Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.     

Synthesis and structural characterisation of [(Ph3P)AuCo(CO)3(PPh3)]

Summary [(Ph₃P)AuCo(CO)₃(PPh₃)] has been synthesised from [(Ph₃P)AuCo(CO)₄], PPh₃v and Me₃NO in acetonitrile. Its molecular structure, determined by single-crystal x-ray crystallography, consists of an almost linear P-Au-Co-P arrangement in which the Co atom is in a slightly distorted trigonalbipyramidal geometry, with the Au and P atoms occupying the apical sites. The Au-Co bond length of 2.450(1) ? is shorter than that reported for [(Ph₃P)AuCo(CO)₄]. The carbonyl ligands are bent towards the Au atom and the mean Au-Co-C angle is 81(1)°.     

Kinetically inert transition metal complexes that reversibly bind to DNA

Transition metal complexes that reversibly bind to DNA have been studied for almost 30 years. In the last few years a variety of new systems have been developed, employing a range of metal ions and ligand architectures. In many cases, high affinity binding and specific selectivities have been observed. These complexes display properties that make them attractive as probes of DNA structure and function, suggesting that they may find a r?le as prototypical tools for a spectrum of applications, from basic molecular biology to medicine. This review presents an overview of some of the structures and properties of such complexes.     

Binary mixtures based on polycaprolactone and cellulose derivatives

Pyrolytic process has a promising potential for the environmentally friendly upgrading of lignocellulosic and plastic waste. Thermogravimetry and pyrolysis-gas chromatography-mass spectrometry (Py-GC/MS) were used to get information about the reactive decomposition of PCL in binary mixtures with microcrystalline cellulose (MC) or sisal fibres (SF). Preliminary thermogravimetric investigation showed that biomass is thermally degraded at lower temperatures than PCL and this process has a predominant influence on the thermal behaviour of the mixtures. Discrepancies between the experimental and predicted TG/DTG profiles were considered as a measurement of the extent of interactions occurring on co-pyrolysis. It was found that reactivity of PCL was slightly increased in PCL-SF binary mixtures. Evolution of acidic products from cellulose and hemicelluloses decomposition may promote PCL degradation in binary mixtures with SF. It seems that the co-pyrolysis process could have potential for the environmentally friendly transformation of biocomposites.     

Synthesis and conformational analysis of novel N(OCH3)-linked disaccharide analogues

N(OMe)-linked disaccharide analogues, isosteric to the corresponding natural disaccharides, have been synthesized by chemoselective assembly of unprotected natural monosaccharides with methyl 6-deoxy-6-methoxyamino-alpha-D-glucopyranoside in an aqueous environment. The coupling reactions were found to be chemo- and stereoselective affording beta-(1-->6) disaccharide mimics when using Glc and GlcNAc; in the case of Gal, the beta-anomer was prevalent (beta:alpha=7:1). An iterative method for the synthesis of linear N(OMe) oligosaccharide analogues was demonstrated, based on the use of an unprotected monosaccharide building block in which an oxime functionality at C-6 is converted during the synthesis into the corresponding methoxyamino group. The conformational analysis of these compounds was carried out by using NMR spectroscopy, ab initio, molecular mechanics, and molecular dynamics methods. Optimized geometries and energies of fourteen conformers for each compound have been calculated at the B3LYP/6-31G* level. Predicted conformational equilibria were compared with the results based on NMR experiments and good agreement was found. It appears that N(OMe)-linked disaccharide analogues exhibit a slightly different conformational behavior to their parent natural disaccharides.     

Rapid screening method for the determination of diethylstilbestrol in edible animal tissue by column liquid chromatography with electrochemical detection

A rapid and sensitive screening method for the determination of residues of diethylstilbestrol in edible animal tissue is described. The analyte was extracted from the tissue with tert.-butyl methyl ether, reextracted with 1 M sodium hydroxide and further cleaned up by solid-phase extraction with C18 cartridges. Analysis was performed by isocratic elution with a phosphate-buffered mobile phase, methanol-0.05 M phosphate buffer pH 3.5 (67:33), on a Nucleosil 5-microns C18 column with electrochemical detection at +0.90 V. The average recovery of trans-diethylstilbestrol in spiked samples is 66%, with a standard deviation of 14% (n = 22) in the range 0.5-2.0 microgram/kg. The detection limit is 0.1-0.2 microgram/kg, although at this level other compounds may interfere and give rise to false positive results.     

Trehalose-based cyclodextrin analogs: cyclotrehalans (CTs)

A new concept for the de novo synthesis of artificial glyconanocavities is presented. The use of alternating α,α′-trehalose building blocks and (thio)urea segments allows the efficient synthesis of a new family of cyclooligosaccharides, namely cyclotrehalans (CTs), featuring a convex-shaped cavity with an apolar environment. CTs are designed to exhibit molecular inclusion abilities similar to that of cyclodextrins (CDs). Contrary to CDs, CTs expose the monosaccharide β-face to the inner cavity, while the (thio)urea tethers provides some conformational adaptability. High-yielding syntheses of a series of CTs and a preliminary evaluation of their inclusion properties are reported.