Decomposition of arborescent linear programs

We apply what we call sequential projection to reformulate certain linear programs as recursive optimization problems. We then apply the standard idea of approximating the return function at each stage of the recursion by using inner (or outer) linearization, and iteratively refining the approximation until the original linear program has been solved. The contribution of the paper lies in its unification of existing decomposition approaches and in showing that they can be generalized to apply to what we call arborescent linear programs.     

The molecular approach to heterogeneous nucleation

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by DeltaG(het) (I) = (F(n) (het)-F(n) (hom))-(F(1) (het)-F(1) (hom)) + DeltaG(hom) where F(n) (het) and F(n) (hom) are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by DeltaG(het) (II) = (F(n) (het)-F(n) (hom)) + DeltaG(hom). The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Angstroms does not lead to a considerable change of the heterogeneous nucleation rate.     

The extendible cell method for closest point problems

The extendible cell method is an application of order preserving extendible hashing to multidimensional point files. We derive some of its performance characteristics and show its expected case optimality for closest point problems.     

Two levels are as good as any

The asymptotic expected efficiency of distributive sorting is studied showing that for “smooth” key distributions it suffices to consider 2-level methods. The expected cost of sorting n such keys satisfies asymptotically: C(n) ? Kn, where K does not depend on the distribution.     

Zirconium-loaded activated charcoal as an adsorbent for arsenic, selenium and mercury

The adsorption of arsenic, selenium and mercury from aqueous solutions onto zirconium-loaded activated charcoal was studied as a function of adsorption time, amount of adsorbent, pH, concentration of adsorbates, sample volume and the oxidation states of the adsorbates. The cross-interference of the analytes was also investigated. Loaded filters were measured by energy-dispersive X-ray fluorescence spectrometry (EDXRF) and the amount of the unadsorbed analytes were determined by vapour generation atomic absorption spectrometry (VGAAS).     

UV photolysis products of propiolic acid in noble-gas solids

Photolysis (193 nm) of propiolic acid (HCCCOOH) was studied with Fourier transform infrared spectroscopy in noble-gas (Ar, Kr, and Xe) solid matrixes. The photolysis products were assigned using ab initio quantum chemistry calculations. The novel higher-energy conformer of propiolic acid was efficiently formed upon UV irradiation, and it decayed back to the ground-state conformer on a time scale of approximately 10 min by tunneling of the hydrogen atom through the torsional energy barrier. In addition, the photolysis produced a number of matrix-isolated 1:1 molecular complexes such as HCCH...CO2, HCCOH...CO, and H2O...C3O. The HCCH...CO2 complex dominated among the photolysis products, and the computations suggested a parallel geometry of this complex characterized by an interaction energy of -9.6 kJ/mol. The HCCOH...CO complex also formed efficiently, but its concentration was strongly limited by its light-induced decomposition. In this complex, the most probable geometry was found to feature the interaction of carbon monoxide with the OH group via the carbon atom, and the computational interaction energy was determined to be -18.3 kJ/mol. The formation of the strong H2O...C3O complex (interaction energy -21 kJ/mol) was less efficient, which might be due to the inefficiency of the involved radical reaction.     

Experimental and computational study of HXeY...HX complexes (X, Y = Cl and Br): an example of exceptionally large complexation effect

The complexes of xenon hydrides HXeY (Y = Cl and Br) with hydrogen halides HX (X = Cl and Br) have been studied both computationally and experimentally in a xenon matrix. The experiments revealed three new complexes: HXeBr...HBr, HXeBr...HCl, and HXeCl...HCl. The experimental assignments were done on the basis of the strong H-Xe stretching absorption of HXeY (Y = Cl and Br) molecules and supported by theoretical results. We experimentally obtained monomer-to-complex blue-shifts of this vibrational mode for all the studied systems (up to approximately 150 cm (-1)). The electronic structure calculations revealed three local structures for each HNgY...HX complexes and their computed interaction energies varied between -460 and -2800 cm (-1). The computational estimates of the vibrational shifts were in agreement with the experimental values. We also found possible experimental absorption belonging to HXeBr...(HBr) 2 trimer and its vibrational shift (+245 cm (-1)) is similar to the computational estimate of a cyclic ternary complex (+252 cm (-1)).