Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus

We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6, and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on "Standard tractors and the conformal ambient metric construction" (A. Cap and A.R. Gover, math.DG/0207016), where the relationship of the normal standard tractor bundle to the ambient construction is described.Comment: 42 pages. No figures. Record of changes: V1, 15 January 2002: Original posting. V2, 17 January 2002: Changing comment fields. Leaving abstract and text of article unchanged. V3, 1 February 2003: Minor changes and typographical corrections throughout articl

High-temperature oxidation and erosion-resistant refractory coatings

Various refractory coating systems were evaluated for rocket nozzle applications by actual rocket test firings. A reference is noted which identifies failure mechanisms and gives results of the firing tests for 18 coating systems. Iridium, iridium-rhenium, and hafnium oxide-zirconium oxide coatings show most promising results

Design procedure for low-drag subsonic airfoils

Airfoil has least amount of drag under given restrictions of boundary layer transition position, lift coefficient, thickness ratio, and Reynolds number based on airfoil chord. It is suitable for use as wing and propeller aircraft sections operating at subsonic speeds and for hydrofoil sections and blades for fans, compressors, turbines, and windmills

Stability of the Submillimeter Brightness of the Atmosphere Above Mauna Kea, Chajnantor and the South Pole

The summit of Mauna Kea in Hawaii, the area near Cerro Chajnantor in Chile, and the South Pole are sites of large millimeter or submillimeter wavelength telescopes. We have placed 860 GHz sky brightness monitors at all three sites and present a comparative study of the measured submillimeter brightness due to atmospheric thermal emission. We report the stability of that quantity at each site.Comment: 6 figure