On the complexity of the disjoint paths problem

In this paper we consider the disjoint paths problem. Given a graphG and a subsetS of the edge-set ofG the problem is to decide whether there exists a family of disjoint circuits inG each containing exactly one edge ofS such that every edge inS belongs to a circuit inC. By a well-known theorem of P. Seymour the edge-disjoint paths problem is polynomially solvable for Eulerian planar graphsG. We show that (assumingPNP) one can drop neither planarity nor the Eulerian condition onG without losing polynomial time solvability. We prove theNP-completeness of the planar edge-disjoint paths problem by showing theNP-completeness of the vertex disjoint paths problem for planar graphs with maximum vertex-degree three. This disproves (assumingPNP) a conjecture of A. Schrijver concerning the existence of a polynomial time algorithm for the planar vertex-disjoint paths problem. Furthermore we present a counterexample to a conjecture of A. Frank. This conjecture would have implied a polynomial algorithm for the planar edge-disjoint paths problem. Moreover we derive a complete characterization of all minorclosed classes of graphs for which the disjoint paths problem is polynomially solvable. Finally we show theNP-completeness of the half-integral relaxation of the edge-disjoint paths problem. This implies an answer to the long-standing question whether the edge-disjoint paths problem is polynomially solvable for Eulerian graphs.Supported by Sonderforschungsbereich 303 (DFG)     

Cycloaldol approach to the isobenzofuran core of eunicellin diterpenes

[reaction: see text] A novel cycloaldol approach to the isobenzofuran core common to many of the eunicellin diterpenes is described. The cycloaldol precursor was prepared by aldol addition of (S)-(+)-carvone and methacrolein followed by etherification to a glycolate ester. Chemoselective enolization of the glycolate ester led to the cycloaldol adduct in high yield and diastereoselectivity. An oxidative rearrangement-allylic diazene rearrangement sequence established the requisite cis ring fusion.     

New Applications of Polyfunctional Organometallic Compounds in Organic Synthesis Frequently used abbreviations are defined at the end of the article

In the second half of the twentieth century much effort was invested in the preparation of highly reactive polar organometallic reagents. The high reactivity of these reagents precluded the presence of many functional groups and often good chemoselectivities and stereoselectivities could only by achieved by transmetalation reactions. The synthesis of increasingly complex target molecules and the desire to avoid tedious protection-deprotection steps has led inevitably to the use of functionalized organometallic reagents in retrosynthesis. In the last fifteen years, the generation of organic derivatives of numerous metals and metalloids (Li, Mg, B, Zn, Sn) was investigated. In this review the most important preparations and applications of organometallic reagents in organic synthesis will be covered, with particular emphasis on organozinc reagents.     

Toward understanding the ionization of biomarkers from micrometer particles by bio-aerosol mass spectrometry

The appearance of informative signals in the mass spectra of laser-ablated bio-aerosol particles depends on the effective ionization probabilities (EIP) of individual components during the laser ionization process. This study investigates how bio-aerosol chemical composition governs the EIP values of specific components and the overall features of the spectra from the bio-aerosol mass spectrometry (BAMS). EIP values were determined for a series of amino acid, dipicolinic acid, and peptide aerosol particles to determine what chemical features aid in ionization. The spectra of individual amino acids and dipicolinic acid, as well as mixtures, were examined for extent of fragmentation and the presence of molecular ion dimers, which are indicative of ionization conditions. Standard mixtures yielded information with respect to the significance of secondary ion plume reactions on observed spectra. A greater understanding of how these parameters affect EIP and spectra characteristics of bio-aerosols will aid in the intelligent selection of viable future biomarkers for the identification of bio-terrorism agents.     

