Global Solutions for 3D Quadratic Schrodinger Equations

This is the firstof the three papers where we present a newmethod based on the concept of space-time resonance to proveglobal existence of small solutions to nonlinear dispersiveequations. The idea is that time resonances (dynamical systemsresonances) correspond to interactions between plane waves;but since for dispersive equations we deal with localized solutions,it is crucial to take also into account the traveling speedsof the different wave packets. Here we show how this idea, andthe analytical method that this naturally suggests, leads toa simple proof of global existence and scattering for quadraticnonlinear Schrödinger equations in three dimensions.     

Heterocycles [<Emphasis Type="Italic">h</Emphasis>]-fused to 4-oxoquinoline-3-carboxylic acid. Part VII: synthesis of some 6-oxoimidazo[4,5-<Emphasis Type="Italic">h</Emphasis>]quinoline-7-carboxylic acids and esters

Abstract  A series of ethyl 2-(substituted)-9-cyclopropyl-4-fluoro-6-oxo-1H-imidazo[4,5-h]quinoline-7-carboxylates has been prepared from ethyl 7,8-diamino-1,4-dihydroquinoline-3-carboxylate via thermally induced reactions with model alkanoic acids or via microwave-assisted cyclocondensation with some arene carboxaldehydes. Acid-catalysed hydrolysis of the resulting ester derivatives furnished the corresponding imidazoquinoline-7-carboxylic acids. The structures of these new acid and ester derivatives are based on microanalytical and spectral (IR, MS, and NMR) data. Graphical abstract        

SPME in environmental analysis: biotransformation pathways

Solid-phase microextraction (SPME) is an organic solvent-free sample preparation tool suitable for direct adsorption of analytes from the headspace or the aqueous phase of a matrix followed by desorption into a gas chromatograph (GC) or high-performance liquid chromatograph (HPLC) for subsequent analysis. The SPME technique is designed to accommodate the use of fibers coated with different polymers suitable for the extraction of chemicals with varied hydrophobic and polar properties. Also, the technique can minimize interference from other artefacts associated with complex samples, such as those encountered in biological matrices or reaction mixtures. The preceding characteristics of SPME make the technique suitable for real-time measurements of intermediate reaction products and, thus, able to provide insight into the fate of target chemicals and their degradation pathways. In the present article, the current state of knowledge on the use of SPME-GC and SPME-HPLC in the determination of frequently encountered environmental chemicals and their (bio)transformation pathways are critically reviewed. Future opportunities of SPME in real time in situ process monitoring such as the use of agricultural feed stocks to bio-based industrial products termed henceforth "process analytical chemistry" are also discussed.     

Two‐stage phase separation of cellulose acetate membranes modified with plasma‐treated natural zeolite: Response surface modeling

Cellulose acetate (CA) microfiltration membranes were prepared by two‐stage vapor‐induced phase separation (VIPS) and immersion precipitation. To improve the hydrophilicity and permeability of the membranes at low operating pressures, plasma‐treated natural zeolite was incorporated into the membranes. A response surface methodology based on the three‐level central composite design (CCD) was used to model and optimize the casting solution composition of the membranes with the aim of maximizing membranes permeability. Three independent variables for CCD optimization were concentration of CA, polyvinylpyrrolidone (PVP) pore former, and plasma‐treated zeolite additive. The results showed that a second‐order polynomial model could properly predict the response (pure water flux) at any input variable values with a satisfying determination coefficient (R²) of 0.954. Also, analysis of variance (ANOVA) confirmed the adequacy of the obtained model. The permeability of the prepared membranes increased by increasing zeolite loading from 0.10 to 0.50 wt%, which was related to the membranes morphology and porosity and confirmed by scanning electron microscopy (SEM) images. Pure water flux of the membranes decreased by increasing CA concentration while an optimum PVP amount was required to reach the maximum flux. The result of the bubble point analysis well matched with surface SEM images of the membranes and permeability trend predicted by CCD model. Also, the prepared CA membranes with different compositions showed no toxicity for mouse L929 fibroblast, which indicated their nontoxic and biocompatible nature.     

Quantum Dynamical Behavior of the Morse Oscillator: the Wigner Function Approach

We explore the quantum dynamical behavior of the Morse oscillator in the phase space using the Wigner function. For an initial wave packet excited with Gaussian probability distribution, we calculate the associated Wigner function and compute its time evolution. By calculating the marginal probabilities, we study the formation of quantum carpets both in the position space and in the momentum space. In addition, in view of these probabilities, we present the time evolution of the position and momentum expectation values. The structure of quantum carpets and the time-evolved expectation values mimic the emergence of quantum revivals and fractional revivals.     

Facile synthesis of model 1,4‐dihydro‐1H‐1,3,4‐benzotriazepin‐5‐ones

2‐Aminobenzoic acid reacts readily, in the presence of triethylamine, with hydrazonoyl chlorides ( 5a‐c ) (precursors of the reactive nitrile imine 1,3‐dipolar species) to afford high yields of the corresponding acyclic amidrazone adducts ( 6a‐c ). The latter adducts undergo, in THF in presence of 1,1‐carbonyldiimida‐zole, smooth intramolecular cyclization involving the activated carboxyl and the NH‐ termini to deliver unequivocally the respective dihydro‐1,3,4‐benzotriazepin‐5‐ones ( 7a‐c ).     

A combined experimental and theoretical study of the alkylation of 3,5‐dithioxo‐[1,2,4]triazepines

The chemo‐ and regioselective alkylation reactions of 3,5‐dithioxo[1,2,4]triazepine 1 in a basic medium with α,ω‐dibromoalkanes 2a – c , Br(CH₂)_nBr (n = 1–3), are studied experimentally and theoretically. These alkylations, which occur at the thioxo sulfur atom in position 5, afford mainly 5‐bromomethylthio‐2,7‐dimethyl‐ 2,3‐dihydro‐ 4H[1,2,4]triazepin‐3‐one 3 for n = 1, 6,8‐dimethyl‐5‐thioxo‐2,3,4,5‐tetrahydro‐6H[1,3]thiazolo[4,5‐d][1,2,4]triazepine 4 for n = 2 and 7,9‐dimethyl‐6‐thioxo‐2,3,4,5,6,7‐hexahydro[1,3]thiazino [4,5‐d][1,2,4]triazepine 5 for n = 3. Theoretical calculations have been carried out at the B3LYP/6‐31G* and B3LYP(benzene)/6‐311+G*//B3LYP/6‐31G* levels, in order to rationalize the experimental observations. Both chemo‐ and regio‐selectivities of the alkylation reactions are analyzed. Copyright © 2008 John Wiley & Sons, Ltd.