Rank-perfect and" weakly rank-perfect graphs

An edge e of a perfect graph G is critical if G−e is imperfect. We would like to decide whether G−e is still “almost perfect” or already “very imperfect”. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.     

On rank-perfect subclasses of near-bipartite graphs

Shepherd95 proved that the stable set polytopes of near-bipartite graphs are given by constraints associated with the complete join of antiwebs only. For antiwebs, the facet set reduces to rank constraints associated with single antiwebs by Wagler2004. We extend this result to a larger graph class, the complements of fuzzy circular interval graphs, recently introduced in ChudnovskySeymour2004. Received: November 2004 / Revised version: June 2005     

Resolvent estimates in W−1,p related to strongly coupled‐linear parabolic systems with coupled nonsmooth capacities

We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W^{?1, p} spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain L^p estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd.     

From terminal alkynes directly to branched amines

The one-pot synthesis of several branched secondary aliphatic amines is described. Hydroamination of terminal alkynes with aliphatic primary amines in the presence of Cp₂Ti(η²-Me₃SiCCSiMe₃) gives the corresponding aldimines as intermediates. Reaction of these in situ produced aldimines with organolithium reagents (n-BuLi, PhLi) provides the α-branched amines in an easy way in upto 78% overall yield.     

Cyclohexylphosphonic acid

The title compound, C₆H₁₃O₃P, displays a crystallographic mirror plane. Bond lengths in the phosphonic acid moiety are P—O = 1.5557 (13) Å and P=O = 1.5089 (18) Å. The mol­ecules are linked via intermolecular hydrogen bonding to form a one‐dimensional chain of fused rings. There are no significant contacts between planes.     

Biologically active compounds through catalysis: efficient synthesis of N-(heteroarylcarbonyl)-N'-(arylalkyl)piperazines

A practical route for the synthesis of new biologically active 5-HT(2 A) receptor antagonists has been developed. In only three catalytic steps, this class of central nervous system (CNS) active compounds can be synthesized efficiently with high diversity. As the initial step, an anti-Markovnikov addition of amines to styrenes provides an easy route to N-(arylalkyl)piperazines, which constitute the core structure of the active molecules. Here, base-catalyzed hydroamination reactions of styrenes with benzylated piperazine proceeded in high yield even at room temperature. After catalytic debenzylation, the free amines were successfully carbonylated with different aromatic and heteroaromatic halides and carbon monoxide to yield the desired compounds in good to excellent yields. The two key reactions, base-catalyzed hydroamination of styrenes and palladium-catalyzed aminocarbonylation of haloarenes/heterocycles, showed tolerance towards various functional groups, thereby demonstrating the potential to synthesize a wide variety of new derivatives of this promising class of pharmaceuticals.     

Chloroantimonate(III): Die Kristallstruktur des 4,4′-Dipyridylium-pentachloroantimonats, (C10H8N2H2)SbCl5

Chloroantimonates(III): Crystal Structure of 4,4′-Dipyridylium Pentachloroantimonate, (C₁₀H₈N₂H₂)SbCl₅ (C₁₀H₈N₂H₂)SbCl₅ crystallizes in the triclinic space group P1 with a= 843.1(5), b = 958.6(8), c = 1098.0(10) pm, α = 112.45(6), β = 101.95(6), γ = 97.78(6)° and Z = 2. The structure is built up of 4,4 °-dipyridylium cations and pentachloroantimonate anions. The Sb atoms are distorted octahedrally coordinated. Mean distances are Sb? Cl = 242 pm (1×), Sb? Cl = 255 pm (2×), Sb ? Cl = 275 pm (2×) and Sb…?Cl.= 319 pm (1× ). The anions build up dimers.     

An algebraic approach to manifold-valued generalized functions

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.     

Ionic liquid 1-ethyl-3-methylimidazolium acetate: an attractive solvent for native chemical ligation of peptides

The ionic liquid 1-ethyl-3-methylimidazolium acetate ([C₂mim][OAc]) was successfully used as alternative solvent for native chemical ligation of peptide fragments to produce model peptide LYRAXCRANK (X = G, A, L, N, Q, K, and F). The commonly used buffer system including thiol additives such as thiophenol and benzyl mercaptan can be replaced by the nontoxic ionic liquid [C₂mim][OAc]. In addition to improving the solubility of the peptides in [C₂mim][OAc], yields and rates of the ligation reactions were found to be efficiently enhanced.