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.     

Organic phase conversion of bulk (wurtzite) ZnO to nanophase (wurtzite and zinc blende) ZnO

We describe the all-organic phase conversion of bulk commercial ZnO in the wurtzite modification to sub-30 nm ZnO that we find to be partially in the zinc blende [, a=4.568(3) Å] modification. The conversion involves refluxing ZnO in 2,4-pentanedione (acetylacetone) at 413 K to form the zinc 2,4-pentanedionate, which is decomposed by heating at 573 K in an appropriate high-temperature solvent such as dibenzylether to form nanophase ZnO. This nanophase, partially zinc blende ZnO can also be obtained in a single step by heating commercial zinc 2,4-pentanedionate in refluxing dibenzylether. Thermodiffractometry suggests that the conversion of zinc blende ZnO to wurtzite ZnO commences near 650 K.     

Potential energy curve of 1Σ+ Li+/He

The potential energy curve of the system Li⁺/He has been determined with moderately large basis sets for 0.5 ? r ? 10.0 a₀ both at the SCF level and including correlation. The present SCF results predict a deeper well (?0.00248 au) at a smaller r(3.66 a₀) compared with earlier calculations. Correlation deepens the well further (?0.00274 au), but pulls it inward slightly (3.63 a₀). In the repulsive part the calculated curve lies above the experimental one, especially at shorter distances. A similar behavior has been noted in the systems Li⁺/H₂, Li⁺/CO and Li⁺/N₂, suggesting that the experimental determinations may underestimate the interaction in this region by 10–20%.     

A novel transformation of O-methyldalbergin

O-methyldalbergin and related 4-phenylcoumarins are markedly different from ordinary coumarins in their behaviour towards alkali. They are stable in boiling alkali and on addition of mercuric oxide yield coumarilic acids. Phenyl-coumarilic acids undergo decarboxylation readily when boiled with aqueous alcoholic mercuric chloride to yield phenyl substituted coumarones.     

An ab initio method for approximation of the frozen molecular fragment

An ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by frozen molecular fragment is presented. In the following method the SCF calculations are performed in two series. First the molecular orbitals resulting from the first SCF calculation (modest basis set) are localized. In the second SCF run, the basis set is extended for the active part of the molecule, while molecular orbitals of the inactive part, selected from the localized set, are kept frozen. The results are in good agreement with the extended basis set calculation.