Enantioselective synthesis of trans-4-methylpipecolic acid

An asymmetric synthesis for the preparation of both enantiomers of trans-methylpipecolic acids is described. It is based on Sharpless epoxidation as a chirality source, regioselective ring opening with allylamine, and ring-closing metathesis to construct the piperidine ring. The stereogenic center at C-4 is set by stereoselective hydrogenation that is directed by the alcohol functionality of an intermediate and proceeds with good diastereomeric control (trans/cis 16/1). Crystallization of the Boc-protected amino acid afforded the target products with excellent chemical (98% de) and enantiomeric purity (99% ee).     

A Sufficient Condition for Lipschitz Stability of Controlled Invariant Subspaces

Given a pair of matrices (A, B) we study the Lipschitz stability of its controlled invariant subspaces. A sufficient condition is derived from the geometry of the set formed by the quadruples (A, B, F, S) where S is an (A, B)-invariant subspace and F a corresponding feedback.     

On triconnected and cubic plane graphs on given point sets

Let S be a set of n4 points in general position in the plane, and let h<n be the number of extreme points of S. We show how to construct a 3-connected plane graph with vertex set S, having max{3n/2,n+h−1} edges, and we prove that there is no 3-connected plane graph on top of S with a smaller number of edges. In particular, this implies that S admits a 3-connected cubic plane graph if and only if n4 is even and hn/2+1. The same bounds also hold when 3-edge-connectivity is considered. We also give a partial characterization of the point sets in the plane that can be the vertex set of a cubic plane graph.     

Propanolysis of Esters Using Chlorotrimethylsilane

A variety of methyl esters are converted into the corresponding propyl esters upon treatment with l-propanol and chlorotrimethylsilane. Among them acyclic aliphatic esters have the best conversion rate.     

Selective mode suppression in coplanar waveguides using metamaterial resonators

In this paper, it is shown that split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs) can be used to selectively suppress the odd (slot) mode or the even (fundamental) mode, respectively, in coplanar waveguides. To this end, it is necessary to symmetrically etch the SRRs and the CSRRs in the line. An interpretation of this behavior is reported. The paper is also supported by experimental results, and some applications are highlighted.