Degenerate stochastic differential equations with Hölder continuous coefficients and super-Markov chains

We consider the operator

acting on functions in . We prove uniqueness of the martingale problem for this degenerate operator under suitable nonnegativity and regularity conditions on and . In contrast to previous work, the need only be nonnegative on the boundary rather than strictly positive, at the expense of the and being Hölder continuous. Applications to super-Markov chains are given. The proof follows Stroock and Varadhan's perturbation argument, but the underlying function space is now a weighted Hölder space and each component of the constant coefficient process being perturbed is the square of a Bessel process.

     

Improved reagent for electrophilic amination of stabilized carbanions

[reaction: see text]. Enolate amination using O-di(p-methoxyphenyl)phosphinylhydroxylamine 2 is reported. Reagent 2 reacts efficiently with stabilized sodium or potassium enolates derived from malonates, phenylacetates, and phenylacetonitriles and is sufficiently soluble for use in solution at -78 degrees C.     

Singlet-energy transfer in quadruple hydrogen-bonded oligo(p-phenylenevinylene)perylene-diimide dyads

The photophysical properties of a supramolecular donor-acceptor dyad consisting of an oligo(p-phenylenevinylene) unit and a perylene-diimide unit are described. The dyad is created by functionalising the two chromophores with quadruple hydrogen bonding 2-ureido-4[1H]-pyrimidinone units, which provide a high association constant (K approximately 10(8) M-1 in toluene). This feature enabled us to study the time-resolved photoinduced singlet-energy transfer reaction between the two chromophores in dilute solution with transient pump-probe spectroscopy. This energy transfer occurs with a time constant of 5.1 ps.     

Mean Field Magnetic Phase Diagrams for the Two Dimensional <Emphasis Type="Italic">t</Emphasis> — <Emphasis Type="Italic">t</Emphasis>′ — <Emphasis Type="Italic">U</Emphasis> Hubbard Model

We study the ground state phase diagram of the two dimensional t — t′ — U Hubbard model concentrating on the competition between antiferro-, ferro-, and paramagnetism. It is known that unrestricted Hartree–Fock- and quantum Monte Carlo calculations for this model predict inhomogeneous states in large regions of the parameter space. Standard mean field theory, i.e., Hartree–Fock theory restricted to homogeneous states, fails to produce such inhomogeneous phases. We show that a generalization of the mean field method to the grand canonical ensemble circumvents this problem and predicts inhomogeneous states, represented by mixtures of homogeneous states, in large regions of the parameter space. We present phase diagrams which differ considerably from previous mean field results but are consistent with, and extend, results obtained with more sophisticated methods. PACS: 71.10.Fd, 05.70.Fh, 75.50.Ee     

Metal-halogen bonding studies with group IV A trialkylmetal halides

Halogen redistribution reactions have been found to take place between benzyl bromide or benzyl iodide and the Group IVA silicon, germanium, tin, and lead containing triakylmetal chlorides. However, for the reactions of the Si, Ge and Sn compounds, a quaternary ammonium halide catalyst was necessary to enable the equilibria to be established at reasonably rapid rates. The equilibrium constants at 50°C have been measured for each at these halogen redistributions. They have been found to increase gradually on going down in Group IV A from silicon to lead, being considerably less than unity in the case of silicon and somewhat greater than unity in the case of lead for both the R₃MCl + BzBr and R₃MCl + BzI reactions. The ΔG° values for these equilibria have been calculated, and it is suggested that their differences may be explained in terms of the relative importance of pπdπ contributions to the halogen—metal bonding in the various Group IV A trialkylmetal halide systems.     

A Re-investigation of the Wavelength-dependent Photoreduction of 1-Piperidinoanthraquinone: Evidence for a Mechanism of Impurity Sensitization

The reported wavelength-dependence of the photoreactivity of 1-piperidinoanthra-quinone (1-PAQ) in hydrogen-donor solvents is ascribed to a chemical sensitization by trace amounts of 1-chloroanthraquinone, as the action spectrum for photoreactivity of the former matches the absorption spectrum of the latter. The photochemistry and photophysics of 1-PAQ seem therefore not to violate the Kasha-Vavilov rule, i.e. its photoreactivity does not involve an upper n — π* triplet state.     

Darstellung von 2,3,4,5-tetrakis(dimethyl)sulfocyclo-pentasilan und 2,3,4,5-etrakis(dimethyl)selenacyclopenta-silan

Octamethylcyclotetrasillan reacts with elemental sulfur or selenium in benzene at 80°C to give the five-membered ring products, cyclo-(Me₂Si)₄S and cyclo-(Me₂Si)₄Se.