Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in fading memory spaces

We use a new concept of weighted ergodic function based on the measure theory to investigate the existence and uniqueness of weighted pseudo almost periodic solution for a class of partial functional differential equations with infinite delay in fading memory spaces. We illustrate our theoretical results by studying some Lotka-Voltera reaction-diffusion systems with infinite delay.     

Quantifying of Quantum Correlations in an Optomechanical System with Cross-Kerr Interaction

Journal of Russian Laser Research - Under the cross-Kerr effect, we investigate two different forms of quantum correlations in an optomechanical system consisting of a mechanical mode coupled with...     

Reaction of dimethylplatinum(II) complexes with PhCH2CH2Br: Comparative reactivity with CH3CH2Br and PhCH2Br and synthesis of Pt(IV) complexes

Oxidative addition of 2‐phenylethylbromide (PhCH₂CH₂Br) to dimethylplatinum(II) complexes [PtMe₂(NN)] ( 1a , NN = 2,2′‐bipyridine (bpy); 1b , NN = 1,10‐phenanthroline (phen)) afforded the new organoplatinum(IV) complexes [PtMe₂(Br)(PhCH₂CH₂)(bpy)], as a mixture of trans ( 2a ) and cis ( 3a ) isomers, and [PtMe₂(Br)(PhCH₂CH₂)(phen)], as a mixture of trans ( 2b ) and cis ( 3b ) isomers, respectively. The new Pt(IV) complexes were readily characterized using multinuclear (¹H and ¹³C) NMR spectroscopy and elemental microanalysis. The crystal structure of 2a was further determined using X‐ray crystallography indicating an octahedral geometry around the platinum centre. A comparison of reactivity of RCH₂Br reagents (R = CH₃, Ph or PhCH₂) in their oxidative addition reactions with complex 1a , with an emphasis on the effects of the R groups of alkyl halides, was also conducted using density functional theory.     

A Simple Spot Test Method with Digital Imaging for Chromium Speciation in Water Samples

Journal of Analytical Chemistry - A simple and environmentally friendly method for the speciation of chromium based on a spot test obtained from digital images has been developed. Due to rapidity...     

Backbiting and β‐scission reactions in free‐radical polymerization of methyl acrylate

Multiple mechanisms of backbiting and β‐scission reactions in free‐radical polymerization of methyl acrylate are modeled using different levels of theory, and the rigid‐rotor harmonic‐oscillator (RRHO) and hindered‐rotor (HR) approximations. We identify the most cost‐effective computational method(s) for studying the reactions and assess the effects of different factors (e.g., functional type and chain length) on thermodynamic quantities, and then identify the most likely mechanisms with first‐principles thermodynamic calculations and simulations of nuclear magnetic resonance (NMR) spectra. To this end, the composite method G4(MP2)‐6X is used to calculate the energy barrier of a representative backbiting reaction. This calculated barrier is then compared with values obtained using density functional theory (DFT) (B3LYP, M06‐2X, and PBE0) and a wavefunction‐based quantum chemistry method (MP2) to establish the benchmark method. Our study reveals that the barriers predicted using B3LYP, M06‐2X, and G4(MP2)‐6X are comparable. The entropies calculated using the RRHO and HR approximations are also comparable. DFT calculations indicate that the 1:5 backbiting mechanism with a six‐membered ring transition state and 1:7 backbiting with an eight‐membered ring transition state are energetically more favored than 1:3 backbiting and 1:9 backbiting mechanisms. The thermodynamic favorability of 1:5 versus 1:7 backbiting depends on the live polymer chain length. The activation energies and rate constants of the left and right β‐scission reactions are nearly equal. The calculated and experimental ¹³C and ¹H NMR chemical shifts of polymer chains affected by backbiting and β‐scission reactions agree with each other, which provides further evidence in favor of the proposed mechanisms. © 2013 Wiley Periodicals, Inc.