The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming

A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and nonlinear constraints. A sequence of linear or quadratic integer-relaxed subproblems are first solved to rapidly generate a tight linear relaxation of the original MINLP problem. After an initial overestimated set has been obtained the algorithm solves a sequence of mixed-integer linear programming or mixed-integer quadratic programming subproblems and refines the overestimated set by generating more supporting hyperplanes in each iteration. Compared to the extended cutting plane algorithm ESH generates a tighter overestimated set and unlike outer approximation the generation point for the supporting hyperplanes is found by a simple line search procedure. In this paper it is proven that the ESH algorithm converges to a global optimum for convex MINLP problems. The ESH algorithm is implemented as the supporting hyperplane optimization toolkit (SHOT) solver, and an extensive numerical comparison of its performance against other state-of-the-art MINLP solvers is presented.     

Stereochemistry and rearrangement reactions of hydroxylignanolactones

Various conflicting data on the rearrangement and absolute stereochemistry of hydroxylignano-9,7'-lactones are resolved using 18O labeled compounds, also confirmed by an X-ray analysis of a pure lignano-9,7'-lactone enantiomer, obtained for the first time. Under NaH/DMF rearrangement conditions a silyl protected hydroxylignano-9,9'-lactone underwent an unexpected silyl migration.     

Feasibility of density functional methods to predict dielectric properties of polymers

Feasibility of density functional theory (DFT) to predict dielectric properties such as polarizability of saturated polymers is investigated. Small saturated molecules, methane and propane, which is a monomer of polypropylene chain, are used in testing the methods. Results for polarizabilities based on several density functionals together with different basis sets are compared and contrasted with each other, with results by Hartree-Fock and second-order Moller-Plesset perturbation theory, as well as experimental data. The generalized gradient approximation PW91 method together with the 6-311++G(**) basis set is found to be the most suitable method, in terms of sufficient accuracy and computational efficiency, to calculate polarizabilities for large oligomers of polypropylene. The dielectric constant is then determined using the calculated polarizabilities and the Clausius-Mossotti equation. The molecular DFT methods at the PW916-311++G(**) level together with the Clausius-Mossotti equation give dielectric constants for saturated polymers such as polypropylene in good accordance with the experimental values.     

Influence of long-term aqueous exposure on surface properties of plasma-sprayed oxides Cr2O3 and Cr2O3-25 wt% TiO2

The influence of water exposure on the surface properties of plasma-sprayed Cr(2)O(3) and Cr(2)O(3)-25 wt% TiO(2) was studied. It was shown that both plasma-sprayed materials contained Cr(VI) hydrous oxide phases, which dissolved rapidly at the beginning of water exposure. The dissolution continued slowly during the whole water exposure time. The Cr(VI) dissolution was accompanied by a rapid increase in surface IEP value. Both Cr(2)O(3) and Cr(2)O(3)-25 wt% TiO(2) showed similar dissolution, zeta potential, and surface oxidation states. Thus the addition of TiO(2) did not influence the surface properties of the plasma-sprayed Cr(2)O(3).     

Sterically hindered phenols in negative ion mobility spectrometry–mass spectrometry

Negative corona discharge atmospheric pressure chemical ionization (APCI) was used to investigate phenols with varying numbers of tert‐butyl groups using ion mobility spectrometry–mass spectrometry (IMS‐MS). The main characteristic ion observed for all the phenolic compounds was the deprotonated molecule [M–H]⁻. 2‐tert‐Butylphenol showed one main mobility peak in the mass‐selected mobility spectrum of the [M–H]⁻ ion measured under nitrogen atmosphere. When air was used as a nebulizer gas an oxygen addition ion was seen in the mass spectrum and, interestingly, this new species [M–H+O]⁻ had a shorter drift time than the lighter [M–H]⁻ ion. Other phenolic compounds primarily produced two IMS peaks in the mass‐selected mobility spectra measured using the [M–H]⁻ ion. It was also observed that two isomeric compounds, 2,4‐di‐tert‐butylphenol and 2,6‐di‐tert‐butylphenol, could be separated with IMS. In addition, mobilities of various characteristic ions of 2,4,6‐trinitrotoluene were measured, since this compound was previously used as a mobility standard. The possibility of using phenolic compounds as mobility standards is also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Global solution of optimization problems with signomial parts

In this paper a new approach for the global solution of nonconvex MINLP (Mixed Integer NonLinear Programming) problems that contain signomial (generalized geometric) expressions is proposed and illustrated. By applying different variable transformation techniques and a discretization scheme a lower bounding convex MINLP problem can be derived. The convexified MINLP problem can be solved with standard methods. The key element in this approach is that all transformations are applied termwise. In this way all convex parts of the problem are left unaffected by the transformations. The method is illustrated by four example problems.     

Dimethylmercury in mixtures of thermotropic nematogens

Abstract

The geometry of dimethylmercury was studied in several mixtures of the liquid crystals ZLI 1167 and phase 4. The variation of the geometry is not very large but systematic changes can be detected as a function of the liquid crystal composition. The anisotropics, δ[sgrave], of the ¹H, ¹³C and ¹⁹⁹Hg shielding tensors were investigated by applying two methods based on mixing liquid crystals with opposite diamagnetic anisotropies and by applying various referencing methods. Apart from these, the anisotropy, δJ _HgC, of the ¹⁹⁹Hg–¹³C spin–spin coupling tensor was studied in four mixtures of these liquid crystals, and was found to vary with the solvent.     

Environmental and food analysis by desorption atmospheric pressure photoionization‐mass spectrometry

Desorption atmospheric pressure photoionization‐mass spectrometry (DAPPI‐MS) is a versatile surface analysis technique for a wide range of analytes, especially for neutral and non‐polar analytes. Here, a set of analytes typically found in environmental or food samples was analyzed by DAPPI‐MS. The set included five polyaromatic hydrocarbons (PAHs), one N‐PAH, one brominated flame retardant, and nine pesticides, which were studied with three different spray solvents: acetone and toluene in positive ion mode, and anisole in negative ion mode. The analytes showed [M + H]⁺, M^+?, and [M–H]^? ions as well as fragmentation and substitution products. Detection limits for the studied compounds ranged from 30 pg to 1 ng (from 0.14 to 5.6 pmol). To demonstrate the feasibility of the use of DAPPI‐MS two authentic samples – a circuit board and orange peel – and a spiked soil sample were analyzed. Tetrabromobisphenol A, imazalil, and PAHs were observed from the three above‐mentioned samples, respectively. The method is best suited for rapid screening analysis of environmental or food samples. Copyright © 2010 John Wiley & Sons, Ltd.     

Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions

We study the driven translocation of polymers under time-dependent driving forces using N-particle Langevin dynamics simulations. We consider the force to be either sinusoidally oscillating in time or dichotomic noise with exponential correlation time, to mimic both plausible experimental setups and naturally occurring biological conditions. In addition, we consider both the case of purely repulsive polymer-pore interactions and the case with additional attractive polymer-pore interactions, typically occurring inside biological pores. We find that the nature of the interaction fundamentally affects the translocation dynamics. For the non-attractive pore, the translocation time crosses over to a fast translocation regime as the frequency of the driving force decreases. In the attractive pore case, because of a free energy well induced inside the pore, the translocation time can be a minimum at the optimal frequency of the force, the so-called resonant activation. In the latter case, we examine the effect of various physical parameters on the resonant activation, and explain our observations using simple theoretical arguments.