The quantum duality principle

The "quantum duality principle" states that the quantization of a Lie bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a quantization of the dual Lie bialgebra (through its associated formal Poisson group) - via a quantum formal series Hopf algebra (QFSHA) - and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more precisely, there exist functors QUEA --> QFSHA and QFSHA --> QUEA, inverse of each other, such that in either case the Lie bialgebra associated to the target object is the dual of that of the source object. Such a result was claimed true by Drinfeld, but seems to be unproved in literature: we give here a complete detailed proof of it.Comment: 19 pages, AMS-TeX file. The paper has been entirely re-written: in particular, we add a discussion of the possible generalisation of the main result to the infinite dimensional case. This is the author's file of the final version (after the refereeing process), as sent for publicatio

A fail safe laser activated switch used as an emergency control link at the Langley Vortex Research Facility

A fail safe light activated switch was used as an emergency control link at the Langley Vortex Research Facility. In this facility aircraft models were towed through a still air test chamber by a gasoline powered vehicle which was launched from one end of a 427-meter track and attained velocities to 31 m/sec in the test chamber. A 5 mW HeNe laser with a mechanical copper provided a connecting link with the moving tow vehicle on which a silicon photodiode receiver with a specially designed amplifier provided a fail safe switching action. This system provided an emergency means of stopping the vehicle by turning off the laser to interrupt the power to the vehicle ignition and brake release systems

Characteristics of capacitor-type micrometeoroid flux detectors when impacted with simulated micrometeoroids

A series of impact tests are described and data presented which characterize the operation of the capacitor-type micrometeoroid flux detectors used on the Meteoroid Technology Satellite (MTS). Capacitor-type detectors with silicon dioxide dielectric thickness of 0.4 and 1.0 microns were tested in the micrometeoroid impact simulator at the Langley Research Center, a 4-MV Van de Graaff electrostatic accelerator. The carbonyl iron projectiles were from 0.5 to 5.0 microns in diameter with velocities from 4 to 10.0 km/sec. The detector bias voltage was varied from -20 to -60 V; some tests were at detector temperatures of 90 C to -100 C; and the angle of impact varied from 0 deg to 75 deg from the normal to the detector. These tests showed that: (1) the detector operation is reliable when the bias voltage is greater than 30 V; (2) after an impact the detector returns to its original condition with an insignificant loss of active area; and (3) the sensitivity of the detector is inversely proportional to the detector thickness. The test results suggest a theoretical model in which the signal is an arc triggered by the impacting projectile, and the detector bias voltage must be high enough to insure that an arc will form

Twisting algebras using non-commutative torsors

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchange