Reversed phase StrataTM-X resin as sorbent for automatic on-line solid phase extraction atomic absorption spectrometric determination of trace metals: comparison of polymeric-based sorbent materials

A novel on-line flow injection solid phase extraction method for the preconcentration of trace toxic metals prior determination by flame atomic absorption spectrometry (FI-SPE-FAAS) was developed. The potential application of the hydrophobic reversed phase co-polymer sorbent Strata^TM-X packed into an on-line microcolumn for the quantification of Cd(II), Pb(II), Cu(II) and Cr(VI) was demonstrated for the first time. The method was based on the on-line formation of metal complexes using sodium diethyl-dithiocarbamate (DDTC) and on the subsequent retention of them onto the sorbent material. The target analytes were completely eluted by methanol and, subsequently, directed to FAAS for quantification. All chemical and flow variables affecting the performance of the developed method were thoroughly studied and optimised. For a preconcentration time of 90 s and a sampling frequency of 28 h^?1, enhancement factors of 72, 140, 185, 63 and detection limits of 0.18, 1.6, 0.20 and 1.2 μg L ^?1 were obtained for Cd(II), Pb(II), Cu(II) and Cr(VI), respectively. The accuracy of the FI-SPE-FAAS method was evaluated by analysing certified reference materials as well as spiked environmental water samples. Furthermore, a comparative study of the analytical characteristics, the properties as well as the chemical structures of commercial polymeric based sorbent materials was employed. Strata-X sorbent was compared against Hypersep^TM SCX, Bond Elut® Plexa^TM PCX, Oasis-HLB^TM and Nobias^TM PA-1, regarding the adaptation in on-line FI-SPE-FAAS systems for metal determination, and herein presented.     

An agent-based model for the bibliometric h-index

We model a virtual scientific community in which authors publish and cite articles. Citations are attributed according to a preferential attachment mechanism. From the numerical simulations, the h-index can be computed. This bottom-up approach reproduces well real bibliometric data. We consider two versions of our model. (1) The single-scientist is controlled by two parameters which can be tuned to reproduce the value of the h-index of many real scientists. Moreover, this model shows how the h-index grows with the number of citations, for a fixed number of articles. We also define an average h-index that can be used to compare the scientific productivity of institutions of different sizes. (2) The multi-scientist model considers a population of scientists and allows us to study the impact of removing citations from the low h-index researchers on the community. Simulations on real bibilometric data, as well as the predictions of the model, show that the h-index eco-system can be strongly affected by such a filtering.     

The Polynomial Behavior of Weight Multiplicities for the Affine Kac–Moody Algebras A(1)r

We prove that the multiplicity of an arbitrary dominant weight for an irreducible highest weight representation of the affine Kac–Moody algebra A ⁽¹⁾ _r is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks.     

Efficient formulations for pricing under attraction demand models

We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly.     

Price of anarchy for supply chains with partial positive externalities

We consider the impact of partial positive externalities (imperfect complementarity) among downstream retailers on supply chain performance. We show that double marginalization may fail to exist in a decentralized setting when some retailers carry multiple imperfect complements. By giving a precise characterization on the degree of complementarity, we prove that a decentralized supply chain loses at least 25% of the optimal profit and that its performance degrades rapidly with the complementarity effect.     

Convenient preparation of 1,2-alkylenedioxy-benzofuroxans and benzofurazans

Nitration of the dioxolo-annelated benzenes 11 led to the corresponding dinitro derivatives 12 . Nucleophilic substitution of the latter with azide ion furnished the monoazides 13 which on thermolysis afforded the benzofuroxans 14 . Deoxygenation of furoxans 1a,b,e,f, 2a-c,e,f, 5, 7, 9 and 14 with triphenylphosphine, furnished the respective benzofurazans 3a,b,e,f, 4a-c,e,f, 6, 8, 10 and 15 .     

Solving variational inequality and fixed point problems by line searches and potential optimization

We introduce a general adaptive line search framework for solving fixed point and variational inequality problems. Our goals are to develop iterative schemes that (i) compute solutions when the underlying map satisfies properties weaker than contractiveness, for example, weaker forms of nonexpansiveness, (ii) are more efficient than the classical methods even when the underlying map is contractive, and (iii) unify and extend several convergence results from the fixed point and variational inequality literatures. To achieve these goals, we introduce and study joint compatibility conditions imposed upon the underlying map and the iterative step sizes at each iteration and consider line searches that optimize certain potential functions. As a special case, we introduce a modified steepest descent method for solving systems of equations that does not require a previous condition from the literature (the square of the Jacobian matrix is positive definite). Since the line searches we propose might be difficult to perform exactly, we also consider inexact line searches.Preparation of this paper was supported, in part, from the National Science Foundation NSF Grant 9634736-DMI, as well as the Singapore-MIT AllianceAcknowledgments.We are grateful to the associate editor and the referees for their insightful comments and suggestions that have helped us improve both the exposition and the content of this paper.