Qualitative analysis on the critical points of the Robin function

Let \O\subset\R^N be a smooth bounded domain with $N\ge2$ and \O_\e=\O\backslash B(P,\e) where B(P,\e) is the ball centered at P\in\O and radius \e. In this paper, we establish the number, location and non-degeneracy of critical points of the Robin function in \O_\e for \e small enough. We will show that the location of $P$ plays a crucial role on the existence and multiplicity of the critical points. The proof of our result is a consequence of delicate estimates on the Green function near to \partial B(P,\e). Some applications to compute the exact number of solutions of related well-studied nonlinear elliptic problems will be showed

Ruthenacycles and Iridacycles as Catalysts for Asymmetric Transfer Hydrogenation and Racemisation

Ruthenacycles, which are easily prepared in a single step by reaction between enantiopure aromatic amines and [Ru(arene)Cl2]2 in the presence of NaOH and KPF6, are very good asymmetric transfer hydrogenation catalysts. A range of aromatic ketones were reduced using isopropanol in good yields with ee’s up to 98%. Iridacycles, which are prepared in similar fashion from [IrCp*Cl2]2 are excellent catalysts for the racemisation of secondary alcohols and chlorohydrins at room temperature. This allowed the development of a new dynamic kinetic resolution of chlorohydrins to the enantiopure epoxides in up to 90% yield and 98% enantiomeric excess (ee) using a mutant of the enzyme Haloalcohol dehalogenase C and an iridacycle as racemisation catalyst.

Activation and Deactivation of a Robust Immobilized Cp*Ir-Transfer Hydrogenation Catalyst: A Multielement in Situ X-ray Absorption Spectroscopy Study

A highly robust immobilized [Cp*IrCl2]2 precatalyst on Wang resin for transfer hydrogenation, which can be recycled up to 30 times, was studied using a novel combination of X-ray absorption spectroscopy (XAS) at Ir L3-edge, Cl K-edge, and K K-edge. These culminate in in situ XAS experiments that link structural changes of the Ir complex with its catalytic activity and its deactivation. Mercury poisoning and “hot filtration” experiments ruled out leached Ir as the active catalyst. Spectroscopic evidence indicates the exchange of one chloride ligand with an alkoxide to generate the active precatalyst. The exchange of the second chloride ligand, however, leads to a potassium alkoxide–iridate species as the deactivated form of this immobilized catalyst. These findings could be widely applicable to the many homogeneous transfer hydrogenation catalysts with Cp*IrCl substructure

Qualitative properties of solutions to elliptic singular problems

We investigate the singular boundary value problem in , on , where . For , we find the estimate where depends on only, denotes the distance from to and is suitable constant. For , we prove that the function is concave whenever is convex. A similar result is well known for the equation , with . For , and we prove convexity sharpness results.</p

Asymmetric Hydrogen Transfer Reactions Promoted by Homogeneous Transition Metal Catalysts

CHEM. REV

Synthesis and spectroscopic characterization of ternary complexes of copper(II) glycylglycine and substituted phenanthrolines

Complexes of Cu(glygly)phen {glygly =glycylglycine; phen=4,7-dimethyl [(1)], 5,6-dimethyl [(2)], 5-NO2[(3)], 5-Cl[(4)], 2-oxazolinyl (2-ox) [(5)] phenanthroline} and bis(2-oxazolinylphenanthroline)copper(II) [(6)] were synthesized and characterized by conductivity measurements, e.p.r., i.r. and reflectance electronic spectroscopies. A broad u.v.-vis. band in the 620-640 nm range and a shoulder at ca. 825 nm suggest that these complexes are five-coordinate. The e.p.r. spectra indicate a stronger equatorial ligand field in the ternary complexes which is absent in the binary Cu-phen complexes, suggesting square pyramidal coordination, whose base contains the three donor atoms from glygly (O, N, N) and one donor from the phenanthroline nitrogen atom. The other nitrogen-containing ligand of the phenanthroline is in an apical position. The spectroscopic results can be correlated with electronic and steric effects attributable to the different substituents on the phenanthroline ligands. Only small variations in the structure of the ternary complexes occur as a function of the electronic effects of substituents on the aromatic phenanthroline ring ligands. Steric hindrance predominates in determining coordination geometry around copper(II)

Hydrocarboalkoxylation of N-vinylphtalimide catalyzed by palladium complexes

The hydrocarboalkoxylation of N-vinylphthalimide catalyzed by palladium tertiary phosphine complexes occurs with high selectivity towards the linear isomer when the alcohol is used also as the solvent but towards the branched isomer in the presence of an additional solvent. When triphenylphosphine is employed as the ligand, the yield and the regioselectivity towards the branched isomer increase with increasing pco or decreasing concentration of the phosphine. Reaction in the presence of molecular hydrogen leads to higher yields, with minor changes in regioselectivity. High regioselectivities towards either the linear or the branched isomer are observed also in the presence of chiral di- or mono-phosphines, but the degree of asymmetric induction is very low

Alkoxy- and Hydroxycyclization of Enynes Catalyzed by Pd(II) and Pt(II) Catalysts

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