Convergence of path measures arising from a mean field or polaron type interaction

Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag T_EX ProbTh macro package 1991.     

Infinite-dimensional diffusion processes as gibbs measures onC[0,1]^{Z^d }

Summary An infinite lattice system of interacting diffusion processes is characterized as a Gibbs distribution on with continuous local conditional probabilities. Using estimates for the Vasserstein metric onC[0, 1], Dobrushin's contraction technique is applied in order to obtain information about macroscopic properties of the entire diffusion process.     

Improved access to 19-nor-7β, 8β-methylene-taxoids and formation of a 7-membered C-ring analog of doxetaxel by electrochemistry

A new route to semisynthetic 19-nor-7β, 8β-methylene taxoids, such as compound 8, from the 7-O-trifluoromethanesulfonyl derivative 6 is reported. Evidence for a dissociation of the triflate to form a carbocation at C-7 under the reaction conditions is presented. Electrochemical reduction of the cyclopropane taxoid 8 gives, besides the expected 10-dehydroxy-cyclopropane analog 10, the 7-membered C-ring derivative 11.     

Hypericin and Pseudohypericin. Purity Criteria and Quantitative Determination in Extracts of Saint John’s Wort (Hypericum perforatum)

Summary. Hypericin and pseudohypericin in extracts of St. Johns Wort (Hypericum perforatum) are assayed using UV-Vis, measuring the absorbance at 588nm of a methanolic solution of the compounds. The value of the absorption coefficient is difficult to define insofar as none of the routine purity criteria can be applied to these two compounds. Analysis of the entire UV-Vis spectrum from 220 to 740nm would seem to be a reliable way of comparing different samples. A UV-Vis spectrum was recorded for each of the compounds using a Photodiode array detection system. A more accurate way of determining the levels of hypericin and pseudohypericin in extracts of St. Johns Wort using these reference spectra is described.     

Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations

Density expansions for hypoelliptic diffusions (X¹,…,X^d) are revisited. We are particularly interested in density expansions of the projection at time T > 0 with l ≤ d. Global conditions are found that replace the well‐known “not‐in‐cut‐locus” condition known from heat kernel asymptotics. Our small‐noise expansion allows for a “second order” exponential factor. As an application, new light is shed on the Takanobu‐Watanabe expansion of Brownian motion and Lévy's stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in the companion paper 12 .© 2013 Wiley Periodicals, Inc.     

Surface order large deviations for high-density percolation

Summary We derive surface order large deviation estimates for the volume of the largest cluster and for the volume of the largest region surrounded by a cluster of a Bernoulli percolation process restricted to a big finite box, with sufficiently large parameter. We also establish a useful version of the isoperimetric inequality, which is the main tool of our proofs.     

Markov Chain Approximations to Nonsymmetric Diffusions with Bounded Coefficients

We consider a certain class of nonsymmetric Markov chains and obtain heat kernel bounds and parabolic Harnack inequalities. Using the heat kernel estimates, we establish a sufficient condition for the family of Markov chains to converge to nonsymmetric diffusions. As an application, we approximate nonsymmetric diffusions in divergence form with bounded coefficients by nonsymmetric Markov chains. This extends the results by Stroock and Zheng to the nonsymmetric divergence forms. © 2012 Wiley Periodicals, Inc.     

Direct access to 2-debenzoyl taxoids by electrochemistry, synthesis of 2-modified docetaxel analogs

A new route to semisynthetic 2-modified docetaxel analogs is described using electrochemical cleavage of the 2-benzoate as the key reaction. Subsequent reacylation at C-2 followed by sequential deprotections afforded the title analogs. Biological results of selected 2-docetaxel analogs are presented.     

Hydrodynamic limit for the Ginzburg–Landau ∇ϕ interface model with non-convex potential

The hydrodynamic limit of the Ginzburg–Landau $??$ interface model was derived in Funaki and Spohn (1997) and Nishikawa (2003) for strictly convex potentials. This paper deals with non-convex potentials under suitable assumptions on the free energy and identification of the extremal Gibbs measures which have been recently established at sufficiently high temperature in Cotar and Deuschel (2012). Because of the non-convexity, many difficulties arise, especially, on the identification of equilibrium states. We show the equivalence between the stationarity and the Gibbs property under quite general settings, and we complete the identification of equilibrium states. We also establish some uniform estimates for variances of extremal Gibbs measures.