On the cut polytope

The cut polytopeP _C (G) of a graphG=(V, E) is the convex hull of the incidence vectors of all edge sets of cuts ofG. We show some classes of facet-defining inequalities ofP _C (G). We describe three methods with which new facet-defining inequalities ofP _C (G) can be constructed from known ones. In particular, we show that inequalities associated with chordless cycles define facets of this polytope; moreover, for these inequalities a polynomial algorithm to solve the separation problem is presented. We characterize the facet defining inequalities ofP _C (G) ifG is not contractible toK ₅. We give a simple characterization of adjacency inP _C (G) and prove that for complete graphs this polytope has diameter one and thatP _C (G) has the Hirsch property. A relationship betweenP _C (G) and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied.     

AgNi3(PO4)(HPO4)2: an alluaudite‐like structure

The new title phosphate, silver trinickel phosphate bis(hydrogenphosphate), has been synthesized by the hydro­thermal method. It has an alluaudite‐like structure but shows some differences owing to the presence of the H atoms. The structure is isomorphous with the compounds of general formula AM₃(XO₄)(HXO₄)₂ (A is Na or Ag, M is Co, Zn or Mn, and X is As or P), with the Ag atom, one Ni atom and one P atom lying on twofold axes.     

Total synthesis of dolastatin 10 through ruthenium-catalyzed asymmetric hydrogenations

A total synthesis of dolastatin 10, a potent inhibitor of microtubule assembly, which displayed remarkable antineoplastic activity, is reported. Our synthetic approach was based upon ruthenium-promoted asymmetric hydrogenation of β-keto esters derived from (S)-Boc-proline and (S)-Boc-isoleucine for the construction of the two key units: (2R,3R)-Boc-dolaproine (Dap) and (3R)-Boc-dolaisoleucine (Dil).     

Chevalley Cohomology for linear graphs

The space of linear polyvector fields on is a Lie subalgebra of the (graded) Lie algebra , equipped with the Schouten bracket. In this paper, we compute the cohomology of this subalgebra for the adjoint representation in , restricting ourselves to the case of cochains defined with purely aerial Kontsevich’s graphs, as in Pac. J. Math. 218(2):201–239, 2005. We find a result which is very similar to the cohomology for the vector case Pac. J. Math. 229(2):257–292, 2007. This work was supported by the CMCU contract 06 S 1502. W. Aloulou and R. Chatbouri thank the Université de Bourgogne and D. Arnal the Faculté des Sciences de Monastir for their kind hospitalities during their stay.     

Hydrogen bonding interactions of pyridine*+ with water: stepwise solvation of distonic cations

The solvation energies of the pyridine*+ radical cation by 1-4 H2O molecules were determined by equilibrium measurements in a drift cell. The binding energies of the pyridine*+(H2O)n clusters are similar to the binding energies of protonated pyridine-water clusters, (C5H5NH+)(H2O)n, which involve NH+..OH2 bonds and different from those of the solvated benzene radical cation-water clusters, C6H6*+(H2O)n, which involve CHdelta+..OH2 bonds. These relations indicate that the observed pyridine*+ ions have the distonic *C5H4NH+ structures that can form NH+..OH2 bonds. The observed thermochemistry and ab initio calculations show that these bonds are not affected significantly by an unpaired electron at another site of the ion. Similar observations also identify the 2-fluoropyridine*+ distonic ion. The distonic structure is also consistent with the reactivity of pyridine*+ in H atom transfer, intra-cluster proton transfer and deprotonation reactions. The results present the first measured stepwise solvation energies of distonic ions, and demonstrate that cluster thermochemistry can identify distonic structures.     

Microstructure and Tensile Mechanical Properties of Anisotropic Rigid Polyurethane Foam

An understanding of the mechanical properties of solid foams facilitates effective use of such materials, which are often deployed in load-bearing applications such as impact absorbers, cushioning and sandwich structures. This study is an experimental investigation that focuses on the deformation response of rigid polyurethane foam to tension. Microstructural features such as the size and geometry of constituent cells and the struts that define the cell edges, as well as their stiffness and tensile strength, are examined. The nature of cell deformation and fracture are identified through microscopy and the associated micromechanics analyzed. Results show that the cells are elongated and thus the foam exhibits anisotropic properties. Flexure of the struts that define the cell edges is the primary mechanism governing deformation and failure. Information on the mechanical, microstructural and deformation characteristics elicited through this investigation will facilitate formulation of idealized cell-based models to account for the mechanical response of rigid polymeric foams.     

Magnesium doping in InAlAs and InGaAs/Mg films lattice-matched to InP grown by MOVPE

Mg-doped InAlAs and InGaAs films were grown at 560 °C lattice matched to InP semi-insulting substrate by metalorganic vapor phase epitaxy (MOVPE) under various Cp₂Mg flow conditions. Hall effect, photoluminescence (PL), high-resolution X-ray diffraction (HR-XRD), and secondary ion mass (SIMS) were the tools used in this work. The crystalline quality and the n-p conversion of the InAlAs and InGaAs/Mg films are described and discussed in relation to the Cp₂Mg flow. Distinguishing triple emission peaks in PL spectra is observed and seems to be strongly dependent on the Cp₂Mg flow. SIMS is employed to analyze the elements in the epitaxial layers. The variation of indium and magnesium components indicates a decrease of magnesium incorporation during the growth of InAlAs layers leading to a contracted lattice. In addition, the magnesium incorporation in the InGaAs lattice during growth has been confirmed by SIMS.     

The effect of pressure on the characteristics of supercritical carbon dioxide extracts from Calamintha nepeta subsp. nepeta

Chemists and industrialists are continuously attempting to develop greener and more environmentally benign chemical processes to extract essential oils and bioactive metabolites of high purity, finding various applications in cosmetics, detergents, nutraceuticals and pharmaceuticals. An increase preferenced for natural products over synthetic ones has made supercritical fluid technology a primary alternative for the generation of high-value bioactive ingredients. This effective technique requires only moderate temperatures, eliminates clean-up steps and avoids the use of harmful organic solvents. In this context, our study was focused on the chemical analysis of Calamintha nepeta subsp. nepeta aromatic extracts obtained with supercritical carbon dioxide. The effect of different operating conditions on the capacity of the lipophilic solvent to extract the targeted volatile components was also studied. The process was carried out at a fairly low constant temperature of 40°C, and with varying the pressure from 90 to 300 bar. The chemical composition of the extracts was analyzed by gas chromatography–mass spectroscopy. The results showed that the composition pattern, the concentrations of individual components and the quality of the extractable analytes were affected by pressure increase. The extraction yields varied from 0.73 to 1.21 wt% at 90 and 300 bar, respectively.