We consider chordal SLE(kappa) curves for kappa > 4, where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension min {2-8/kappa,1}. We study the random sets of points at which the curve collides with the real line at a specified "angle" and compute an almost sure dimension spectrum describing the metric size of these sets. We work with the forward SLE flow and a key tool in the analysis is Girsanov's theorem, which is used to study events on which moments concentrate. The two-point correlation estimates are proved using the direct method.Comment: 21 page

Efficient synthesis of unsaturated FA esters of ascorbic acid is possible with only a small excess of one of the reactants in t-amyl alcohol using Candida antarctica lipase as biocatalyst. Using free acids, we obtained yields that were comparable to yields reached using vinyl-activated acyl donors (71, 80, and 86% yields of esters with FA excesses of 1:1, 1:1.5, and 1:2, respectively). As very low water activity is needed to achieve sufficiently high yields of product, molecular sieves were used to improve the ascorbyl ester yields. Ascorbyl oleate is more amorphous and has a much lower m.p. and lower enthalpy of fusion than ascorbyl palmitate. This leads to a higher solubility of ascorbyl oleate in oil, resulting in an increased antioxidant effect compared to that of the palmitate. In an accelerated storage test using deodorized rapeseed oil, samples incubated with ascorbyl palmitate showed noticeable oxidation after 1 wk of storage, whereas samples incubated with ascorbyl oleate displayed negligible oxidation for 9 and 4 wk at 30 and 40°C, respectively.Paper no. J10512 in JAOCS 80, 795-799 (August 2003).Ascorbyl palmitate is a fat-soluble antioxidant commonly used in foods to prevent oxidation of sensitive fats and oils. Ascorbyl palmitate has a disadvantage, however, in that it has relatively low solubility in oils. The solubility can be improved by the addition of lecithin, although this causes the product to become hygroscopic. Another way to improve the solubility of an ascorbyl FA ester is to modify its structure to make it less crystalline. This can be done, for example, by introducing a double bond in the FA. Oleic acid is unsaturated, readily available, inexpensive, and approved for use in foods. This makes it an attractive candidate to replace the palmitic acid in an ascorbyl ester. The chemical synthesis of saturated ascorbyl FA esters is straightforward (1). A similar procedure for the synthesis of ascorbyl oleate has been described in the literature (2) but has proven hard to repeat. The difficulties are due to the double bond of oleic acid, which is too sensitive for the reaction conditions needed for the chemically catalyzed esterification. Enzymatic catalysis, however, can be performed at lower reaction temperatures and under milder conditions, enabling the enzymatic synthesis of ascorbyl oleate (Scheme 1). Because the reactants differ in polarity, the number of suitable solvents available is limited. We used t-amyl alcohol because it dissolves the reactants at high concentrations and does not deactivate the enzyme.In 1971, Arakawa et al.(3) reported on the first enzymatic synthesis of ascorbyl laurate in aqueous solution. In 1990, Enomoto et al. (4) filed a patent on the esterification in organic solvents, and esterfications in t-amyl alcohol were reported by Humeau et al. (5) in 1995. Since then, not only saturated FA have been used, but also various unsaturated FA (6-8) as well as of phenyl butyric acid (9) and methyl lactate (10). These syntheses have typically reached yields below 50% unles...

We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green's function is the probability that the LERW passes through a given edge in the domain. We prove that this probability, multiplied by the inverse mesh size to the power 3/4, converges in the lattice size scaling limit to (a constant times) an explicit conformally covariant quantity which coincides with the SLE 2 Green's function.The proof does not use SLE techniques and is based on a combinatorial identity which reduces the problem to obtaining sharp asymptotics for two quantities: the loop measure of random walk loops of odd winding number about a branch point near the marked edge and a "spinor" observable for random walk started from one of the vertices of the marked edge.