Highly regio- and stereoselective intramolecular 1,3-dipolar cycloadditions of norbornadiene-tethered nitrile oxides

[reaction: see text] Intramolecular cycloadditions with high regio- and stereocontrol are important methods for the efficient assembly of complex molecular structures. Efficient routes to the synthesis of norbornadiene-tethered nitrile oxides have been developed, and their intramolecular 1,3-dipolar cycloadditions were studied. The cycloadditions occurred in good yields for a variety of substrates and were found to be highly regio- and stereoselective.     

Infrared spectra of aluminum hydrides in solid hydrogen: Al2H4 and Al2H6

The reaction of laser-ablated Al atoms and normal-H(2) during co-deposition at 3.5 K produces AlH, AlH(2), and AlH(3) based on infrared spectra and the results of isotopic substitution (D(2), H(2) + D(2) mixtures, HD). Four new bands are assigned to Al(2)H(4) from annealing, photochemistry, and agreement with frequencies calculated using density functional theory. Ultraviolet photolysis markedly increases the yield of AlH(3) and seven new absorptions for Al(2)H(6) in the infrared spectrum of the solid hydrogen sample. These frequencies include terminal Al-H(2) and bridge Al-H-Al stretching and AlH(2) bending modes, which are accurately predicted by quantum chemical calculations for dibridged Al(2)H(6), a molecule isostructural with diborane. Annealing these samples to remove the H(2) matrix decreases the sharp AlH(3) and Al(2)H(6) absorptions and forms broad 1720 +/- 20 and 720 +/- 20 cm(-1) bands, which are due to solid (AlH(3))(n). Complementary experiments with thermal Al atoms and para-H(2) at 2.4 K give similar spectra and most product frequencies within 2 cm(-1). Although many volatile binary boron hydride compounds are known, binary aluminum hydride chemistry is limited to the polymeric (AlH(3))( solid. Our experimental characterization of the dibridged Al(2)H(6) molecule provides an important link between the chemistries of boron and aluminum.     

A Monte Carlo simulation of diffusion-controlled reactions in inhomogeneous systems

A random-walk model has been developed to treat the kinetics of reactions taking place in spurs at different solute concentrations. The dependence of the molecular yields on solute concentration has been studied using Monte Carlo techniques for simulation of the formation of spurs and of the random movement of the reactive species.     

Spectroscopic detection and theoretical confirmation of the role of Cr2(CO)5(C5R5)2 and .Cr(CO)2(ketene)(C5R5) as intermediates in carbonylation of N=N=CHSiMe3 to O=C=CHSiMe3 by .Cr(CO)3(C5R5) (R = H, CH3)

Conversion of N=N=CHSiMe3 to O=C=CHSiMe3 by the radical complexes .Cr(CO)3C5R5 (R = H, CH3) derived from dissociation of [Cr(CO)3(C5R5)]2 have been investigated under CO, Ar, and N2 atmospheres. Under an Ar or N2 atmosphere the reaction is stoichiometric and produces the Cr[triple bond]Cr triply bonded complex [Cr(CO)2(C5R5)]2. Under a CO atmosphere regeneration of [Cr(CO)3(C5R5)]2 (R = H, CH3) occurs competitively and conversion of diazo to ketene occurs catalytically as well as stoichiometrically. Two key intermediates in the reaction, .Cr(CO)2(ketene)(C5R5) and Cr2(CO)5(C5R5)2 have been detected spectroscopically. The complex .Cr(13CO)2(O=13C=CHSiMe3)(C5Me5) has been studied by electron spin resonance spectroscopy in toluene solution: g(iso) = 2.007; A(53Cr) = 125 MHz; A(13CO) = 22.5 MHz; A(O=13C=CHSiMe3) = 12.0 MHz. The complex Cr2(CO)5(C5H5)2, generated in situ, does not show a signal in its 1H NMR and reacts relatively slowly with CO. It is proposed to be a ground-state triplet in keeping with predictions based on high level density functional theory (DFT) studies. Computed vibrational frequencies are also in good agreement with experimental data. The rates of CO loss from 3Cr2(CO)5(C5H5)2 producing 1[Cr(CO)2(C5H5)]2 and CO addition to 3Cr2(CO)5(C5H5)2 producing 1[Cr(CO)3(C5H5)]2 have been measured by kinetics and show DeltaH approximately equal 23 kcal mol(-1) for both processes. Enthalpies of reduction by Na/Hg under CO atmosphere of [Cr(CO)n(C5H5)]2 (n = 2,3) have been measured by solution calorimetry and provide data for estimation of the Cr[triple bond]Cr bond strength in [Cr(CO)2(C5H5)]2 as 72 kcal mol(-1). The complex [Cr(CO)2(C5H5)]2 does not readily undergo 13CO exchange at room temperature or 50 degrees C implying that 3Cr2(CO)5(C5H5)2 is not readily accessed from the thermodynamically stable complex [Cr(CO)2(C5H5)]2. A detailed mechanism for metalloradical based conversion of diazo and CO to ketene and N2 is proposed on the basis of a combination of experimental and theoretical data.     

