On multiplicities of simple subquotients in generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.     

Schur indices of perfect groups

It has been noticed by many authors that the Schur indices of the irreducible characters of many quasi-simple finite groups are at most . A conjecture has emerged that the Schur indices of all irreducible characters of all quasi-simple finite groups are at most . We prove that this conjecture cannot be extended to the set of all finite perfect groups. Indeed, we prove that, given any positive integer , there exist irreducible characters of finite perfect groups of chief length which have Schur index .

     

Tandem enantioselective conjugate addition--cyclopropanation. Application to natural products synthesis

A tandem asymmetric conjugate addition-cyclopropanation was developed, in which a cyclic or linear enone was converted to a TMS-protected 3-substituted-cyclopropanol in an efficient one-pot reaction. These compounds were then selectively cleaved to yield alpha-methyl-beta-alkyl ketones, alpha-methylene-enones, or chain extended gamma-alkyl-enones. This methodology was applied to the formal total synthesis of (-)-(S,S)-clavukerin A and (+)-(R,S)-isoclavukerin.     

Transition-metal nanoparticles in imidazolium ionic liquids: recyclable catalysts for biphasic hydrogenation reactions

1-n-Butyl-3-methylimidazolium hexafluorophosphate room-temperature ionic liquid is not only suitable as a medium for the preparation and stabilization of iridium nanoparticles but also ideal for the generation of recyclable biphasic catalytic systems for hydrogenation reactions. Thus, Ir(0) nanoparticles with a mean diameter of 2 nm have been prepared by reduction of Ir(I) dissolved in the ionic liquid with H2. This catalytic solution can be reused several times for the biphasic hydrogenation of olefins under mild reaction conditions.     

Regularity of CR maps between convex hypersurfaces of finite type

We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in

     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

Nucleophilic addition to 3-substituted pyridinium salts: expedient syntheses of (-)-L-733,061 and (-)-CP-99,994

[reaction: see text] The addition of nucleophiles to 3-substituted pyridinium salts prepared from N-methylbenzamide and various pyridines has been investigated. Good to excellent regioselectivities favoring the 2,3-disubstituted 1,2-dihydropyridines were observed. The resulting 1,2-dihydropyridines led to the corresponding 2,3-disubstituted pyridines upon treatment with Mn(OAc)3/NaIO4. This methodology was also successfully applied to the enantioselective syntheses of (-)-L-733,061 and (-)-CP-99,994, two members of a new class of highly potent, nonpeptide, Substance P antagonists.     

Adenosylcobinamide plus exogenous, sterically hindered, putative axial bases: a reinvestigation into the cause of record levels of Co-C heterolysis

A reinvestigation of an earlier Ph.D. thesis (Sirovatka, J. M. Ph.D. Thesis, Colorado State University, Fort Collins, CO, 1999) is reported herein. That thesis examined the thermolysis reaction of AdoCbi(+)BF(4)(-) in ethylene glycol solution with exogenous bases, N-methylimidazole (N-Me-Im) and the sterically hindered 1,2-dimethylimidazole, (1,2-Me(2)-Im), 2-methylpyridine (2-Me-py), and 2,6-dimethylpyridine (2,6-Me(2)-py). In the present work, multiple purities of each base have been utilized as a check to see if impurities in the nitrogenous bases are causing the observed homolysis and heterolysis product distributions as others have implied (Trommel, J. S.; Warncke, K.; Marzilli, L. G. J. Am. Chem. Soc. 2001, 123, 3358). The "impurity hypothesis" is disproven by a series of results, including the following: N-Me-Im displays an invariant 52 +/- 10% heterolysis and the 1,2-Me(2)-Im system displays an invariant 83 +/- 7% heterolysis as a function of different base purification methods. Moreover, 2-Me-py and 2,6-Me(2)-py also display an invariant approximately 16 +/- 5% heterolysis as a function of different purification methods. What is responsible for the high levels of Co-C heterolysis in the AdoCbi(+) plus sterically bulky base thermolyses was uncovered via a revisitation of our four, earlier alternative hypotheses for the enhanced Co-C heterolysis (Sirovatka, J. M.; Finke, R. G. Inorg. Chem. 1999, 38, 1697). Our prior number one alternative hypothesis is shown to be correct: the added bases simply deprotonate the ethylene glycol solvent, forming ethylene glycolate anion and base-H(+)() as the key agents behind the previously ill-understood Co-C heterolyses. Also reported are Co(II)Cbi(+) titrations with five bases (1,2-Me(2)-Im, N-Me-Im, pyridine, 2-MePy, and 2,6-Me(2)-py). These experiments confirm Marzilli and co-workers' (op. cit.) results by showing that sterically hindered bases do not bind to Co(II)Cbi(+); therefore, Co(II)Cbi(+) EPR literature showing binding of bulky pyridines is erroneous as is the previously reported binding of bulky pyridine bases to Co(II)Cbi(+) by UV-vis spectroscopy (Sirovatka, J. Ph.D. Thesis, op. cit.). Also reported is our current best synthesis and purification of AdoCbi(+)BF(4)(-), work that builds off our 1987 synthesis of AdoCbi(+)BF(4)(-) (Hay, B. P.; Finke, R. G. J. Am. Chem. Soc. 1987, 109, 8012). Finally, the multiple, compounding errors which have caused problems in this project are listed, notably errors in the protein X-ray crystallography literature, the EXAFS literature, the Co(II)Cbi(+) plus bulky-bases EPR literature, the misleading B(12)-model literature, the erroneous experimental work (Sirovatka, op. cit.) and thus incorrect conclusions in one of our prior papers, as well as the erroneous implications in parts of the Marzilli and co-workers paper (op. cit.). It is hoped that a forthright reporting of these errors will help others avoid similar mistakes in the future when studying complex, bioinorganic systems.