An identification of the connections of Quillen and Beilinson-Schechtman

Given a family of Riemann surfaces and a holomorphic vector bundle Beilinson and Schechtman construct a canonical connection on the associated determinant bundle. We prove the conjecture which states that their connection coincides with the Quillen connection. This is done by reducing to the case where along fibers are invertible. Both connection forms become more accessible in this case.Supported in part by N.S.F. Grant No. DMS-9201022Supported in part by National Science Council of Republic of China Grant No. NSC 82-0208-M-002-125-T, and NSERC of Canada Grant No. OGP 0121883     

Molecular-dynamics studies of bending mechanical properties of empty and C60-filled carbon nanotubes under nanoindentation

This paper utilizes molecular-dynamics simulations to investigate the mechanical characteristics of a suspended (10, 10) single-walled carbon nanotube (SWCNT) during atomic force microscopy (AFM) nanoindentation at different temperatures. Spontaneous topological transition of the Stone-Wales (SW) defects is clearly observed in the indentation process. The present results indicate that under AFM-bending deformation, the mechanical properties of the SWCNT, e.g., the bending strength, are dependent on the wrapping angle. In addition, it is also found that the radial dependence of the reduced formation energy of the SW defects is reasonably insensitive only for the small tubes. However, for tube diameters greater than 2.4 nm [corresponding to the (18, 18) CNT], the SW defects tend to be more radius sensitive. The results indicate that the bending strength decreases significantly with increasing temperature. This study also investigates the variation in the mechanical properties of the nanotube with the density of C60 encapsulated within the nanotube at various temperatures. It is found that, at lower temperatures, the bending strength of the C60-filled nanotube increases with C60 density. However, the reverse tendency is observed at higher temperatures. Finally, the "sharpest tip" phenomena between the probe and the tube wall and the elastic recovery of the nanotube during the retraction process are also investigated.     

Defect clusters and precipitation/oxidation of MgO-Co1−xO solid solution

MgO and Co_1−xO powders in 9:1 and 1:9 molar ratio (denoted as M₉C₁ and M₁C₉, respectively) were sintered and homogenized at 1600°C followed by annealing at 850°C and 800°C, respectively to form defect clusters and precipitates. Analytical electron microscopic observations indicated the protoxide remained as rock salt structure with complicated planar diffraction contrast for M₉C₁ sample, however with spinel paracrystal precipitated from the M₁C₉ sample due to the assembly of charge- and volume-compensating defects of the 4:1 type, i.e., four octahedral vacant sites surrounding one Co³⁺-filled tetrahedral interstitial site. The spacing of such defect clusters is 4.5 times the lattice spacing of the average spinel structure of Mg-doped Co_3−δO₄, indicating a higher defect cluster concentration than undoped Co_3−δO₄. The {111} faulting of Mg-doped Co_3−δO₄/Co_1−xO in the annealed M₁C₉ sample implies the possible presence of zinc blend-type defect clusters with cation vacancies assembled along oxygen close packed (111) plane.     

Time-weighted average sampling of airborne n-valeraldehyde by a solid-phase microextration device

A solid-phase microextraction (SPME) device was used as a time-weighted average sampler for n-valeraldehyde. The SPME device was first modified to improve the wearer's acceptance as a passive sampler. Then a poly(dimethylsiloxane)-divinylbenzene fiber was used and O-2,3,4,5,6-(pentafluorobenzyl)hydroxylamine hydrochloride (PFBHA) was loaded onto the fiber. Vapors of known concentrations around the threshold limit values time-weighted average of n-valeraldehyde and specific relative humidities (RHs) were generated by syringe pumps in a dynamic generation system. n-Valeraldehyde vapors in gas bags were also generated. An exposure chamber was designed to allow measurement of face velocities, temperatures, exposing vapor concentrations, and RHs. Gas chromatography with flame ionization detection was used for sample analysis. The appropriate adsorption time for SPME coating PFBHA was determined to be 2 min and the desorption time for oxime formed after sampling was optimized to be 2 min. The experimental sampling constant was found to be (3.86+/-0.13) x 10(-2) cm3/min and face velocity was not expect to have effect on the sampler.     

An α-γ coincidence technique for measuring226Ra concentrations in water

The application of an α-γ coincidence method for measuring²²⁶Ra concentrations in water is investigated. the experimental system, sample preparation, and results of several measurements are discussed. In addition, the lower limit of detection for the coincidence system is calculated.     

Completely geometrically optimized DFT/ONIOM triple-helical collagen-like structures containing the ProProGly, ProProAla, ProProDAla, and ProProDSer triads

We report completely optimized ONIOM DFT/AM1 molecular orbital calculations on several collagen-like triple helices based upon the repeating triad, ProProGly. The requirement of Gly as every third amino acid in collagen can be attributed to its enantiomorphic nature, as it behaves as a Damino acid in collagen. We, therefore, explored related collagen-like triple helices with one of the central Gly's mutated to either L or DAla; l-Ala appreciably destabilizes, while d-Ala slightly stabilizes the triple helical structure. Mutation of the same Gly to DSer, which is simply DAla with an OH in place of one of the methyl H's, induces a much greater stabilization due to an additional H-bond formed between this OH and a C=O on an adjacent peptide strand. Energies are presented for the triple helices and their component strands (both optimized and distorted to their triple helical geometries) relative to the component amino acids. The variation of relative energies with the chosen reference is delineated.     

On the stereochemistry of photoaddition between α,β-unsaturated ketones and olefins—II

Some years ago an empirical rule, which allows the prediction of product stereochemistry in cis-photocycloaddition reactions of α,β-unsaturated ketones and olefins was tentatively proposed. Several additional examples, both selected from the literature and synthesized in our laboratory, seem to strengthen the validity of the rule.