On the Wiener index of a graph

A modification of the Weiner index which properly takes into account the symmetry of a graph is proposed. The explicit formulae for the modified Wiener index of path, cycle, complete bipartite, cube and lattice graphs are derived and compared with their standard Wiener index.     

The non-orientable genus of some metacyclic groups

We describe non-orientable, octagonal embeddings for certain 4-valent, bipartite Cayley graphs of finite metacyclic groups, and give a class of examples for which this embedding realizes the non-orientable genus of the group. This yields a construction of Cayley graphs for which is arbitrarily large, where and are the orientable genus and the non-orientable genus of the Cayley graph.Work supported in part by the Research Council of Slovenia, Yugoslavia and NSF Contract DMS-8717441.Supported by NSF Contract DMS-8601760.     

Ultrasound effects on photochemical reactions, part 1: photochemical reactions of ketones with alkenes

Ultrasound considerably enhances and simplifies photochemical reaction of cyclohexanone with cyclohexene. The Paterno-Büchi reaction of acetone with ethyl vinyl ether is enhanced by ultrasound and yields a different ratio of cis/trans oxetanes under sonication by comparison with the silent reaction. Sonication appears to affect the first reaction by homogenization of excited intermediates and by quenching the excited triplet state at the second reaction.     

Transition Metal Ion-binding Properties of a 14-Membered N2O2S2- Macrobicyclic Ligand

The selective liquid–liquid extraction of various transition metal cations from the aqueous phase to the organic phase was carried out using a 14-membered N₂O₂S₂-macrobicycle. Metal picrates such as Pb²⁺, Co²⁺, Zn²⁺, Ni²⁺,Cu²⁺ and Cd²⁺ were used in this extraction studies. It was found that the ligand showed moderate selectivity towards Pb²⁺ only among the other metals. The extraction constant (log K _ex) was determined to be 13.8 for Pb²⁺ complex.     

Site specificity in cycloadditions of diphenylnitrile imine with 8-substituted-8-azaheptafulvenes and tricarbonyl (8-azaheptafulvene) iron complexes

The reaction of diphenylnitrile imine with 8-substituted-8-azaheptafulvenes is both site and regiospecific and resulted in a mixture of two [8+4]-adducts in high yield. The mechanism of the reaction was investigated. The [8+4]-adducts underwent easily a reversible thermal 1,7-sigmatropic shift involving an sp³ nitrogen centre. Diphenylnitrile imine reacted also with tricarbonyl(8-azaheptafutvene)iron complexes lo give adducts to the CN double bond, the degradative oxidation of which with trimethylamine-N-oxide was investigated. The specificity of the cycloadditions is briefly discussed on the basis of a simple perturbation theory approach.     

Precipitation and association in a mixture of dodecylammonium chloride and sodium dodecyl sulfate in aqueous medium

The precipitation boundary in aqueous mixtures of dodecylammonium chloride (DDACl) and sodium dodecyl sulfate (NaDS) was determined in the absence and in the presence of 1 mol dm^–3 NaCl. The structure and the composition of the solid phase was characterized by x-ray and chemical analysis, respectively. Activities of Cl^– and Na⁺ ions in the aqueous phase were measured by ion-selective electrodes. As determined by calorimetry, precipitation is an exothermic process.The DDA·DS precipitate was formed in the equimolar region of the precipitation components. Its crystallographic structure is described. In an excess of sodium dodecyl sulfate, the precipitate incorporated substantial amounts of NaDS, as detected by analyses of both solid and liquid phases. X-ray analysis of the dry sample showed peaks of crystalline NaDS. According to the polarization microscopy of wet samples, one may conclude that liquid crystals, containing an excess of NaDS, are incorporated in the solid DDA·DS phase. The same was found in the case of an excess of DDACl; mixed liquid crystals with an excess of DDACl were incorporated in the solid DDA·DS.Interpretation of the solubility boundary points to the presence of DDA⁺·DS^– ion pairs. Formation of these species at low ionic strengths is characterized by the equilibrium constantK _a ⁰ 10⁶. However, in the 1 mol dm^–3 NaCl, the association of DDA⁺ and DS^– ions into pairs is inhibited (K _a ⁰ 0). This finding can be explained in terms of ionic clouds around the charged surfactant heads: if these heads are not in close contact, but separated due to structural effects of the chains, the dense distribution of counterions around them at high ionic strengths may compensate for electrostatic attraction and, thus, inhibit ion-pairing.     

Study of SNAr Reactions of Halobenzenes with Imidazole under Ultrasonic and Microwave Irradiation

Summary. Nucleophilic aromatic substitution reactions with imidazole of haloarenes having strongly electron-withdrawing groups were studied under ultrasonic and microwave irradiations. The course of the S_NAr reactions was found to be strongly dependent on the electron-withdrawing properties of the substituents as well as on the leaving ability of the halogen atom. Microwave irradiation allowed to shorten the reaction time and to increase the yields compared with ultrasonic irradiation.     

Analysis of equilibrium in heme model systems, by a successive linear regression method

A method for determination of equilibrium constants in heme model systems is proposed, based on successive linear regression applied to spectrophotometric titrations. The method is illustrated for bis(dimethylglyoximate) iron(II) complexes with pyridine and 4-cyanopyridine ligands.     

A novel approach to the synthesis of 1,2-cis-glycopyranosides

Methyl 3,4,6-tri-O-benzyl-α-D-glucopyranoside and methyl 3,4,6-tri-O-benzyl-β-D-mannopyranoside were directly obtained by m-chloroperbenzoic acid treatment of (Z)-(2R,3R,4R)-6-methoxy-1,3,4-tribenzyloxy-5-hexen-2-ol.     

Cobalt oxide/tetraruthenated cobalt-porphyrin composite for hydrogen peroxide amperometric sensors

A new composite material constituted by mu-{5,10,15,20-tetra(4-pyridyl)porphyrinato cobalt(iii)}-tetrakis-{chloro-bis-(2,2'-bipyridine)ruthenium(ii)} complex (or CoTRP) and cobalt oxide, exhibiting high stability and sensitivity for the quantification of hydrogen peroxide, was obtained by the electrochemical polymerization of the tetraruthenated cobalt porphyrin in alkaline medium. The optimized experimental conditions for the preparation of the modified glassy carbon electrodes and for analysis of H2O2 were carefully determined. Fast sequential analysis (120 determinations h(-1)) in a wide linear dynamic range (5.0 x 10(-7) mol L(-1) to 2.0 x 10(-3) mol L(-1)), with high sensitivity and low detection limit (2.0 x 10(-7) mol L(-1)), was achieved by using these electrodes and the batch injection analysis (BIA) technique. Such characteristics allied to a good stability were explored for the specific determination of hydrogen peroxide in six commercial cosmetics and pharmaceutical product samples, giving results in excellent agreement with those obtained by the spectrophotometric method.