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The first demonstration of laser action in ruby was made in 1960 by T. H. Maiman of Hughes Research Laboratories, USA. Many laboratories worldwide began the search for lasers using different materials, operating at different wavelengths. In the UK, academia, industry and the central laboratories took up the challenge from the earliest days to develop these systems for a broad range of applications. This historical review looks at the contribution the UK has made to the advancement of the technology, the development of systems and components and their exploitation over the last 60 years.
We present Faint Object Camera (FOC) ultraviolet images of the central 14 x 14″ of Messier 31 and Messier 32. The hot stellar population detected in the composite UV spectra of these galaxies is partially resolved into stars, and we measure their colors and apparent magnitudes. We detect 433 stars in M31 and 138 stars in M32, down to limits of mF275W = 25.5 mag and mF175W = 24.5 mag. We investigate the luminosity functions of the sources, their spatial distribution, their color-magnitude diagrams, and their total integrated far-UV flux. Although M32 has a weaker UV upturn than M31, the luminosity functions and color-magnitude diagrams of M31 and M32 are surprisingly similar, and are inconsistent with a majority contribution from any of the following: post-AGB stars more massive than 0.56 M⊙, main sequence stars, or blue stragglers. The luminosity functions and color-magnitude diagrams are consistent with a dominant population of stars evolving from the extreme horizontal branch (EHB) along tracks of mass 0.47–0.53 M⊙. These stars are well below the detection limits of our images while on the zero-age EHB, but become detectable while in the more luminous (but shorter) post-HB phases. Our observations require that only a very small fraction of the main sequence population (2% in M31 and 0.5% in M32) in these two galaxies evolve though the EHB and post-EHB phases, with the remainder rapidly evolving through bright post-AGB evolution with few resolved stars expected in the small field of view covered by the FOC.
Two players with differing amounts of money simultaneously choose an amount to bet on an even-money win-or-lose bet. The outcomes of the bets may be dependent and the player who has the larger amount of money after the outcomes are decided is the winner. This game is completely analyzed. In nearly all cases, the value exists and optimal strategies for the two players that give weight to a finite number of bets are explicitly exhibited. In a few situations, the value does not exist.
We consider a generalization of the house-selling problem to selling k houses. Let the offers, X1, X2, · ··, be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N1, · ··, Nk, one for each component. The payoff is the sum over j of the jth component of minus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.
Cowan (1992) has addressed the question of how a team should allocate its players to achieve the optimal balance between offence and defence. He posed a simple territorial game called ‘Teamball' and derived a saddle-point solution under conditions which are claimed to be fairly general. In this paper we find that some restrictions are indeed required, leading to an interesting analysis.
The full-information secretary problem in which the objective is to minimize the expected rank is seen to have a value smaller than 7/3 for all n (the number of options). This can be achieved by a simple memoryless threshold rule. The asymptotically optimal value for the class of such rules is about 2.3266. For a large finite number of options, the optimal stopping rule depends on the whole sequence of observations and seems to be intractable. This raises the question whether the influence of the history of all observations may asymptotically fade. We have not solved this problem, but we show that the values for finite n are non-decreasing in n and exhibit a sequence of lower bounds that converges to the asymptotic value which is not smaller than 1.908.
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