Two-edge connected spanning subgraphs and polyhedra

This paper studies the problem of finding a two-edge connected spanning subgraph of minimum weight. This problem is closely related to the widely studied traveling salesman problem and has applications to the design of reliable communication and transportation networks. We discuss the polytope associated with the solutions to this problem. We show that when the graph is series-parallel, the polytope is completely described by the trivial constraints and the so-called cut constraints. We also give some classes of facet defining inequalities of this polytope when the graph is general.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and CP Rail and the German Research Association (Deutsche Forschungsgemeinschaft SFR 303).     

Unsteady three-dimensional buoyancy-driven convection in a circular cylindrical cavity and its damping by magnetic field

The oscillatory convection in an electrically conducting liquid-metal confined in a cylindrical cavity of moderate length is investigated using a spectral numerical method involving direct resolution of the Navier-Stokes equations for three-dimensional flows. Time signals, symmetry properties and energy budgets are presented in order to characterize the flow oscillations. The damping of the oscillatory flows by a vertical magnetic field is then studied up to the stabilization to a steady flow.     

On the Laguerre-Hahn Intertwining Operator and Application to Connection Formulas

In this paper, we show that the lowering operator D _u indexed by a linear functional on polynomials u, introduced by F. Marcellán and R. Sfaxi, namely the Laguerre-Hahn derivative, is intertwining with the standard derivative D by a linear isomorphism S _u on polynomials. This allows us to establish an intertwining relation between the nonsingular Laguerre-Hahn polynomials of class zero of Hermite type and the Hermite polynomials, as well as some new connection formulas between such Laguerre-Hahn polynomials and the canonical basis.     

Synthesis of 3,4‐Dihydropyrimidinones via Phase Transfer Catalysis

3,4‐Dihydropyrimidinone and derivatives were synthesized by the one‐pot, three‐component Biginelli condensation of an aldehyde, β‐dicarbonyl compound and urea. Synthesis was carried out in aqueous sodium hydroxide using Aliquat‐336 as a phase transfer agent. Compared to the classical Biginelli reaction conditions, this new method cousistently has the advantage of excellent yields and short reaction time.     

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.