Existence and uniqueness of rectilinear slit maps

We consider a generalization of the parallel slit uniformization in which the angle of inclination of each image slit is assigned independently. Koebe proved that for domains of finite connectivity there is, up to a normalization, a unique rectilinear slit map achieving any given angle assignment. Koebe's theorem is partially extended to domains of infinite connectivity. A uniqueness result is shown for domains of countable connectivity and arbitrary angle assignments, and an existence result is proved for arbitrary domains under the assumption that the angle assignment is continuous and has finite range. In order to prove the existence result a new extremal length tool, called the crossing-module, is introduced. The crossing-module allows greater freedom in the family of admissible arcs than the classical module. Several results known for the module are extended to the crossing-module. A generalization of Jenkins' module condition for the parallel slit problem is given for the rectilinear slit problem in terms of the crossing-module and it is shown that rectilinear slit maps satisfying this crossing-module condition exist.

     

Simulation from Wishart Distributions with Eigenvalue Constraints

Abstract

This article provides an efficient algorithm for generating a random matrix according to a Wishart distribution, but with eigenvalues constrained to be less than a given vector of positive values. The procedure of Odell and Feiveson provides a guide, but the modifications here ensure that the diagonal elements of a candidate matrix are less than the corresponding elements of the constraint vector, thus greatly improving the chances that the matrix will be acceptable. The Normal hierarchical model with vector outcomes and the multivariate random effects model provide motivating applications.     

Reaction of silanes in supercritical CO2 with TiO2 and Al2O3

Infrared spectroscopy was used to investigate the reaction of silanes with TiO2 and Al2O3 using supercritical CO2 (Sc-CO2) as a solvent. It was found that contact of Sc-CO2 with TiO2 leads to partial removal of the water layer and to the formation of carbonate, bicarbonate, and carboxylate species on the surface. Although these carbonate species are weakly bound to the TiO2 surface and can be removed by a N2 purge, they poison the surface, resulting in a lower level of reaction of silanes with TiO2. Specifically, the amount of hexamethyldisilazane adsorbed on TiO2 is about 10% of the value obtained when the reaction is performed from the gas phase. This is not unique to TiO2, as the formation of carbonate species also occurs upon contact of Al2O3 with Sc-CO2 and this leads to a lower level of reaction with hexamethyldisilazane. This is in contrast to reactions of silanes on SiO2 where Sc-CO2 has several advantages over conventional gaseous or nonaqueous methods. As a result, caution needs to be applied when using Sc-CO2 as a solvent for silanization reactions on oxides other than SiO2.     

Multiorbital interactions during Acyl radical addition reactions involving imines and electron-rich olefins

Ab initio and DFT calculations reveal that acyl radicals add to imines and electron-rich olefins through simultaneous SOMO --> pi*, pi --> SOMO, and HOMO --> pi*C=O interactions between the radical and the radicalophile. At the CCSD(T)/aug-cc-pVDZ//QCISD/cc-pVDZ level, energy barriers of 15.6 and 17.9 kJ mol(-1) are calculated for the attack of the acetyl radical at the carbon and nitrogen ends of methanimine, respectively. These barriers are 17.1 and 20.4 kJ mol(-1) at BHandHLYP/cc-pVDZ. In comparison, barriers of 34.0 and 23.4 kJ mol(-1) are calculated at BHandHLYP/cc-pVDZ for reaction of the acetyl radical at the 1- and 2-positions in aminoethylene, repectively. Natural bond orbital (NBO) analysis at the BHandHLYP/6-311G** level of theory reveals that SOMO --> pi*imine, pi imine--> SOMO, and LPN --> pi*C=O interactions are worth 90, 278, and 138 kJ mol-1, respectively, in the transition state (2) for reaction of acetyl radical at the nitrogen end of methanimine; similar interactions are observed for the chemistry involving aminoethylene. These multiorbital interactions are responsible for the unusual motion vectors associated with the transition states involved in these reactions. NBO analyses for the remaining systems in this study support the hypothesis that the acetyl radical is ambiphilic in nature.     

