A hybrid heuristic for the diameter constrained minimum spanning tree problem

We propose a hybrid GRASP and ILS based heuristic for the diameter constrained minimum spanning tree problem. The latter typically models network design applications where, under a given quality requirement, all vertices must be connected at minimum cost. An adaptation of the one time tree heuristic is used to build feasible diameter constrained spanning trees. Solutions thus obtained are then attempted to be improved through local search. Four different neighborhoods are investigated, in a scheme similar to VND. Upper bounds within 2% of optimality were obtained for problems in two test sets from the literature. Additionally, upper bounds stronger than those previously obtained in the literature are reported for OR-Library instances.     

LC–UV Method with Pre-Column Derivatization for the Determination of Ciclopirox Olamine in Raw Material and Topical Solution

A rapid, simple and sensitive liquid chromatographic method has been developed to assay ciclopirox olamine in raw material and topical solution. The analysis used a reversed-phase C₁₈ end-capped column, with UV detection at 305 nm and pre-column derivatization with dimethyl sulphate. A linear response (r ² > 0.999) was observed in the range of 0.4–200 μg mL⁻¹. The method showed good recoveries for the raw material and topical solution and the relative standard deviation intra and inter-day were ≤2.00%. Validation parameters such as specificity and robustness were also determined. The proposed method provided an accurate and precise analysis of ciclopirox olamine in raw material and topical solution.

     

Localized states in polymeric molecules. IV. Polyacetylene beyond simple Hückel Model

We have used the transfer matrix technique to study the electronic structure of trans-polyacetylene, within a model Hamiltonian which includes second-neighbors interactions. The results show that the valence and conduction band widths and the energy of the localized state are dependent on the strength of the second neighbors couplings. However, for the physically reasonable range of parameters, the electronic structure of the material is only slightly modified, indicating that a simple Hückel treatment is quite accurate for this system.Work partially supported by the Brazilian Agencies FINEP and CNPq     

Solid Phase Spectrophotometry for the Determination of Cobalt in Pharmaceutical Preparations

 A new sensitive method exploiting solid-phase spectrophotometry is proposed for the determination of cobalt in pharmaceutical preparations. The chromogenic reagent 1-(2-thiazolylazo)-2-naphthol (TAN) was immobilized on C18 bonded silica loaded into a home-made cell with 1.5 mm of optical path for cobalt determination. Cobalt(II) reacts with TAN on C18 material, at pH 6.0–7.5, to give a coloured complex which has maximum absorption at 572 nm. In this way, the sample was passed through the cell and Co(II) ions were quantitatively retained on the solid-phase. After the direct measurement of light-absorption in the solid phase, only the cobalt was eluted with 0.1 mol L⁻¹ hydrochloric acid. The cell was washed with water and then another sample solution could be passed through the cell. The procedure allowed the determination of cobalt in the range of 10–160 μg L⁻¹ with coefficient of variation of 4.7% (n=10) and apparent molar absorptivity of 2.62 × 10⁶ L mol⁻¹ cm⁻¹ using sample volume of 3-mL. Received May 15, 2000. Revision August 28, 2000.     

Universality in active chaos

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles).     

Why are chaotic attractors rare in multistable systems?

We show that chaotic attractors are rarely found in multistable dissipative systems close to the conservative limit. As we approach this limit, the parameter intervals for the existence of chaotic attractors as well as the volume of their basins of attraction in a bounded region of the state space shrink very rapidly. An important role in the disappearance of these attractors is played by particular points in parameter space, namely, the double crises accompanied by a basin boundary metamorphosis. Scaling relations between successive double crises are presented. Furthermore, along this path of double crises, we obtain scaling laws for the disappearance of chaotic attractors and their basins of attraction.     

Poincaré recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors

We study Poincaré recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is no longer supported solely by unstable periodic orbits of finite length inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincaré first return times from a Poissonian. Consequently, by taking into account the contribution of these special recurrent trajectories, a corrected estimate of the measure is obtained. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size, and only unstable periodic orbits of finite length can be detected.     

Chaotic advection,diffusion, and reactions in open flows

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.