Clean triangulations

A polyhedron on a surface is called a clean triangulation if each face is a triangle and each triangle is a face. LetS _p (resp.N _p ) be the closed orientable (resp. nonorlentable) surface of genusp. If (S) is the smallest possible number of triangles in a clean triangulation ofS, the results are: (N ₁)=20, (S ₁)=24, lim(S _p )p ^–1=4, lim(N _p )p ^–1=2 forp.     

Polyelectrolytes in thin liquid films

The review addresses the influence of polyelectrolytes on the statics and dynamics of thin liquid films. Both, changes of interfacial and bulk properties, contribute to the overall behaviour of thin films formed from aqueous polyelectrolyte solutions. Therefore, the chapter is separated into two parts: polyelectrolytes at film interfaces and polymers in film bulk.     

Antimicrobial activity and spectral, magnetic and thermal studies of some transition metal complexes of a Schiff base hydrazone containing a quinoline moiety

A series of new copper(II), cobalt(II), nickel(II), manganese(II), iron(III), and uranyl(VI) complexes of the Schiff base hydrazone 7-chloro-4-(benzylidene-hydrazo)quinoline (HL) were prepared and characterized. The Schiff base behaves as a monobasic bidentate ligand. Mononuclear complexes with the general composition [ML2(Cl)m(H2O)2(OEt)n] x xEtOH (M = Cu(II), Co(II), Ni(II), Mn(II), Fe(III) or UO2(VI); m and n = 0-1; x = 1-3) were obtained in the presence of Li(OH) as a deprotonating agent. The nature of bonding and the stereochemistry of the complexes have been deduced from elemental analyses, infrared, electronic spectra, magnetic susceptibility and conductivity measurements. An octahedral geometry was suggested for all the complexes except the Cu(II) and UO2(VI) ones. The Cu(II) complex has a square-planar geometry distorted towards tetrahedral, while the UO2(VI) complex displays its favored heptacoordination. The Schiff base ligand, HL, and its complexes were tested against one strain gram +ve bacteria (Staphylococcus aureus), gram -ve bacteria (Escherichia coli), and Fungi (Candida albicans). The prepared metal complexes exhibited higher antibacterial activities than the parent ligand and their biopotency is discussed.     

Synthesis and properties of alkynethiolate gold(I) complexes

A series of alkynethiolate gold(I) derivatives have been synthesised by the cleavage of 4-monosubstituted 1,2,3-thiadiazoles in the presence of strong bases. The syntheses of the 1.2,3-thiadiazoles with p-cyanophenyl, p-tolyl, 2-thienyl, 3-thienyl and 9,9-dimethylfluoren-2-yl fragments are also described. All the complexes have been characterised by spectroscopic techniques and the complexes [Au(p-CH3-C6H4-C[triple bond]C-S)PPh3], [Au(3-C4H3S-C[triple bond]C-S)PPh3] and PPN[Au(p-CH3-C6H4-C[triple bond]C-S)(C6F5)] by X-ray analysis. The electrochemically polymerizable mononuclear bis(alkynethiolate) gold(I) complex PPN[Au(3-C4H3S-C[triple bond]C-S)2] is also described, including its electropolymerization and electrochemical properties.     

Determination of hydroxy metabolites of polycyclic aromatic hydrocarbons by fully automated solid-phase microextraction derivatization and gas chromatography-mass spectrometry

A fully automated sample pretreatment method was developed for the detection of mono and dihydroxy metabolites of polycyclic aromatic hydrocarbons (PAHs) by gas chromatography-mass spectrometry in the selected ion monitoring mode. Direct immersion solid-phase microextraction for the extraction of target compounds and the headspace on-fiber silylation with N,O-bis(trimethylsilyl)trifluoroacetamide were performed automatically by a multipurpose autosampler (MPS2). The operating conditions including extraction time, derivatization time, ionic strength, pH, and incubation temperature were optimized. Calibration responses of nine metabolites of PAHs over a concentration range of 0.1-100 microg L(-1) with a correlation coefficient of 0.999 were obtained. The detection limits of the nine metabolites in mini pore water, minimal salts medium and soil extract culture medium were in the range of 0.001-0.013, 0.002-0.024 and 0.002-0.134 microg L(-1), respectively, while the respective quantification limits were 0.003-0.044, 0.005-0.081 and 0.008-0.447 microg L(-1). The reliability was confirmed by the traditional solid-phase extraction method. The proposed method could be used to analyze the metabolites of PAHs degraded by microorganisms such as algae and to determine the biodegradation pathways of PAHs.     

Ru–bis(pyridine)pyrazolate (bpp)‐Based Water‐Oxidation Catalysts Anchored on TiO2: The Importance of the Nature and Position of the Anchoring Group

Three distinct functionalisation strategies have been applied to the in,in‐[{Ru^II(trpy)}₂(μ‐bpp)(H₂O)₂]³⁺ (trpy=2,2′:6′,2′′‐terpyridine, bpp=bis(pyridine)pyrazolate) water‐oxidation catalyst framework to form new derivatives that can adsorb onto titania substrates. Modifications included the addition of sulfonate, carboxylate, and phosphonate anchoring groups to the terpyridine and bis(pyridyl)pyrazolate ligands. The complexes were characterised in solution by using 1D NMR, 2D NMR, and UV/Vis spectroscopic analysis and electrochemical techniques. The complexes were then anchored on TiO₂‐coated fluorinated tin oxide (FTO) films, and the reactivity of these new materials as water‐oxidation catalysts was tested electrochemically through controlled‐potential electrolysis (CPE) with oxygen evolution detected by headspace analysis with a Clark electrode. The results obtained highlight the importance of the catalyst orientation with respect to the titania surface in regard to its capacity to catalytically oxidize water to dioxygen.     

Algebraic signatures of convex and non-convex codes

A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as they arise from the activity of neurons that have convex receptive fields. In this paper, we develop algebraic methods to determine if a code is convex. Specifically, we use the neural ideal of a code, which is a generalization of the Stanley–Reisner ideal. Using the neural ideal together with its standard generating set, the canonical form, we provide algebraic signatures of certain families of codes that are non-convex. We connect these signatures to the precise conditions on the arrangement of sets that prevent the codes from being convex. Finally, we also provide algebraic signatures for some families of codes that are convex, including the class of intersection-complete codes. These results allow us to detect convexity and non-convexity in a variety of situations, and point to some interesting open questions.     

The heavy quarkonium spectrum at order mαslnαs

We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at O(mα_s⁵) in the heavy quarkonium spectrum. These leading logs, when Λ_QCDmα_s², give the complete O(mα_s⁵lnα_s) corrections to the heavy quarkonium spectrum.