Refinement of higher-order logic programs

A refinement calculus provides a method for transforming specifications to executable code, maintaining the correctness of the code with respect to its specification. In this paper we extend the refinement calculus for logic programs to include higher-order programming capabilities in specifications and programs, such as procedures as terms and lambda abstraction. We use a higher-order type and term system to describe programs, and provide a semantics for the higher-order language and refinement. The calculus is illustrated by refinement examples.

Zirconium alloying and grain refinement of magnesium alloys

Factors that influence alloying zirconium to magnesium with a Mg-33.3Zr master alloy and the subsequent grain refinement are discussed based on a large number of experiments conducted at the laboratory scale (up to 30 kg of melt). It is shown that the zirconium particles released from the Zirmax(R) master alloy must be brought into thorough contact with the melt by an appropriate stirring process in order to attain a good dissolution of zirconium. The influence of alloying temperature on the recovery of zirconium was found to be negligible in the range from 680 to 780 degreesC. An ideal zirconium alloying process should end up with both high soluble and high total zirconium in the melt in order to achieve the best grain refinement in the final alloy. The distribution of zirconium in the final alloy microstructure is inhomogeneous and almost all of the zirconium in solution is concentrated in zirconium-rich cores in the microstructure.

A new zirconium-rich master alloy for the grain refinement of magnesium alloys

A new zirconium-rich magnesium-zirconium master alloy (designated AM-cast) has been developed by the CRC for Cast Metals Manufacturing in collaboration with Australian Magnesium Corporation for use as a grain refiner for magnesium alloys that do not contain aluminium. This work describes the microstructural characteristics of this new grain refiner and its grain refining ability when added to different magnesium alloys under various conditions (alloying temperature from 680 °C to 750 °C; weight of melt from 1 kg to 150 kg and sample thickness from 7 mm to 62 mm). Owing to its highly alloyable microstructure, AM-cast can be readily introduced into molten magnesium at any temperature when assisted by a few minutes of stirring or puddling. Little sludge has been found at the bottom of the alloying vessel in these trials due to the fine zirconium particles contained in the master alloy. The recovery of zirconium is normally in the range from 40% to 60% with respect to 1% zirconium addition as the master alloy. It is shown that this new master alloy is an excellent grain refiner for aluminium-free magnesium alloys.

MACPROP:a revised program for the refinement of satellite orbital parameters

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Global non-dynamic refinement of radial orbit error for altimetric earth satellites

The accuracy of altimetrically derived oceanographic and geophysical information is limited by the precision of the radial component of the satellite ephemeris. A non-dynamic technique is proposed as a method of reducing the global radial orbit error of altimetric satellites. This involves the recovery of each coefficient of an analytically derived radial error correction through a refinement of crossover difference residuals. The crossover data is supplemented by absolute height measurements to permit the retrieval of otherwise unobservable geographically correlated and linearly combined parameters. The feasibility of the radial reduction procedure is established upon application to the three day repeat orbit of SEASAT. The concept of arc aggregates is devised as a means of extending the method to incorporate longer durations, such as the 35 day repeat period of ERS-1. A continuous orbit is effectively created by including the radial misclosure between consecutive long arcs as an infallible observation. The arc aggregate procedure is validated using a combination of three successive SEASAT ephemerides. A complete simulation of the 501 revolution per 35 day repeat orbit of ERS-1 is derived and the recovery of the global radial orbit error over the full repeat period is successfully accomplished. The radial reduction is dependent upon the geographical locations of the supplementary direct height data. Investigations into the respective influences of various sites proposed for the tracking of ERS-1 by ground-based transponders are carried out. The potential effectiveness on the radial orbital accuracy of locating future tracking sites in regions of high latitudinal magnitude is demonstrated.