Trees and the dynamics of polynomials

The basin of infinity of a polynomial map f : {\bf C} \arrow {\bf C} carries a natural foliation and a flat metric with singularities, making it into a metrized Riemann surface $X(f)$. As $f$ diverges in the moduli space of polynomials, the surface $X(f)$ collapses along its foliation to yield a metrized simplicial tree $(T,\eta)$, with limiting dynamics F : T \arrow T. In this paper we characterize the trees that arise as limits, and show they provide a natural boundary \PT_d compactifying the moduli space of polynomials of degree $d$. We show that $(T,\eta,F)$ records the limiting behavior of multipliers at periodic points, and that any divergent meromorphic family of polynomials \{f_t(z) : t \mem \Delta^* \} can be completed by a unique tree at its central fiber. Finally we show that in the cubic case, the boundary of moduli space \PT_3 is itself a tree. The metrized trees $(T,\eta,F)$ provide a counterpart, in the setting of iterated rational maps, to the ${\bf R}$-trees that arise as limits of hyperbolic manifolds.Comment: 60 page

Insecticide treated bednets: A review

The functioning and efficacy of Insecticide Treated Nets (ITNs) in controlling malaria are discussed in the present review. ITNs Insecticide Treated Nets (ITNs) have been shown to have a beneficial impact in reducing malaria mortality and morbidity in children. However, a few issues are still unresolved: for instance the short and long term effects of an artificially induced reduction in the intensity of malaria transmission on the immune system and the mortality of children is not entirely understood; further studies are needed on whether the spread of resistance to pyrethroids, which is the only class of insecticide currently recommended on nets, affects the effectiveness of ITNs so that resistance to these insecticides would constitutes a serious threat for the success of the malaria vector control programs. Lastly, the economic aspects are presented. The main problem is to find a way for a sustainable implementation of this methodology, that includes purchasing new bednets, delivery and the regular re-impregnation of the existing nets. Free delivery and retreatment in poor countries is not only more equitable but also more efficient than marketing methods

Variation of solar-selective properties of black chrome with plating time

The spectral reflectance properties of a commercially prepared black chrome over dull nickel, both plated on steel, for various plating times of the black chrome were measured. The plating current was 180 amperes per square foot. Values of absorptance integrated over the solar spectrum, and of infrared emittance integrated over black-body radiation at 250 F were obtained. It is shown that plating between one and two minutes produces the optimum combination of highest heat absorbed and lowest heat lost by radiation