wave (the outer shell) and estimate the age of the remnant to be $\sim$ 6 kyr for the assumed dynamics. Projection is also required to explain the complicated morphology of Kes 79.Comment: 12 pages, 6 figures (3 in color), ApJ, in press, April 20, 200

Bidding Strategies in Internet Yankee Auctions: Theory and Evidence

In the past few years, we have witnessed a tremendous proliferation of transactions using the Internet as a virtual marketplace. U.S. News and World Report estimates the value of electronic commerce around $13 billion in 1998. In addition to transactions where prices are posted, sellers also use Internet auctions to sell goods such as clothing, collectibles, computers, and electronics. Current estimates place the value of auction transactions in the Internet at$30 million per week. A popular format for Internet auctions is the Yankee format. Here, a seller offers k identical units for sale, and bidders specify how many units they want and the per-unit price they want to pay. Bidding takes place progressively over a predetermined time period and the k highest bids at closing win the units at their specified prices. Ties are broken on the basis of quantities first and time of bidding second. Two features make these auctions different from standard auctions. First, unlike "live" auctions with fixed participation costs, entering each bid may be costly in a Yankee auction since bidding takes place over several hours (or days) and, in addition to connectivity cost, several minutes time must spend several registering the new price. Second, each time the bidder visits the auction site, she is uncertain about the competition since it is possible for more bidders to decide to enter before the closing. Here, we derive and characterize equilibrium strategies in simple Yankee auctions with stochastic demand. We show that costly bidding may induce bidders to bid high or jump bid in earlier rounds. These jump bids play a signaling role; they attempt to discourage later bidders from competing with established bidders. This way, under some conditions, both sender and receiver of the signal may be better off in equilibrium. The sender because deterring competition saves her the costs of additional bids, and the receiver because she avoids the costs of fruitless early competition. Here, we derive conditions on bidding costs and bidder types that result in a signaling equilibrium of this nature. We show that the characteristics of the equilibrium are closely related to the structure of demand uncertainty faced by the bidders since signal bidding has more strategic value when bidders anticipate further competition later in the auction. We use data from hundreds of Yankee Auctions to test some predictions of the jump-bidding model. In confirmation, we find (a) over 40% of the bidders in our sample enter jump bids, (b) any individual bidder is more likely to enter a jump bid as his first bid, (c) earlier bidders are more likely to enter jump bids than later bidders, (d) the relative size of a jump bid is increasing in the number of bidders relative to units being sold, and (e) the relative size of a jump bid is decreasing in the object's average value. We conclude with a discussion of the implications of costly bidding and jump-bidding strategies on Internet auction design.