Photoreactivity of iron(III)-aerobactin: photoproduct structure and iron(III) coordination

UV photolysis of the ferric aerobactin complex results in decarboxylation of the alpha-hydroxy carboxylic acid group of the central citrate moiety of aerobactin. The structure determination of the photooxidized ligand shows that decarboxylation occurs at the citrate moiety forming a 3-ketoglutarate moiety. Proton and carbon-13 NMR establish the presence of keto and enol tautomers of the apo-photoproduct, with the enol form prevailing in water. The photoproduct retains the ability to coordinate iron(III). The values of the ligand protonation constants, the pKa of the Fe(III)-ligand complex, and the Fe(III) stability constant of the photoproduct of aerobactin are all close to those of aerobactin. CD spectroscopy suggests that the chirality of the ferric complexes of aerobactin and its photoproduct are similar. Like aerobactin, the photoproduct promotes iron acquisition by the source bacterium, Vibrio sp. DS40M5.     

Post-Hartree-Fock studies on the structure of bis(ortho-substituted phenyl)methylenes

Long-lived triplet bisarylmethylenes are now well-known. Experimental data (primarily ESR hyperfine parameters) suggest that the carbon framework of long-lived bisarylmethylenes approaches D(2)(d)() symmetry, as ortho-substitution forces the central angle to approach 180 degrees . According to DFT modeling, the approach of the central angle to 180 degrees is accompanied by a dramatic shortening of the central CC bonds and severe quinoid distortion of the phenyl rings. In contrast, X-ray investigation of bis(2,4,6-trichlorophenyl)methylene shows a structure closer to the carbene valence bond representation with less seriously distorted phenyl rings, a more acute central angle, and a longer bond from the methylene carbon to the aryl substituent. We address the difficulty of achieving a balance of cumulene and carbene character, treating the model systems diethynylmethylene, dicyanomethylene, and diisocyanomethylene by post-Hartree-Fock methods CAS and CCSD as well as DFT models, and applying the perturbation-corrected CAS methods to the chloro and methyl ortho-substituted bisphenyl carbenes.     

Origin of Stability in Branched Alkanes

The potential origins of stability in branched alkanes are investigated, paying close attention to two recent hypotheses: geminal steric repulsion and protobranching. All alkane isomers through C₆H₁₄ along with heptane and octane were investigated at the MPW1B95/6‐311++G(d,p) level. Their geminal steric repulsion, total steric repulsion, and orbital interactions were evaluated by using natural bond orbital analysis. All measures of steric repulsion fail to explain the stability of branched alkanes. The extra stability of branched alkanes and protobranching, in general, is tied to stabilizing geminal σ→σ* delocalization, particularly of the type that involves adjacent C? C bonds and, thus, preferentially stabilizes branched alkanes. This picture is corroborated by valence bond calculations that attribute the effect to additional ionic structures (e.g., CH₃⁺ :CH₂ :CH₃^? and CH₃:^? CH₂: CH₃⁺ for propane) that are not possible without protobranching.     

A study of the ionic conduction of mica surface by admittance spectroscopy

The ionic conduction on the surface of humid mica has been analyzed by admittance spectroscopy as a function of relative humidity for different surface treatments. Measurements at low frequency indicate that water adsorption proceeds first in the form of a strongly adsorbed uniform thin layer, then with the formation of highly inhomogeneous thick aggregates.     

Click-modified hexahomotrioxacalix[3]arenes as fluorometric and colorimetric dual-modal chemosensors for 2,4,6-trinitrophenol

A new type of chemosensor-based approach to the detection of 2,4,6-trinitrophenol (TNP) is described in this paper. Two hexahomotrioxacalix[3]arene-based chemosensors 1 and 2 were synthesized through click chemistry, which exhibited high binding affinity and selectivity toward TNP as evidenced by UV–vis and fluorescence spectroscopy studies. ¹H NMR titration analysis verified that CH?O hydrogen bonding is demonstrated as the mode of interaction, which possibly facilitates effective charge-transfer.