A branch-and-cut method for the obnoxious p-median problem

The obnoxious p-median (OpM) problem is the repulsive counterpart of the ore known attractive p-median problem. Given a set I of cities and a set J of possible locations for obnoxious plants, a p-cardinality subset Q of J is sought, such that the sum of the distances between each city of I and the nearest obnoxious site in Q is maximised. We formulate (OpM) as a {0,1} linear programming problem and propose three families of valid inequalities whose separation problem is polynomial. We describe a branch-and-cut approach based on these inequalities and apply it to a set of instances found in the location literature. The computational results presented show the effectiveness of these inequalities for (OpM). The work of the first author has been partially supported by the Coordinated Project C.A.M.P.O. and that of the third author by a short mobility grant, both of the Italian National Research Council.     

Water diffusion through hydrogel membranes: A novel evaporation cell free of external mass-transfer resistance

A novel evaporative cell is used to measure steady-state gradient-driven diffusion rates of water through hydrogel membranes in the absence of external mass-transfer resistance. In this cell, the bottom surface of a hydrogel membrane is exposed to pure water vapor at known activity (a_w) less than unity, while a sealed liquid-water reservoir bathes the upper membrane surface. Induced by the chemical-potential gradient between the two surfaces, the water evaporation rate is monitored by the rate of weight loss of the water reservoir.Results at ambient temperature are compared with those from measured water flux through soft-contact-lens (SCL) materials and with other published experimental results. Concentration-dependent water diffusivities are obtained by interpreting measured water fluxes for 0.11 ≤ a_w ≤ 0.93 with extended Maxwell–Stefan (EMS) diffusion theory. Thermodynamic non-ideality is taken into account through Flory–Rehner polymer–solution theory. Shrinking/swelling is modeled by conservation of the total polymer mass assuming volume additivity. In spite of correction for thermodynamic non-ideality, EMS–water-diffusion coefficients increase with the water volume fraction, especially strongly for those hydrogel materials with low liquid-saturated water contents. The evaporation cell described here provides a simple robust method to establish water transport rates through soft-contact-lenses and other hydrogel membranes without the need to correct for external mass-transfer resistance.     

Groups with finitely many normalizers of non-abelian subgroups

Abstract A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite commutator subgroup. Here the structure of locally graded groups with finitely many normalizers of (infinite) non-abelian subgroups is investigated, and the above result is extended to this more general situation. Keywords: normalizer subgroup, metahamiltonian group Mathematics Subject Classification (2000): 20F24     

Analysis of complex mixtures by capillary gas chromatography with statistical estimation of the number of components

Evaluation of the number of components by the Davis-Giddings single chromatogram method is applied to capillary gas chromatograms of a dichloromethane extract of camomile. Various runs with OV-1 or Carbowax 20M as the stationary phase were done under different experimental conditions (column temperature programming rate and column length). The results showed that the number of components obtained by this statistical procedure does not depend greatly on the nature of the stationary phase or on the experimental conditions. The component number of the camomile extract was about 200 and the stand-alone probability at unit resolution was 0.2–0.3.     

3,6-bis(2′,-pyridyl)pyridazine dinuclear complexes: Palladium(II), platinum(II) and first row transition metal(II) mixed complexes

New Pd(II) and Pt(II) 3,6-bis(2′-pyridyl)pyridazine (dppn) mononuclear complexes of the type M(dppn)Cl₂ were prepared and characterized. From M(dppn)Cl₂, the bimetallic homonuclear complexes M(dppn)MCl₄ were prepared by reaction with Pd(PhCN)₂Cl₂ or K₂PtCl₄. Bimetallic heteronuclear species of the type M(dppn)M′Cl₄, were prepared reacting the mononuclear complexes with the stoichiometric amount of M′Cl₂ (M′ = Cu, Co, Ni). All the described reaction give product in high yield. The isolated compounds, almost completely insoluble in most organic solvents, were characterized by elemental analysis, IR, ESR, reflectance spectra, and magnetic moment measurements. On the basis of these data the geometries around the metals are discussed.     

Special matchings and Kazhdan-Lusztig polynomials

In 1979 Kazhdan and Lusztig defined, for every Coxeter group W, a family of polynomials, indexed by pairs of elements of W, which have become known as the Kazhdan-Lusztig polynomials of W, and which have proven to be of importance in several areas of mathematics. In this paper, we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these polynomials. Our results also imply, and generalize, the recent one in [Adv. in Math. 180 (2003) 146-175] on the combinatorial invariance of Kazhdan-Lusztig polynomials.     

Combinatorial Expansions of Kazhdan-Lusztig Polynomials

We introduce two related families of polynomials, easily computableby simple recursions into which any Kazhdan–Lusztig (andinverse Kazhdan–Lusztig) polynomial of any Coxeter groupcan be expanded linearly, and we give combinatorial interpretationsto the coefficients in these expansions. This yields a combinatorialrule for computing the Kazhdan–Lusztig polynomials interms of paths in a directed graph, and a completely combinatorialreformulation of the nonnegativity conjecture [15, p. 166].