On Einstein four-manifolds with <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-actions

We study closed Einstein 4-manifolds which admit S¹ actions of a certain type, i.e., warped products. In particular, we classify them up to isometry when the fixed point of the S¹ action satisfies certain natural geometric conditions. The proof uses the Bochner-Weitzenböck formula for 1-forms and the theory of minimal surfaces in 3-manifolds.in final form: 22 January 2003     

Uncertainty principle and the horizon size of our universe

Quantum uncertainties prevent simultaneous measurement of the expansion factor S(t) and its time derivative . Consequently the Hubble size has an inherent uncertainty in the quantum state that describes the semiclassical evolution of the universe. We show that the quantum uncertainty in the Hubble size of the universe is amplified to unacceptably large values in any inflationary process.This essay received an honorable mention from the Gravity Research Foundation, 1986-Ed.     

Structure and extinction of counterflow diffusion flames above condensed fuels: Comparison between poly(methyl methacrylate) and its liquid monomer,both burning in nitrogen–air mixtures

Since poly(methyl methacrylate) is known to depolymerize largely to its monomer when heated, the chemical kinetics in the gaseous diffusion flame produced by this polymer in a fire may coincide with that of burning liquid methyl methacrylate. To test this hypothesis, flat diffusion flames were probed and extinguished adjacent to surfaces of each of these fuels. Profiles of temperature and of concentrations of stable chemical species are reported, as are gas velocities of approach flow required to produce extinction for various oxygen/nitrogen ratios of the stream. Results revealed structural differences attributable to differing thermal properties of the fuels. Many fuel species were observed in the gas phase, their profiles being partially rationalized on the basis of a suggested decomposition mechanism for gaseous methyl methacrylate. Overall kinetic parameters for gasphase combustion, obtained by use of extinction results in a previously developed theory, are nearly the same for the polymer and monomer but appear to differ by amounts exceeding experimental uncertainties. It is suggested that this may be traced to small differences in fuel species leaving the condensed phase which, for the polymer, is covered by a thin, two-phase region.     

Spectrophotometric determination of rhenium with di(2-pyridyl)ketone-2-furancarbothiohydrazone and other thiohydrazones

A simple rapid method is proposed for the determination of rhenium (as perrhenate) in which the brown-violet complex produced is measured at 546 nm. The system obeys Beer's law in the range 0.7–14.0 μg Re ml^-1; the molar absorptivity is 1.51 × 10⁴ l mol^-1 cm^-1 in ethanol and 1.64 × 10⁴ l mol^-1 cm^-1 for the complex extracted into methyl isobutyl ketone. Molybdenum (100-fold), tungsten (40-fold), copper (10-fold), and palladium (10-fold) are tolerable. Reactions of other metal ions such as Cu(II), Ni(II), Co(II) and Fe(II) with this ligand and reactions of perrhenate with analogous reagents are discussed.