Facilitated transport from ternary cation mixtures through water—chloroform—water membrane systems containing macrocyclic ligands

Cation fluxes were determined for various three-component, equimolar mixtures of alkali metal, alkaline earth, and Pb²⁺ cations in a H₂O---CHCl₃---H₂O liquid membrane system incorporating macrocyclic polyethers as carriers. Carrier ligands studied were 18-crown-6, dicyclohexano-18-crown-6, 1,10-diaza-18-crown-6, 21-crown-7, dibenzo-24-crown-8, and cryptand [2.2.2]. Correlations were found between transport and relative cation:polyether cavity radii, the type of substituents present on the polyether ring, and the type and number of donor atoms present. All the ligands studied transported Pb²⁺ at higher rates than the other Mⁿ⁺ in the mixtures. Transport behavior in these multi-cation systems can be predicted from Mⁿ⁺—polyether complex stability constant data in most cases.     

Estimating the number of zero-one multi-way tables via sequential importance sampling

In 2005, Chen et al. introduced a sequential importance sampling (SIS) procedure to analyze zero-one two-way tables with given fixed marginal sums (row and column sums) via the conditional Poisson (CP) distribution. They showed that compared with Monte Carlo Markov chain (MCMC)-based approaches, their importance sampling method is more efficient in terms of running time and also provides an easy and accurate estimate of the total number of contingency tables with fixed marginal sums. In this paper, we extend their result to zero-one multi-way ( $d$ -way, $d \ge 2$ ) contingency tables under the no $d$ -way interaction model, i.e., with fixed $d-1$ marginal sums. Also, we show by simulations that the SIS procedure with CP distribution to estimate the number of zero-one three-way tables under the no three-way interaction model given marginal sums works very well even with some rejections. We also applied our method to Samson’s monks data set.     

Ehrhart Polynomials of Matroid Polytopes and Polymatroids

We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that, for fixed rank, Ehrhart polynomials of matroid polytopes and polymatroids are computable in polynomial time. The proof relies on the geometry of these polytopes as well as a new refined analysis of the evaluation of Todd polynomials. In the second half we discuss two conjectures about the h ^*-vector and the coefficients of Ehrhart polynomials of matroid polytopes; we provide theoretical and computational evidence for their validity.