A note on the parametric maximum flow problem and some related reoptimization issues

In this paper, we will extend the results about the parametric maximum flow problem to networks in which the parametrization of the arc capacities can involve both the source and the sink, as in Gallo, Grigoriadis, and Tarjan (1989), and also an additional node. We will show that the minimum cuts of the investigated networks satisfy a relaxed form of the generalized nesting property (Arai, Ueno, and Kajitani, 1993). A consequence is that the corresponding parametric maximum flow value function has at most n −1 breakpoints. All the minimum cut capacities can therefore be computed by O(1) maximum flow computations. We will show then that, given O(n) increasing values of the parameter, it is possible to compute the corresponding maximum flows by O(1) maximum flow computations, by suitably extending Goldberg and Tarjan’s maximum flow algorithm.     

Naphthalene‐1,5‐diammonium bis[trifluoridostannate(II)]

The structure of the title compound, (C₁₀H₁₂N₂)[SnF₃]₂, is made up of alternating layers of cations and anions, where the anion layers form extended polymeric sheets through a series of secondary Sn...F bonds. Strong N—H...F hydrogen bonds crosslink adjacent cation and anion layers, thereby building a three‐dimensional network.     

Multiresidue Analysis of Organic Pollutants in Water by SPE with a C8 and SDVB Combined Cartridge

Abstract

A multi-component target method for screening purposes to determine organic pollutants of different polarities in water is reported. The following classes of chemicals were tested: base-neutral and acidic herbicides, phenolic compounds, polycyclic aromatic hydrocarbons and phthalic acid esters.

Data was initially obtained from the extraction of one liter of water sample, using separate octyl bonded porous silica (C8) and highly crosslinked polystyrene based polymer columns (SDVB) cartridges. A second set of data was obtained using for the extraction a combined cartridge containing both phases. The analysis was carried out directly by GC-MS in SIM mode, without any derivatisation, with the exception of acidic herbicides, derivatised with pentafluorobenzylbromide. The obtained results showed recoveries between 75% and 98% at two different spiking levels, with relative standard deviations below 15%.     

Blends of synthetic and natural polymers as special performance materials

The interest for blends of synthetic and natural polymers is growing and several applications in many different fields are now becoming evident. The biological-synthetic polymers interactions play a relevant role in controlling the mechanism that constitutes the basis of biocompatibility of materials used in medicine. This work concerns with the preparation and chemico-physical and mechanical characterization of blends in which the biological component is hyaluronic acid or its benzyl ester derivatives, and the synthetic component is poly(vinyl alcohol) or ethylene-vinyl alcohol copolymers.     

Selecting Portfolios with Fixed Costs and Minimum Transaction Lots

The original Markowitz model of portfolio selection has received a widespread theoretical acceptance and it has been the basis for various portfolio selection techniques. Nevertheless, this normative model has found relatively little application in practice when some additional features, such as fixed costs and minimum transaction lots, are relevant in the portfolio selection problem. In this paper different mixed-integer linear programming models dealing with fixed costs and possibly minimum lots are introduced. Due to the high computational complexity of the models, heuristic procedures, based on the construction and optimal solution of mixed integer subproblems, are proposed. Computational results obtained using data from the Milan Stock Exchange show how the proposed heuristics yield very good solutions in a short computational time and make possible some interesting financial conclusions on the impact of fixed costs and minimum lots on portfolio composition.     

Exponential stability of a linear viscoelastic bar with thermal memory

In this paper we study a one-dimensional evolution problem arising in the theory of linear thermoviscoelasticity with hereditary heat conduction. Depending on the istantaneous conductivity K₀, both Coleman-Gurtin (K₀>0) and Gurtin-Pipkin (K₀=0) heat flow theories are involved. In any case, the exponential stability of the corresponding semigroup is proved for a class of memory functions including weakly singular kernels. In order to achieve the exponential decay of the energy, we assume that mechanical and thermal memory kernels decay exponentially for large time. Entrata in Redazione il 23 luglio 1998.