Alternatives to a Semi-Parametric Estimator of Parameters of Rare Events—The Jackknife Methodology*

In this paper, and in a context of regularly varying tails, we propose different alternatives to a well-known estimator of the tail index—the Hill estimator (Hill, 1975). These alternatives have essentially in mind a reduction in bias, preferably without increasing Mean Square Error, by the use of suitable Generalized Jackknife methodologies (Gray and Schucany, 1972). The first estimate obtained through this methodolgy is the one introduced by Peng (1998), under a different context. Other Generalized Jackknife estimators are linear combinations of Hill estimators at different levels. This methodology of affine combinations of Hill estimators at different levels may be easily generalized to other semi-parametric estimators of the tail index, like Pickands' estimator (Pickands, 1975) or the Moment's estimator (Dekkers et al., 1989), and consequently to a general real tail index, seeming to be a promising field of research.     

A Single-Gallery Model for the In Situ Production of Polyethylene-Clay Nanocomposites

Polyolefin-clay nanocomposites are finding many new applications because of their improved properties, such as high modulus, elevated scratch resistance and low gas permeability. Currently, these composites are produced by melt blending organically modified clay with polyolefins. The most challenging step in this process is the intercalation and exfoliation of the clay to produce a homogenously dispersed phase at the nanoscale. A promising alternative to melt blending is in-situ polymerization, where the polymer is produced between the clay layers in the polymerization reactor. In-situ polymerization of olefins with metallocene catalysts supported on clay can produce nanocomposites using conventional polymerization reactors, provided that the clay can be used as a support for the olefin polymerization catalyst. In this approach, the clay fulfills the functions of catalyst support and dispersed phase in the final nanocomposite. In this work, a mathematical model describing particle growth during in-situ polymerization of ethylene with a metallocene catalyst supported on clay will be discussed. The model expands the approach of the multi-grain model used in heterogeneous olefin polymerization to account for the layered structure of clays.     

A density functional theory test study on the N2··· He dimer

 In the present contribution we report a study of the weakly bound van der Waals N₂–He molecule in the framework of the supermolecule approach by means of the PWPW and mPW1PW exchange–correlation functionals, using density functional theory local-spin-optimized atom-centered basis sets complemented with bond functions optimized at the mPW1PW level of theory. Calculations show that the mPW1PW functional using bond functions gives a realistic representation of the interaction-energy potentials for this van der Waals dimer, comparable to reference M?ller–Plesset perturbation theory calculations. In contrast, the PWPW functional is unable to describe the bonding properties of this system and all values of the bonding properties obtained at different geometries with this functional are considered out-of-scale compared with the rest of the calculations presented in this study. Received: 30 October 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Development of a sensor for calcium based on quartz crystal microbalance

A new sensor for calcium based on a piezoelectric quartz crystal is presented. The selectivity depends on the ratio lipophilic salt/ionophore of the composition of the coating of the quartz crystal. A crystal coated with a THF solution of PVC (34.5% w/w), DOS (62.1% w/w) and 10,19-bis[(octadecylcarbamoyl) methoxyacetyl]-1,4,7,13,16-pentaoxa-10,19-diaza cycloheneicosane (3.4% w/w) and a salt/ionophore molar proportion of 60%, corresponding to a frequency decrease of the dry crystal of 6.0 kHz, showed a detection limit to calcium of 2.2 mg/L. Both a standard calcium chloride solution and a commercially balanced salt solution for tissue culture were analyzed subsequent to ion chromatographic separation. The results obtained with the sensor developed were compared with those obtained with a conductivity detector. Although the results from both detectors agreed for the standard solution, only the quartz crystal sensor was able to give reliable results for the tissue culture solution.     

Efficient Preparation of γ-Hydroxynitriles via Nitrile Enolate-Epoxide Reactions: Scope and Diastereoselectivity

The nucleophilic opening of epoxides by nitrile enolates using an efficient, convenient protocol is described. The diastereoselectivity of this reaction was explored and found to give syn:anti ratios ranging from 1.1:1.0 to 4.8:1.0.

     

Thermal and evolved gas analyses of the oxidation of a cellulose/copper(II) oxide mixture

Cellulosic biomass is a promising alternative energy resource from the viewpoint of sustainability. The use of waste materials as cellulosic biomass could additionally contribute to a recycling society. It is thus essential to develop safer processes in order to expand utilization of cellulosic biomass as a useful resource in the future. For example, in some cases, construction wastes contain wood preservatives, including metal oxides that can act as catalysts for the oxidation of organic materials. Copper(II) oxide (CuO) is a major component in wood preservatives and is known to catalyze the oxidation of cellulose. There is, therefore, possibility for spontaneous ignition within large piles of wood chips from construction wastes. In this study, we focused on the thermal behavior of a cellulose/CuO mixture, measured using a Calvet-type heat flux calorimeter. In addition, Fourier transform infrared spectroscopy and gas chromatography were applied to analyze the oxidative decomposition gases of the cellulose/CuO mixture, and a reaction mechanism was proposed. It was revealed that CuO promotes the oxidative decomposition of cellulose and increases the quantity of the gases that evolved from cellulose with a catalytic cycle. The influence of CuO on oxidation of cellulose is greater at lower temperatures and spontaneous ignition, fires, and explosions are likely to increase when wood chips containing CuO are stored for long periods of time.