Calculation of Exact Estimators by Integration Over the Surface of an n-Dimensional Sphere

This paper reconsiders the problem of calculating the expected set of probabilities , given the observed set of items {m_i}, that are distributed among n bins with an (unknown) set of probabilities {p_i} for being placed in the ith bin. The problem is often formulated using Bayes theorem and the multinomial distribution, along with a constant prior for the values of the p_i, leading to a Dirichlet distribution for the {p_i}. The moments of the p_i can then be calculated exactly. Here a new approach is suggested for the calculation of the moments, that uses a change of variables that reduces the problem to an integration over a portion of the surface of an n-dimensional sphere. This greatly simplifies the calculation by allowing a straightforward integration over (n-1) independent variables, with the constraints on the set of p_i being automatically satisfied. For the Dirichlet and similar distributions the problem simplifies even further, with the resulting integrals subsequently factorising, allowing their easy evaluation in terms of Beta functions. A proof by induction confirms existing calculations for the moments. The advantage of the approach presented here is that the methods and results apply with minimum or no modifications to numerical calculations that involve more complicated distributions or non-constant prior distributions, for which cases the numerical calculations will be greatly simplified

A new intermediate for the production of flexible stable polymers

Method of incorporating ether linkages into perfluoroalkylene segment of a dianydride intermediate yields intermediate that may be used in synthesis of flexible, stable polyimides for use as high-temperature, solvent-resistant sealants

Development of improved potting and conformal coating compounds

Improved organic potting and conformal coating materials protect fragile electronic components and circuitry from mechanical shock and vibration, moisture, and corrosion. These materials meet specifications covering resistance to cycling, radiation, flammability, and sterilizing agents for certain space applications

Making teaching a profession : a comparative view

The traditional role of a 'teacher is that of the guardian and transmitter of spiritual wisdom. Thus in the Christian-west, teaching was originally the prerogative of the priest; in Islam that of the imam or mullah; in India that of the guru. In Europe, despite the growth of humanism and the gradula secion of education during the sixteenth centuries, the teacher in grammar school, gymnasium or lycee retained a special status. He may no longer have solely been concerned with the world of the spirit, but he still had esoteric and professionally useful knowledge that he could pass on to a privileged elite, a status that has been retained to the present century by teachers in universities and selective secondary schools.peer-reviewe

Latest developments in cryogenic safety

The Cryogenic Safety Manual, sponsored by the British Cryogenics Council, was published over 10 years ago. A new updated version is now available. Some general aspects of cryogenic safety are highlighted, and attention is drawn to some of the more unusual hazardous situations. An awareness of the physical properties of the cryogenic fluids being dealt with is important in directing attention to hazardous situations which may arise. Because of this, the more important properties of the cryogenic fluids are given, such as molecular weight, boiling point and freezing point. From these properties, hazardous situations can be deduced. There are hidden dangers that are not always easy to spot. Some of the unexpected hazards, most of which have led to deaths, are: asphyxiation (anoxia), frost bites and hypothermia, explosions, and combustion. The aim of this publication is to help bring about increased safety in the production and use of cryogenic products through a deeper appreciation of the scientific, technological and administrative steps which must be made if accidents, some fatal, are to be voided in the future

Possible safety hazards associated with the operation of the 0.3-m transonic cryogenic tunnel at the NASA Langley Research Center

The 0.3 m Transonic Cryogenic Tunnel (TCT) at the NASA Langley Research Center was built in 1973 as a facility intended to be used for no more than 60 hours in order to verify the validity of the cryogenic wind tunnel concept at transonic speeds. The role of the 0.3 m TCT has gradually changed until now, after over 3000 hours of operation, it is classified as a major NASA research facility and, under the administration of the Experimental Techniques Branch, it is used extensively for the testing of airfoils at high Reynolds numbers and for the development of various technologies related to the efficient operation and use of cryogenic wind tunnels. The purpose of this report is to document the results of a recent safety analysis of the 0.3 m TCT facility. This analysis was made as part of an on going program with the Experimental Techniques Branch designed to ensure that the existing equipment and current operating procedures of the 0.3 m TCT facility are acceptable in terms of today's standards of safety for cryogenic systems