Profinite completions and canonical extensions of Heyting algebras

We show that the profinite completions and canonical extensions of bounded distributive lattices and of Boolean algebras coincide. We characterize dual spaces of canonical extensions of bounded distributive lattices and of Heyting algebras in terms of Nachbin order-compactifications. We give the dual description of the profinite completion H of a Heyting algebra H, and characterize the dual space of H. We also give a necessary and sufficient condition for the profinite completion of H to coincide with its canonical extension, and provide a new criterion for a variety V of Heyting algebras to be finitely generated by showing that V is finitely generated if and only if the profinite completion of every member of V coincides with its canonical extension. From this we obtain a new proof of a well-known theorem that every finitely generated variety of Heyting algebras is canonical

MPGDs in Compton imaging with liquid-xenon

The interaction of radiation with liquid xenon, inducing both scintillation and ionization signals, is of particular interest for Compton-sequences reconstruction. We report on the development and recent results of a liquid-xenon time-projection chamber, dedicated to a novel nuclear imaging technique named "3 gamma imaging". In a first prototype, the scintillation is detected by a vacuum photomultiplier tube and the charges are collected with a MICROMEGAS structure; both are fully immersed in liquid xenon. In view of the final large-area detector, and with the aim of minimizing dead-zones, we are investigating a gaseous photomultiplier for recording the UV scintillation photons. The prototype concept is presented as well as preliminary results in liquid xenon. We also present soft x-rays test results of a gaseous photomultiplier prototype made of a double Thick Gaseous Electron Multiplier (THGEM) at normal temperature and pressure conditions.Comment: presented at MPGD09, CRETE, June 2009; to be published in JINST Proceedings, PDF, 10 pages, 11 figure

Sequentially Continuous Linear Mappings in Constructive Analysis

this paper we derive some results about sequentially continuous linear mappings within BISH. These results tend to reinforce our hope that such mappings may turn out to be bounded (continuous) after all. For background material on BISH, see [1], and for information about the relation between BISH, INT, and RUSS, see [2]. 2 Sequential continuity preserves Cauchynes

United States Geological Survey Bulletin 367

Report containing experiments that illustrate the possibility of increasing steam power by increasing the amount of air passing through coal fuel beds and boilers in steam engines