Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation

In this work we present a condition for the regularity, in both space and Malliavin sense, of strong solutions to SDEs driven by Brownian motion. We conjecture that this condition is optimal. As a consequence, we are able to improve the regularity of densities of such solutions. We also apply these results to construct a classical solution to the stochastic transport equation when the drift is Lipschitz.     

A computational study on the role of chiral N-oxides in enantioselective Pauson-Khand reactions

Density functional calculations were carried out to ascertain the origin of enantioselectivity in the brucine N‐oxide (BNO)‐assisted enantioselective Pauson–Khand reaction (PKR) of norbornene with 2‐methyl‐3‐butyn‐2‐ol. The computed ee value in acetone is 68 % (R), which compares well to the previously reported experimental value of 58 % (R). In DME the computed ee value of 76 % (R) is in excellent agreement with the experimentally determined value of 78 % (R). The mechanism of enantioselectivity consists of several steps. First, the dicobalt complex is activated by BNO with chirality transfer from enantiopure BNO to the dicobalt complex. Second, competition occurs between a racemization process and complexation with the olefin reagent, which leads to the products. The lower ee value in acetone is due to the lower energy barrier of the racemization process. Calculations show that replacement of BNO by a hypothetical more enantioselective chiral N‐oxide will hardly increase the ee value beyond 90 %.