Proton bound homodimers and heterodimers of amides and amines in the gas phase. Equilibrium studies by Fourier transform ion cyclotron resonance spectrometry

By injection of the proton bound homodimer [DMF.H+.DMF] of N,N-dimethylformamide (DMF) generated in an external ion source into a mixture of DMF and a second base within the cell of a Fourier transform ion cyclotron resonance (FT-ICR) spectrometer the equilibria between [DMF.H+.DMF] and the other possible proton bound dimers [DMF.H+.base] and [base.H+.base] have been studied for 13 different bases. Strongly polar bases like aliphatic amides and dimethyl sulfoxide (DMSO) exchange both DMF in [DMF.H+.DMF] by a two step process, while the almost non-polar amines exchange only one DMF. If the base is a primary or secondary amine, the proton bound heterodimer [DMF.H+.amine] reacts further by the addition of one DMF to create a proton bound trimer [(DMF)2.H+.amine]. The affinity deltaG(DMFH+) of the bases towards protonated DMF relative to neutral DMF depends linearly on the difference deltaGB of the gas phase basicity of DMF and the other base, but different correlation lines are obtained for polar and non-polar ligands (deltaGDMFH+ = 0.44GB(base)-375 [kJ/mol] (r = 0.97) and deltaGDMFH+ = 0.46GB(base)-397 [kJ/mol] (r = 0.99), respectively). This different behavior is explained by a different character of the proton bridge in the heterodimers containing only polar ligands and those incorporating a non-polar ligand besides DMF. The former dimers contain a more or less symmetric proton bridge while the latter can be viewed as a protonated base solvated by DMF. The available data have been used to calculate the molecular pair gas phase basicity of DMF and the 13 bases used and to estimate the dissociation energies of the bonds of the proton bridge in various proton bound heterodimers.     

Heme-protein active site models via self-assembly in water

[structure: see text] Water-soluble models of heme-protein active sites are obtained via the self-assembly of cationic porphyrins 1 and tetrasulfonato calix[4]arene 2 (K(1.2)() = 10(5) M(-)(1)). Selective binding of ligands either outside or inside the cavity of assemblies 1.2 via coordination to the zinc center has been observed. Small ligands such as 4-methylpyridine and 1-methylimidazole are encapsulated, while the bulkier caffeine is bound outside. Assemblies Co-1.2, in which the Zn porphyrin moiety has been replaced by a Co(II) porphyrin, can act as O(2) carriers.     

Single- and multi-channel detection for generalized quantitative analysis in cases of unresolved chromatographic peaks

Computerized quantification of components under overlapping chromatographic peaks is done by calibration of chromatograms against component mixtures. For conventional (single-channel) detectors, the limitations of earlier methods based on ordinary multiple regression, can be circumvented by data reduction with the aid of principal component analysis with the partial least-squares approach. Simulation studies show that the method can be applied even when there is severe peak overlap, unstable baseline, noisy chromatograms or non-linear detector response. Advantages in the quantification of fused peaks by means of multichannel detectors are outlined. Present limitations on the quantitative evaluation of several overlapping component peaks from a single spectro-chromatogram by means of the partial least-squares method combined with multiple regression on the pure component spectra, are discussed with respect to practical high-performance liquid chromatography.     

Capillary electrophoresis - mass spectrometry: survey on developments and applications 2003-2004

The major developments and applications related to CE-MS over the last two years (2003-2004) and most of the reviews and applications found in the ISI Web of Science and publisher data bases are presented in a tabulated way. This article complements our previous review "Capillary electrophoresis - mass spectrometry: 15 years of developments and applications", Electrophoresis, 2003, 24, 3837-3867 for the last two years 2003-2004. All cited articles were analyzed in a way to illustrate (i) in which journals CE-MS-related papers were mostly found over the last decades and (ii) which commercial CE-, MS-instrumentations or CE-MS combinations were mostly used in the European, Asian, and American continent. Additionally, like it was done in our last review, the reader will rapidly find applications classified as forensics, environment, bioanalytics, pharmaceutics, and metabolites.     

Synthesis of α,β-disubstituted ferrocenes via a ferrocenylepoxide intermediate. Preparation and catalytic activity of a new chiral ferrocenyloxazoline

A short synthesis of the chiral oxazoline 10 (>95% e.e.) in six steps from chloroacetylferrocene is described. The ligand can be used successfully in an asymmetric Pd(0)-catalyzed allylic alkylation reaction.