Parallel integer relation detection: techniques and applications

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Estimating Functions of Probability Distributions from a Finite Set of Samples, Part 1: Bayes Estimators and the Shannon Entropy

We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, we present finite sample estimators for the mutual information, covariance, and chi-squared functions of that probability distribution.Comment: uuencoded compressed tarfile, submitte

UK Rules For Unfired Pressure Vessels

The present code PD 5500, formerly BS 5500 [1] evolved partly from the well-known BS 1500 [2] in the 1950's and BS 1515 [3] first published in 1965; the latter permitted higher level allowable stresses and more advanced rules. In 1969, following a report from the Committee of Enquiry into the Pressure Vessel Industry, the British Standards Institution brought all the pressure vessel interests together under one general committee in order to rationalise the activity. This became PVE/ and presides over a large committee structure. There are a series of functional sub-committees who deal with specific aspects and a large number of technical committees as well as many additional sub committees and working groups. Most of these meet regularly. The technical committee PVE/1, Pressure Vessels, has overall responsibility for BS 5500. The functional committee PVE/1/15 Design Methods has an overall responsibility relating to 'Design' with particular reference to the design section of BS 5500 (Section 3). The first edition of BS 5500 was issued in 1976. The actual issue was delayed for some time because, in the early 1970's, there was an attempt in Europe to produce an international pressure vessel standard. A draft of the international standard appeared as ISO DIS 2694 [4] in 1973 but it was not generally accepted and the attempt was abandoned in the mid 70's. It was decided to use some of the material from 2694 within BS 5500 so that although the Standard was long delayed it benefited to some extent from the international efforts. Initially, committee PVE/l set out the concept of a "master" pressure vessel standard which could readily be applied to any vessel in either ferrous or non-ferrous materials and for highly specialised application with the minimum of supplementary requirements. The layout of BS 5500 is consistent with this concept and although the Standard has perhaps not fulfilled this high ideal, it has certainly been employed widely in many industries including non pressure vessel type applications. When issued it had a number of distinctive features compared with other pressure codes viz; weld joint factors were removed, the present three categories of construction were introduced, there was a new novel external pressure section, it has a loose leaf format and an annual updating was introduced. Further editions of BS 5500 have been issued every three years since 1982

Can the curvaton paradigm accommodate a low inflation scale?

The cosmological curvature perturbation may be generated when some `curvaton' field, different from the inflaton, oscillates in a background of unperturbed radiation. In its simplest form the curvaton paradigm requires the Hubble parameter during inflation to be bigger than 10^7\GeV, but this bound may be evaded if the curvaton field (or an associated tachyon) is strongly coupled to a field which acquires a large value at the end of inflation. As a result the curvaton paradigm might be useful in improving the viability of low-scale inflation models, in which the supersymmetry-breaking mechanism is the same as the one which operates in the vacuum.Comment: 8 pages. This version will appear in PLB, contains another inequality with no essential change in the conclusio