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.     

Effective binuclear Pd(II) complexes for Suzuki reactions in water

A series of new ionic binuclear Pd(II) complexes supported by water‐soluble bis(α‐diimine) ligands were prepared and employed as catalysts for the palladium‐catalyzed Suzuki reaction in aqueous media. The binuclear nature of the complexes increased the reaction rate, while electronic and steric modification of the ligand frameworks had a remarkable influence upon the catalytic activity of the palladium complexes. The catalysts were shown to be homogeneous through mercury poisoning experiments and complexes could be recycled more than 10 times without loss of catalytic activity. Copyright © 2013 John Wiley & Sons, Ltd.     

Statistics and characterization of matrices by determinant and trace

The Ramanujan Journal - Answering a question of Erdös, Komlós proved in 1968 that almost all $$n\times n$$ Bernoulli matrices are nonsingular as $$n\rightarrow \infty $$ . In this paper,...     

Enamines of 1,3-dimethylbarbiturates and their symmetrical palladium(II) complexes: synthesis,characterization and biological activity

Transition Metal Chemistry - Three 1,3-dimethylbarbiturate-enamine derivatives and their symmetrical palladium(II) complexes were prepared and characterized by spectroscopic methods. In addition,...     

A novel amperometric hydrogen peroxide biosensor based on pyrrole-PAMAM dendrimer modified gold electrode

Horseradish peroxidase (HRP) was immobilized into an electrochemically prepared copolymer of pyrrole–PAMAM (PAMAM; polyamidoamine) dendrimers for the construction of amperometric hydrogen peroxide biosensor. First, second, and third generation amidoamine–pyrrole dendrons having branched amine periphery and focal pyrrole functionality were synthesized via divergent pathway. Pyrrole dendrimers were covalently attached onto the electrode surface and polymerized by electrochemical copolymerization with pyrrole monomer. The synthesized dendrimers and copolymers have been characterized by FTIR-ATR and NMR. These copolymers have been utilized as conducting films for amperometric hydrogen peroxide sensing. The HRP retains its bioactivity after immobilization into the dendronized pyrrole-copolymers. Amperometric response was measured as a function of concentration of hydrogen peroxide, at fixed potential of +0.35 V vs. Ag/AgCl in a phosphate buffered saline (pH 7.5). The effect of pH and temperature of the medium, storage, and reusability properties were investigated. The results indicate an efficient immobilization of enzyme onto the PAMAM type dendrimer modified surface containing pyrrole monomer, which leads to high enzyme loading, and increased lifetime stability of the electrode.     

Established and emerging strategies for polymer chain-end modification

The development of “controlled” and “living” polymerization processes with high end-group fidelity has enabled an unprecedented range of polymeric materials with specific chain-end functionality to be prepared. This highlight provides an overview of available strategies and evaluation of recent approaches for the chain-end functionalization of polymers prepared through controlled chain-growth polymerizations. As a tribute to Professor Robert B. Grubbs on the occasion of his 75th birthday, we also take this opportunity to highlight methods for the chain-end modification of polymers prepared by ring-opening metathesis polymerization within the broader context of functional group tolerant, living polymerizations. Finally, we focus attention toward new directions in polymer chain-end modifications, describing existing gaps in current strategies, and detailing recently reported protocols that show significant improvements over traditional methods. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2903–2914