Enantioselective decarboxylative alkylation reactions: catalyst development, substrate scope, and mechanistic studies

α-Quaternary ketones are accessed through novel enantioselective alkylations of allyl and propargyl electrophiles by unstabilized prochiral enolate nucleophiles in the presence of palladium complexes with various phosphinooxazoline (PHOX) ligands. Excellent yields and high enantiomeric excesses are obtained from three classes of enolate precursor: enol carbonates, enol silanes, and racemic β-ketoesters. Each of these substrate classes functions with nearly identical efficiency in terms of yield and enantioselectivity. Catalyst discovery and development, the optimization of reaction conditions, the exploration of reaction scope, and applications in target-directed synthesis are reported. Experimental observations suggest that these alkylation reactions occur through an unusual inner-sphere mechanism involving binding of the prochiral enolate nucleophile directly to the palladium center.     

Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation

A method for calculating special grid placement for three-point schemes which yields exponential superconvergence of the Neumann to Dirichlet map has been suggested earlier. Here we show that such a grid placement can yield impedance which is equivalent to that of a spectral Galerkin method, or more generally to that of a spectral Galerkin-Petrov method. In fact we show that for every stable Galerkin-Petrov method there is a three-point scheme which yields the same solution at the boundary. We discuss the application of this result to partial differential equations and give numerical examples. We also show equivalence at one corner of a two-dimensional optimal grid with a spectral Galerkin method.

     

Topological structure of candidates for positive curvature

In light of recent advances in the study of manifolds admitting Riemannian metrics of positive sectional curvature, the study of certain infinite families of seven dimensional manifolds has become a matter of interest. We determine the cohomology ring structures of manifolds belonging to these families. This particular ring structure indicates the existence of topological invariants distinguishing the corresponding homeomorphism and diffeomorphism type. We show that all families contain representatives of infinitely many homotopy types.     

The “food polymer science” approach to flour functionality and ingredient technology in biscuit baking

An overview is made on the “food polymer science” approach developed by the authors. The quality and performance of flours for the production of cookies and crackers have been shown to depend upon the major functional polymeric components of flour: gluten protein, damaged starch, and pentosans. Of these, damaged starch and soluble pentosans in soft-wheat flours are detrimental to the commercial production of low-moisture cookies and crackers. The detrimental effects of soluble pentosans in flours can be eliminated through the use of pentosanase enzyme in cookie and cracker doughs. Three commercialized applications of this industrial enzyme technology have been patented by Nabisco. The “food polymer science” approach to baking technology has also been used to study finished-product attributes such as texture, in the context of the thermomechanical properties (e.g. modulus) of glassy solid and rubbery liquid matrices. Results of various studies have clearly demonstrated that products in a glassy solid physical state (at T < T_g) are hard and crisp in texture, but upon increasing plasticization by water (such that T_g is depressed below the observation T), are transformed to a rubbery or viscous liquid state, wherein textural hardness (and mechanical modulus) and crispness are dramatically reduced.