Continuously extending partial functions

We characterize those Hausdorff spaces in which continuous functions defined on compact subsets can be continuously extended to continuous functions defined on the space.

     

Pseudoconvex and disprisoning homogeneous sprays

The pseudoconvex and disprisoning conditions for geodesics of linear connections are extended to the solution curves of general homogeneous sprays. The main result is that pseudoconvexity and disprisonment are jointly stable in the fine topology on the space of all homogeneous sprays of any degree of homogeneity.Partially supported by NSF grant INT-8921666.     

An ab initio and molecular mechanical investigation of ureas and amide derivatives

Ab initio molecular orbital theory with the 6-31G* basis set has been used to investigate the geometries and preferred conformations for urea, derivatives of urea, and a few complicated amide derivatives. The results from the ab initio calculations provide insight into the gas-phase rotational barrier about the C? N bond and have been used to generate parameters for the MM2(87) molecular mechanics program. When applicable, theoretical structures are compared with corresponding previously reported experimental geometries. Urea is predicted to be nonplanar with pyramidal amino groups.     

Determination of the strange quark content of the nucleon from a next-to-leading-order QCD analysis of neutrino charm production

We present the first next-to-leading-order QCD analysis of neutrino charm production, using a sample of 6090 ^– and -induced opposite-sign dimuon events observed in the CCFR detector at the Fermilab Tevatron. We find that the nucleon strange quark content is suppressed with respect to the non-strange sea quarks by a factor =0.477 _–0.053 ^+0.063 , where the error includes statistical, systematic and QCD scale uncertainties. In contrast to previous leading order analyses, we find that the strange seax-dependence is similar to that of the non-strange sea, and that the measured charm quark mass,m _c =1.70±0.19 GeV/c², is larger and consistent with that determined in other processes. Further analysis finds that the difference inx-distributions betweenxs(x) and is small. A measurement of the Cabibbo-Kobayashi-Maskawa matrix element |V _cd |=0.232 _–0.020 ^+0.018 is also presented.     

The oxidation of diamond: the geometry and stretching frequency of carbonyl on the (100) surface

Microwave plasma deposited (100) diamond films have been thermally oxidized in dry O2 between 500 and 723 degrees C. The roughness of a single crystalline grain following oxidation is consistent with a layer-by-layer mechanism for the removal of carbon monoxide. The resulting surface exhibits infrared absorption bands at 1731 and 905 cm-1, attributed to the stretching and bending modes of a surface bonded carbonyl group. The former is within 1 cm-1 of the structurally analogous molecule 2-adamantanone. These data are consistent with the carbonyl groups being present on diamond (100) terraces.     

Pressure Transients in Gas Phase Adsorptive Reactors

The role of pressure and flow transients caused by strong adsorption on the behavior of gas phase adsorptive reactors was studied using a staged model. The general gas phase reaction A + B C is considered for two cases: (1) the product C is adsorbed and (2) both reactants A and B are adsorbed. Strong adsorption of one or more components causes a decrease in the pressure(s) in the stage(s). The pressure decrease causes variations in the inlet and outlet flow rates and in the case of multiple stages, it causes variations in the flows between tanks. In accordance with Le Chatelier's principle, the pressure decrease aids or inhibits product formation depending on whether there is an increase or decrease in total moles by reaction. Reactant flow into the section where adsorption occurs increases because of increased pressure drop behind the adsorption front. However, the residence time of the reactants behind the adsorption front is lower because of the higher velocity. The flow variations can aid or hinder product formation depending on the specific conditions. Thus, the adsorption-caused pressure variations directly modify reaction rates and product concentrations and, also indirectly, by causing flow variations which affect reaction rates and product concentrations. This study highlights the need to include pressure variations when modeling gas phase adsorptive reactors if adsorption is strong irrespective of the net change in the total moles by reaction. It also demonstrates a method to incorporate axial pressure drop in staged models.     

Electrostatic potentials and fields in the vicinity of engineered nanostructures

We have developed a method for calculating the electrostatic potentials and fields in the vicinity of geometrically complex engineered nanostructures composed of varying materials in electrolytes of arbitrary pH and ionic strength. The method involves direct summation of charged Debye-Hückel spheres composing the nanostructural surfaces and, by including charge redistribution on the surface of conducting materials held at constant potential, is applicable to mixed boundary conditions. The method is validated by comparison to analytical solutions for an infinite plane (Gouy-Chapman), an infinite cylinder (Bessel functions), and an infinite plane which contains a hole and which is held at constant potential. Excellent agreement between the potentials obtained by our numerical method and the closed form solutions is found for these conditions. The method is applied to the calculation of the electric field enhancement in the vicinity of a nanomembrane whose pore wall is held at constant charge and whose membrane surfaces are held at constant potential. The electric field is found to be enhanced by the charge buildup in the rim of the hole of the nanomembrane; the buildup results from the potential being held constant in the conducting region. Ion concentrations are also calculated. Positive ion rejection is found to be enhanced by this charge buildup in the region of the rim when a constant positive potential is applied.     

Activation/driving force relationships for cyclopropylcarbinyl --> homoallyl-type rearrangements of radical anions

By using direct and indirect electrochemical methods, rate constants (ko) for cyclopropane ring opening of radical anions derived from the one-electron reduction of trans-1-benzoyl-2-phenylcyclopropane, trans-1-benzoyl-2-vinylcyclopropane, 2-methylenecyclopropyl phenyl ketone, spiro[anthracene-9,1'-cyclopropan-10-one], 3-cyclopropylcyclohex-2-en-1-one, and 3-(1-methylcyclopropyl)cyclohex-2-en-1-one were determined. Qualitatively, rate constants for ring opening of these (and other cyclopropyl- and cyclobutyl-containing radical anions) can be rationalized on the basis of the thermodynamic stability of the radical anion, the ability of substituents on the cyclopropyl group to stabilize the radical portion of the distonic radical anion, and the stability of the enolate portion of the distonic radical anion. On the basis of this notion, a thermochemical cycle for estimating deltaG(o) for ring opening was presented. For simple cyclopropyl-containing ketyl anions, a reasonable correlation between log(ko) and deltaG(o) was found, and stepwise dissociative electron transfer theory was applied to rationalize the results. Activation energies calculated with density functional theory (UB3LYP/6-31+G*) correlate reasonably well with measured log(ko). The derived log(ko) and deltaG(o) and log(ko) vs E(a) plots provide the basis for a "calibration curve" to predict rate constants for ring opening of radical anions derived from carbonyl compounds, in general.