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.     

Phenylsulfonyl ene-allenes as efficient precursors to bicyclic systems via intramolecular [2 + 2]-cycloaddition reactions

Various phenylsulfonyl allene derivatives were prepared with double bonds tethered either to the alpha-position or the gamma-position of the allene. These substrates underwent a highly regio- and stereospecific thermal [2 + 2]-cycloaddition across the nonactivated cumulene double bond, forming distal cycloadducts (i.e., 57) in the case of alpha-tethered allenes and proximal adducts (i.e., 25) in the case of gamma-tethered allenes. The mechanistic rationale for the observed stereospecificity involves initial diradical formation, followed by a rapid ring closure to the more stable cis-fused ring system. The tether may be equipped with heteroatoms, allowing for the formation of fused heterocycles (e.g., 61), and the cycloaddition can be facilitated by the introduction of sterically bulky groups and/or by conformational rigidity to the tether. Other modes of cyclization were observed in the presence of sodium benzenesulfinate or Lewis acids, in which cases polar mechanisms prevail. The chemoselectivity is reversed for [4 + 2]-cycloadditions, which prefer instead to engage the vinyl sulfone moiety, independent of whether the tether is attached to the alpha- or gamma-position of the allene.     

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.     

Enantioseparation of chiral N-imidazole derivatives by electrokinetic chromatography using highly sulfated cyclodextrins: mechanism of enantioselective recognition

Baseline separation of ten new substituted [1-(imidazo-1-yl)-1-phenylmethyl)] benzothiazolinone and benzoxazolinone derivatives, with one chiral center, was achieved by CD-EKC using highly sulfated CDs (alpha, beta, gamma highly S-CDs) as chiral selectors. The influence of the type and concentration of the chiral selectors on the enantioseparations was investigated. The highly S-CDs exhibit a very high enantioselectivity power since they allow excellent enantiomeric resolutions compared to those obtained with the neutral CDs. The enantiomers were resolved with analysis times inferior to 2.5 min and resolution factors R(s) of 3.73, 3.90, 1.40, and 4.35 for compounds 1, 2, 3, and 5, respectively, using 25 mM phosphate buffer at pH 2.5 containing either highly S-alpha-CD, highly S-beta-CD, and highly S-gamma-CD (3 or 4% w/v) at 298 K, with an applied field of 0.30 kV/cm. The determination of the enantiomer migration order for the various analytes and the study of the analyte structure-enantioseparation relationships display the high contribution of the interactions between the analytes phenyl ring and the CDs to the enantiorecognition process. The thermodynamic study of the analyte-CD affinities permits us to improve our knowledge about the enantioseparation mechanism.     

Enantiomeric analysis of baclofen analogs by capillary zone electrophoresis, using highly sulfated cyclodextrins: Inclusion ionization constant pKa determination

Using cyclodextrin-capillary zone electrophoresis (CD-CZE), baseline separation of baclofen phaclofen, saclofen, and hydroxy-saclofen, potent gamma-aminobutyric acid(B) (GABA(B)) agonist or antagonists was achieved. A method for the enantioresolution of those analogs of GABA was developed using anionic cyclodextrins (highly sulfated CD or highly S-CD) as chiral selectors and capillaries dynamically coated with polyethylene oxide (PEO). With charged CDs we observed good resolutions due to the large electrophoretic mobility of these chiral selectors opposite to the mobility of the solutes. The highly S-alpha-CD and S-beta-CD were found to be complementary and the most effective complexing agent, allowing good enantiomeric resolution in short runtimes. The complete resolution was obtained using 25 mM phosphate buffer at pH 2.5 containing 3% w/v of highly S-alpha-CD or S-beta-CD at 25 degrees C with an applied field of 0.30 kV/cm. The apparent binding constants of the inclusion complexes were evaluated and the migration order was determined. A comparison was possible to investigate the importance of the anionic group of the molecules in the separations. The pK(a) values were determined for all four compounds in order to explain relative electrophoretic migration of the solutes.