Some monotonicity properties of symmetric pólya densities and their exponential families

Summary In this note we observe that for independent symmetric random variables X and Y, when the pdf of X is PF, the conditional distributions of ¦Y¦ given S = X + Y form a MLR family. We then show that for a function : R ⁿR that is symmetric in each coordinate and increasing on (0, )ⁿ, E((S₁,...,S_n)¦S_n = s) is even and increasing in ¦s¦. Here S₁,...,S_n are partial sums with independent symmetric PF summands. Application is made to sequential tests that minimize the maximum expected sample size when the model is a one-parameter exponential family generated by a symmetric PF density.Work supported by NSF grants MPS 72-05082 AO2 and MCS 75-23344     

Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].     

GROMACS: fast, flexible, and free

This article describes the software suite GROMACS (Groningen MAchine for Chemical Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for molecular dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addition, it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequilibrium dynamics and free energy determinations are incorporated. Interfaces with popular quantum-chemical packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and analysis programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.     

Iron speciation by solid phase extraction and flame atomic absorption spectrometry using N,N′-bis-(2-hydroxy-5-bromobenzyl)-2-hydroxy-1,3-diiminopropane

A new Schiff base, N,N′-bis-(2-hydroxy-5-bromobenzyl)-2-hydroxy-1,3-diiminopropane, has been synthesized for the very sensitive determination of iron(III) and iron(II) in natural water samples. It enabled a very selective and rapid method for iron determination to be developed. The method has also been applied to total iron determination in sediment samples. In the preconcentration system, the Schiff base reagent is mixed with the samples and chelates containing iron(III). The complexes are then adsorbed on silica gel within a column system. Elution of the adsorbed chelate from the silica gel was performed with a small volume of acetone containing 2.5% nitric acid. The iron is measured off-line by flame atomic absorption spectrometry. The method can be applied to the preconcentration, separation and speciation of iron. The effects of parameters such as pH, sample flow rate, eluent flow rate, foreign ions and ligand concentration have been investigated. The effect of humic acid that can produce complexes with metal ions in natural systems has also been investigated. The results obtained indicate that the method is not affected by the presence of up to 10 ppm humic acid, which would be a very high concentration to be present in natural systems. The solid phase extraction method developed has been applied to the determination of iron in both natural water samples and sediment samples. The LOD was found to be 0.17 mg L⁻¹ when no preconcentration was used, although preconcentration factors of 100 could be achieved. The recovery values for spiked samples were between 100 and 104%. The results were compared statistically with those from the standard 1,10 phenanthroline method used for iron speciation in water systems. A Student’s t-test indicated no significant difference between the two methods. In addition, this method was applied to the analysis of a certified sediment sample, LGC 6156. Generally, a 10-fold preconcentration factor was required for the analysis of natural water samples.     

Anionic water-soluble sulfonated phthalocyanines: microwave-assisted synthesis,aggregation behaviours,electrochemical and in-situ spectroelectrochemical characterisation

In this work, a phthalonitrile derivative bearing p-sulfonylphenoxy group at the 3-position has been synthesised. The water-soluble non-peripherally tetrasubstituted zinc (3) and cobalt (4) phthalocyanines were obtained by cyclotetramerisation of this phthalonitrile derivative in the presence of anhydrous metal salts by microwave irradiation. The compounds have been characterised by using FT-IR, ¹H NMR, UV–Vis and Mass spectrometry (MS) data. The aggregation behaviours of these compounds were investigated in methanol, DMSO, DMF, and water. We have also studied the aggregation behaviours of the phthalocyanine complex 3 in various DMSO/water mixtures. Additionally, the redox properties of the phthalocyanine complexes were examined in dimethylsulfoxide by voltammetry and in situ spectroelectrochemistry. Redox behaviours of the complexes supported the structures of the complexes. Metal and ring-based reductions were observed for 4 and only ring-based electron transfer processes were observed with 3.     

Development of one-pot benzylic amination reactions of azine N-oxides

An efficient one-pot synthetic methodology has been developed for the benzylic amination reactions of methyl-substituted azine N-oxides that operate under mild conditions. The reaction was found to tolerate quinoline and isoquinoline N-oxides with electron donating and withdrawing substituents as the electrophilic reaction partners as well as a broad range of nucleophilic primary, secondary and aromatic amines, affording the benzylic amination products in up to 82% yield.     

Nuclear-Electron Overhauser Effect in MC800 Liquid Asphalt Solutions

Experimental results on the extrapolated ultimate enhancement factors of o-, m-, and p-xylene protons at 1.53 mT are obtained for MC800 asphalt solutions. The ultimate enhancement factors are found such as ?26.9, ?25.7, and ?11.7 for o-, m-, and p-xylene, respectively. These results show that the solvent proton Overhauser effect cannot reach the extrapolated enhancement of ?330 in the extreme narrowing case because of occurrence of small scalar interactions in addition to the dipole–dipole interactions between solvent protons and asphalt electrons. The ortho, meta, and para positions of the –CH₃ group change the nature of the interactions. The nuclear magnetic resonance (NMR) signal enhancements exhibit a sensitive behavior depending on the chemical environment differing from isomer to isomer. The solvation or association of asphalt in xylene isomers at room temperature is revealed. Quantum chemical calculations for the xylene isomers with the electronic and optical properties; absorption wavelengths, excitation energy, atomic charges, dipole moment and frontier molecular orbital energies, molecular electrostatic potential; are carried out using the density functional theory (DFT) method (B3LYP) with the 6-311G(d,p) basis set by the standard Gaussian 09 software package program. The relative importance of scalar and translational dipolar interaction parameters determined in dynamic nuclear polarization experiments is explained by the electronic structure of HOMO–LUMO of the xylene isomers.     

Synthesis of novel tetra-substituted benzimidazole compounds containing certain heterostructures with antioxidant and anti-urease activities

A new series of 5,6-dimethyl-2-phenyl-1H-benzimidazole derivatives was synthesized. The antioxidant activities of the synthesized compounds were determined according to the cupric reducing antioxidant capacity (CUPRAC), ABTS, and DPPH assays. Many of the target compounds showed good antioxidant activity. Among these compounds, it has been determined that the carbothioamide and 1,2,4-triazole derivatives had a very good antioxidant capacity. Also, all compounds were screened for in vitro inhibitory activity against Jack bean urease. Among the synthesized molecules, the starting compound, acetate, and acetohydrazide derivatives (with IC₅₀ values 12.02, 11.40, and 8.04 μg/mL, respectively) had a higher inhibitory effect on urease and exhibited a lower IC₅₀ values than acetohydroxamic acid (IC₅₀: 20.50 μg/mL) and thiourea (IC₅₀: 14.04 μg/mL) as a reference inhibitors.     

Phase-sensitive specular neutron reflectometry for imaging the nanometer scale composition depth profile of thin-film materials

Neutron reflectometry is a powerful method for probing the molecular scale structure of both hard and soft condensed matter films. Moreover, the phase-sensitive methods which have been developed make it possible for specular neutron reflectometry to be effectively employed as an imaging device of the composition depth profile of thin film materials with a spatial resolution approaching a fraction of a nanometer. The image of the cross-sectional distribution of matter in the film obtained in such a way can be shown to be, in most cases, unambiguous to a degree limited primarily by the range and statistical uncertainty of the reflectivity data available. The application of phase-sensitive neutron reflectometry (PSNR) to the study of several types of soft matter thin film systems are illustrated by a number of specific examples from recent studies. In addition, new software tools available to the researcher to apply PSNR methods and analysis are discussed.