On K-stability of reductive varieties

G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature. In [D3] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson’s results and computations to a new case, that of reductive varieties.Received: November 2003 Revision: January 2004 Accepted: January 2004     

Subregular Representations of {\mathfrak{s}}{\mathfrak{l}}_n and Simple Singularities of Type A n−1

Alexander Premet has stated the following problem: what is a relation between subregular nilpotent representations of a classical semisimple restricted Lie algebra and non-commutative deformations of the corresponding singularities? We solve this problem for type A.     

Polyfunctional compounds containing the 4,6-dialkoxy-7-arylthioheptene moiety as synthetically useful intermediates. The course of lewis acid-induced transformations

Data on the selectivity of the Lewis acids induced transformations of the title compounds are presented, and the routes leading to formation of products containing either cyclohexane or 1,3-diene units are described.     

Synthesis of functionalized m-bistrifluoromethylbenzenes via cyclocondensation of 1,1,1,5,5,5-hexafluoroacetylacetone with enamines

The reaction of 1,1,1,5,5,5-hexafluoroacetylacetone with push-pull enamines having a methyl group at the α-position was investigated. It was found that the reaction is sensitive both to the structure of enamines and to reaction conditions. As a result, a set of bistrifluoromethyldialkylanilines and ethyl bistrifluoromethylsalicylate was prepared. Plausible mechanisms and factors influencing the course of the reaction are discussed.     

Highly selective mono-substitution in Pd-catalyzed cross-coupling reactions of 3,6-dichloropyridazine with organozinc compounds

Pd-catalyzed cross-coupling reactions of 3,6-dichloropyridazine (1) with benzyl, aryl, and alkyl organozinc compounds led to selective mono-substitution of one of the chlorine atoms. The subsequent cross-coupling of the resulting monochlorides with RZnCl afforded unsymmetrical 3,6-carbon-disubstituted pyridazines.     

The electronic structure of FeV-cofactor in vanadium-dependent nitrogenase

The electronic structure of the active-site metal cofactor (FeV-cofactor) of resting-state V-dependent nitrogenase has been an open question, with earlier studies indicating that it exhibits a broad S = 3/2 EPR signal (Kramers state) having g values of ∼4.3 and 3.8, along with suggestions that it contains metal-ions with valencies [1V³⁺, 3Fe³⁺, 4Fe²⁺]. In the present work, genetic, biochemical, and spectroscopic approaches were combined to reveal that the EPR signals previously assigned to FeV-cofactor do not correlate with active VFe-protein, and thus cannot arise from the resting-state of catalytically relevant FeV-cofactor. It, instead, appears resting-state FeV-cofactor is either diamagnetic, S = 0, or non-Kramers, integer-spin (S = 1, 2 etc.). When VFe-protein is freeze-trapped during high-flux turnover with its natural electron-donating partner Fe protein, conditions which populate reduced states of the FeV-cofactor, a new rhombic S = 1/2 EPR signal from such a reduced state is observed, with g = [2.18, 2.12, 2.09] and showing well-defined ⁵¹V (I = 7/2) hyperfine splitting, a_iso = 110 MHz. These findings indicate a different assignment for the electronic structure of the resting state of FeV-cofactor: S = 0 (or integer-spin non-Kramers state) with metal-ion valencies, [1V³⁺, 4Fe³⁺, 3Fe²⁺]. Our findings suggest that the V³⁺ does not change valency throughout the catalytic cycle.

Active site FeV-cofactor of the V-nitrogenase and the EPR spectrum of the reduced cofactor showing ⁵¹V-hyperfine coupling.     

Functionalized nanodiamonds part I. An experimental assessment of diamantane and computational predictions for higher diamondoids

The structures, strain energies, and enthalpies of formation of diamantane 1, triamantane 2, isomeric tetramantanes 3-5, T(d)-pentamantane 6, and D(3d)-hexamantane 7, and the structures of their respective radicals, cations, as well as radical cations, were computed at the B3LYP/6-31G* level of theory. For the most symmetrical hydrocarbons, the relative strain (per carbon atom) decreases from the lower to the higher diamondoids. The relative stabilities of isomeric diamondoidyl radicals vary only within small limits, while the stabilities of the diamondoidyl cations increase with cage size and depend strongly on the geometric position of the charge. Positive charge located close to the geometrical center of the molecule is stabilized by 2-5 kcal mol(-1). In contrast, diamondoid radical cations preferentially form highly delocalized structures with elongated peripheral C-H bonds. The effective spin/charge delocalization lowers the ionization potentials of diamondoids significantly (down to 176.9 kcal mol(-1) for 7). The reactivity of 1 was extensively studied experimentally. Whereas reactions with carbon-centered radicals (Hal)(3)C(*) (Hal=halogen) lead to mixtures of all possible tertiary and secondary halodiamantanes, uncharged electrophiles (dimethyldioxirane, m-chloroperbenzoic acid, and CrO(2)Cl(2)) give much higher tertiary versus secondary selectivities. Medial bridgehead substitution dominates in the reactions with strong electrophiles (Br(2), 100 % HNO(3)), whereas with strong single-electron transfer (SET) acceptors (photoexcited 1,2,4,5-tetracyanobenzene) apical C(4)-H bridgehead substitution is preferred. For diamondoids that form well-defined radical cations (such as 1 and 4-7), exceptionally high selectivities are expected upon oxidation with outer-sphere SET reagents.     

Effects of reduction temperature and metal-support interactions on the catalytic activity of Pt/gamma-Al2O3 and Pt/TiO2 for the oxidation of CO in the presence and absence of H2

TiO2- and gamma-Al2O3-supported Pt catalysts were characterized by HRTEM, XPS, EXAFS, and in situ FTIR spectroscopy after activation at various conditions, and their catalytic properties were examined for the oxidation of CO in the absence and presence of H2 (PROX). When gamma-Al2O3 was used as the support, the catalytic, electronic, and structural properties of the Pt particles formed were not affected substantially by the pretreatment conditions. In contrast, the surface properties and catalytic activity of Pt/TiO2 were strongly influenced by the pretreatment conditions. In this case, an increase in the reduction temperature led to higher electron density on Pt, altering its chemisorptive properties, weakening the Pt-CO bonds, and increasing its activity for the oxidation of CO. The in situ FTIR data suggest that both the terminal and bridging CO species adsorbed on fully reduced Pt are active for this reaction. The high activity of Pt/TiO2 for the oxidation of CO can also be attributed to the ability of TiO2 to provide or stabilize highly reactive oxygen species at the metal-support interface. However, such species appear to be more reactive toward H2 than CO. Consequently, Pt/TiO2 shows substantially lower selectivities toward CO oxidation under PROX conditions than Pt/gamma-Al2O3.