Enantioselective Total Synthesis of (−)‐Blennolide A

Blennolide A can be synthesized through an enantioselective domino‐Wacker/carbonylation/methoxylation reaction of 7 a with 96 % ee and an enantioselective Wacker oxidation of 7 b with 89 % ee. Further transformations led to the α,β‐unsaturated ester (E)‐ 17 , which was subjected to a highly selective Michael addition, introducing a methyl group to give 18 a . After a threefold oxidation and an intramolecular acylation, the tetrahydroxanthenone 4 was obtained, which could be transformed into (?)‐blennolide A (ent‐ 1 ) in a few steps.     

The influence of electrospray ion source design on matrix effects

This study investigates to which extent the design of electrospray ion sources influences the susceptibility to matrix effects (MEs) in liquid chromatography-tandem mass spectrometry (LC-MS/MS). For this purpose, MEs were measured under comparable conditions (identical sample extracts, identical LC column, same chromatographic method and always positive ion mode) on four LC-MS/MS instrument platforms. The instruments were combined with five electrospray ion sources, viz. Turbo Ion Spray, Turbo V(TM) Source, Standard ESI, Jet Stream ESI and Standard Z-Spray Source. The comparison of MEs could be made at all retention times because the method of permanent postcolumn infusion was applied. The MEs ascertained for 45 pesticides showed for each electrospray ion source the same pattern, i.e. the same number of characteristic signal suppressions at equivalent retention times in the chromatogram. The Turbo Ion Spray (off-axis geometry), Turbo V(TM) Source (orthogonal geometry) and the Standard Z-Spray Source (double orthogonal geometry) did not differ much in their susceptibility to MEs. The Jet Stream ESI (orthogonal geometry) reaches a higher sensitivity by an additional heated sheath gas, but suffers at the same time from significantly stronger signal suppressions than the comparable Standard ESI (orthogonal geometry) without sheath gas. No relation between source geometry and extent of signal suppression was found in this study.     

Proof of a conjecture on game domination

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b‐dimensional cube is a Cartesian product I₁×I₂×···×I_b, where each I_i is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b‐dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line—i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number ψ(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least ?log₂ψ(G)?. In this article, we show that for an interval graph G ?log₂ψ(G)??cub(G)??log₂ψ(G)?+2. It is not clear whether the upper bound of ?log₂ψ(G)?+2 is tight: till now we are unable to find any interval graph with cub(G)>?log₂ψ(G)?. We also show that for an interval graph G, cub(G)??log₂α?, where α is the independence number of G. Therefore, in the special case of ψ(G)=α, cub(G) is exactly ?log₂α₂?. The concept of cubicity can be generalized by considering boxes instead of cubes. A b‐dimensional box is a Cartesian product I₁×I₂×···×I_b, where each I_i is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k‐dimensional boxes. It is clear that box(G)?cub(G). From the above result, it follows that for any graph G, cub(G)?box(G)?log₂α?. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323–333, 2010     

A finite element method for the numerical solution of convection-dominated anisotropic diffusion equations

Summary. The proposed method is based on an additive decomposition of the differential operator and the subsequent fitted discretization of the resulting components. For standard situations, the derived stability and error estimates in the energy norm qualitatively coincide with well-known estimates. In the case of small diffusion, a uniform error estimate with reduced order is obtained. Received August 7, 1997 / Revised version received July 15, 1998 / Published online December 6, 1999     

All 2-connected in-tournaments that are cycle complementary

An in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. A digraph D is cycle complementary if there exist two vertex-disjoint directed cycles spanning the vertex set of D. Let D be a 2-connected in-tournament of order at least 8. In this paper we show that D is not cycle complementary if and only if it is 2-regular and has odd order.