The Riesz decomposition of finely superharmonic functions

This paper answers a question of Fuglede about minimal positive harmonic functions associated with irregular boundary points. As a consequence, an old and central problem of fine potential theory, concerning the Riesz decomposition, is resolved. Namely, it is shown that, on certain fine domains, there exist positive finely superharmonic functions which do not admit any positive finely harmonic minorant and yet are not fine potentials.     

Markov processes associated with L p -resolvents and applications to stochastic differential equations on Hilbert space

We give general conditions on a generator of a C₀-semigroup (resp. of a C₀-resolvent) on L^p(E,μ), p ≥ 1, where E is an arbitrary (Lusin) topological space and μ a σ-finite measure on its Borel σ-algebra, so that it generates a sufficiently regular Markov process on E. We present a general method how these conditions can be checked in many situations. Applications to solve stochastic differential equations on Hilbert space in the sense of a martingale problem are given. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday     

Integral representations of harmonic functions in half spaces

In this paper, using a modified Poisson kernel in an upper half-space, we prove that a harmonic function u(z) in a upper half space with its positive part u⁺(x)=max{u(x),0} satisfying a slowly growing condition can be represented by its integral in the boundary of the upper half space, the integral representation is unique up to the addition of a harmonic polynomial, vanishing in the boundary of the upper half space and that its negative part u⁻(x)=max{−u(x),0} can be dominated by a similar slowly growing condition, this improves some classical result about harmonic functions in the upper half space.     

1,3-diallyl-5-[ω-(diphenylphosphino)alkyl] isocyanurates in reactions of complex formation with palladium(ii) dichloride

The reactions of phosphine derivatives of diallyl isocyanurates with palladium(ii) dichloride lead to the formation of complexes, whose structure, composition, and stability depend on the length of the methylene chain between the isocyanurate and diphenylphosphine fragments in the ligand. 1,3-Diallyl-5-[5′-(diphenylphosphino)pentyl and 10′-(diphenyl-phosphino)decyl] isocyanurates with PdCl₂ form monomeric L₂PdCl₂ trans-complexes in which P atoms of the ligands participate in coordination with the metal. 1,3-Diallyl-5-[2′-(diphenylphosphino)ethyl] isocyanurate with PdCl₂ forms a dimeric (LPdCl₂)₂ complex, which decomposes in a solution to the monomer including solvent molecule into the coordination sphere of the metal. The reactions of 1,3-diallyl-5-[4′-(diphenylphosphino)butyl] isocyanurate and 1,3-diallyl-5-[6′-(diphenylphosphino)hexyl] isocyanurate with PdCl₂ give monomeric chelate LPdCl₂ complexes in which one of the allyl groups of the isocyanurate cycle participates in coordination with the central ion along with the phosphorus atom. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1859–1865, September, 1998.     

Self-assembled peptide tubelets with 7 A pores

Here we report the preparation and structural characteristics of self-assembling peptide tubelets composed of 32-membered rings formed of alternating alpha-amino acids and cis-3-aminocyclohexanecarboxylic acids. The tubelets possess a partial hydrophobic core environment, provided by the projection of the cyclohexane C2 methylene moiety into the lumen, and a Van der Waals pore diameter of about 7 A.     

Adducts of Rh2[MTPA]4 with some phosphine chalcogenides: nature of binding and ligand exchange

Adducts of four phosphine chalcogenides with the chiral dirhodium complex ([Rh-Rh]) were investigated by variable-temperature 1H and 31P NMR spectroscopy in order to compare their properties as axial ligands. Whereas the selenide (1) and the sulfide (2) are strong ligands with electrostatic attraction and, in addition, a significant orbital (HOMO-LUMO) interaction, the phosphine oxide compounds (P=O) bind primarily via electrostatic attraction and are relatively weak donors. Moreover, the overall bond strength in these adducts depends on steric congestion around the P=O group.     

Study of the initial stages of alkoxo synthesis involving Ti(OBu)4 and cyclophosphites

The reactivities of cyclophosphite precursors in alkoxo syntheses involving titanium(iv) tetra(n-butoxide) were studied by ³¹P NMR and IR spectroscopy. 2-Diethylamido-4-methyl-1,3,2-dioxaphosphinane and 4-ethyl-2,6,7-trioxaphosphabicyclo[2.2.2]octane in benzene are inert toward Ti(OBu)₄. Gelation is accompanied by hydrolysis 2-diethylamido-4-methyl-1,3,2-dioxaphosphinane to give the corresponding hydrophosphoryl compound, while 4-ethyl-2,6,7-trioxaphosphabicyclo[2.2.2]octane remains intact during gelation.     

Synthesis of Donor–Acceptor Alkynylcyclopropanes by Diastereoselective Cyclopropanation of Electron‐Deficient Alkenes with Alkoxyalkynyl Fischer Carbene Complexes

The reaction of electron‐deficient alkenes with alkoxyalkynyl Fischer carbene complexes (FCCs) represents a straightforward route to a new type of captodative (donor–acceptor) alkynylcyclopropanes, which have been prepared in moderate to high yields and in a diastereoselective manner. Some studies regarding the employment of additives to facilitate the recovery of the metal moiety after the reaction are also described. Finally, the first example of a cyclopropanation reaction through employing Fischer carbene complexes under microwave irradiation is presented; this method proved to be an advantageous alternative to the thermal reaction.     

Theoretical studies of mechanisms of cycloaddition reaction between difluoromethylene carbene and acetone

Mechanisms of the cycloaddition reaction between singlet difluoromethylene carbene and acetone have been investigated with the second‐order Møller–Plesset (MP2)/6‐31G* method, including geometry optimization and vibrational analysis. Energies for the involved stationary points on the potential energy surface (PES) are corrected by zero‐point energy (ZPE) and CCSD(T)/6‐31G* single‐point calculations. From the PES obtained with the CCSD(T)//MP2/6‐31G* method for the cycloaddition reaction between singlet difluoromethylene carbene and acetone, it can be predicted that path B of reactions 2 and 3 should be two competitive leading channels of the cycloaddition reaction between difluoromethylene carbene and acetone. The former consists of two steps: (i) the two reactants first form a four‐membered ring intermediate, INT2, which is a barrier‐free exothermic reaction of 97.8 kJ/mol; (ii) the intermediate INT2 isomerizes to a four‐membered product P_2b via a transition state TS2b with an energy barrier of 24.9 kJ/mol, which results from the methyl group transfer. The latter proceeds in three steps: (i) the two reactants first form an intermediate, INT1c, through a barrier‐free exothermic reaction of 199.4 kJ/mol; (ii) the intermediate INT1c further reacts with acetone to form a polycyclic intermediate, INT3, which is also a barrier‐free exothermic reaction of 27.4 kJ/mol; and (iii) INT3 isomerizes to a polycyclic product P₃ via a transition state TS3 with an energy barrier of 25.8 kJ/mol. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007