Specific ion effects on the electrophoretic mobility of small,highly charged peptides: A modeling study

In this work, we use coarse‐grained modeling to study the free solution electrophoretic mobility of small highly charged peptides (lysine, arginine, and short oligos thereof (up to nonapeptides)) in NaCl and Na₂SO₄ aqueous solutions at neutral pH and room temperature. The experimental data are taken from the literature. A bead modeling methodology that treats the electrostatics at the level of the nonlinear Poisson Boltzmann equation developed previously in our laboratory is able to account for the mobility of all peptides in NaCl, but not Na₂SO₄. The peptide mobilities in Na₂SO₄ can be accounted for by including sulfate binding in the model and this is proposed as one possible explanation for the discrepancy. Oligo arginine peptides bind more sulfate than oligo lysines and sulfate binding increases with the oligo length.     

Improved model for the analysis of back corona in pulse energised electrostatic precipitators

Formation of back corona and its effect on the voltage–current characteristics, etc., have been analysed by several authors. It has also been examined how the harmful effect of back corona can be reduced, for example by the application of pulse energisation. However, to find an optimal solution, modelling of the back corona effect is necessary. Different back corona models were created to estimate the time of its development, the change in current–voltage characteristics, the decrease in particle charge and finally, the collection efficiency of the ESP with back corona. In this paper the authors present an improved numerical ESP model that is capable of determining the parameters of back corona in such cases, when pulse energisation is applied for the power supply of the electrostatic precipitator. Based on the modular structure of the model, different modules calculate the distribution of gas velocity, electric field intensity, particle charging and particle movement. All these parameters are important to determine the properties of back corona while it feeds back on these parameters; therefore iteration is necessary to obtain reliable result. The harmful effects of back corona can be characterised with the help of the evaluation of calculated results.     

An extension of a convexity theorem of the generalized numerical range associated with

For any , let be the following subset of :

We show that if , then is always convex. When , it is an ellipsoid, probably degenerate. The convexity result is best possible in the sense that if we have defined similarly, then there are examples which fail to be convex when and .

The set is also symmetric about the origin for all , and contains the origin when . Equivalent statements of this result are given. The convexity result for is similar to Au-Yeung and Tsing's extension of Westwick's convexity result for .

     

Quasi-Spherical Metrics and Applications

In this paper, using the idea of Bartnik [B2] on quasi-spherical metrics we continue our study on the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary. Unlike the previous work [ST] of the authors and the work of Liu-Yau [LY], we only assume each boundary component has nonnegative curvature which is not identically zero. We also study the case that the boundary is embedded in the quotient of the infinity of the Euclidean space over a finite group. The regularity of the black hole boundary condition of quasi-spherical metrics is also discussed.Research partially supported by NSF of China, Projects 10001001 and 10231010.Research partially supported by Earmarked Grant of Hong Kong #CUHK4032/02P.