Difference schemes on uniform grids performed by general discrete operators

Our aim is to set the foundations of a discrete vectorial calculus on uniform n-dimensional grids, that can be easily reformulated on general irregular grids. As a key tool we first introduce the notion of tangent space to any grid node. Then we define the concepts of vector field, field of matrices and inner products on the space of grid functions and on the space of vector fields, mimicking the continuous setting. This allows us to obtain the discrete analogous of the basic first order differential operators, gradient and divergence, whose composition define the fundamental second order difference operator. As an application, we show that all difference schemes, with constant coefficients, for first and second order differential operators with constant coefficients can be seen as difference operators of the form for suitable choices of q, and  . In addition, we characterize special properties of the difference scheme, such as consistency, symmetry and positivity in terms of q, and  .     

Some remarks on indiscernible sequences

We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of coheirs.     

Incubation period in the 2,2,4,4‐tetramethyl‐1‐piperidinyloxy‐mediated thermal autopolymerization of styrene: Kinetics and simulations

Mechanisms and simulations of the induction period and the initial polymerization stages in the nitroxide‐mediated autopolymerization of styrene are discussed. At 120–125 °C and moderate 2,2,4,4‐tetramethyl‐1‐piperidinyloxy (TEMPO) concentrations (0.02–0.08 M), the main source of radicals is the hydrogen abstraction of the Mayo dimer by TEMPO [with the kinetic constant of hydrogen abstraction (k_h)]. At higher TEMPO concentrations ([N?] > 0.1 M), this reaction is still dominant, but radical generation by the direct attack against styrene by TEMPO, with kinetic constant of addition k_ad, also becomes relevant. From previous experimental data and simulations, initial estimates of k_h ≈ 1 and k_ad ≈ 6 × 10^?7 L mol^?1 s^?1 are obtained at 125 °C. From the induction period to the polymerization regime, there is an abrupt change in the dominant mechanism generating radicals because of the sudden decrease in the nitroxide radicals. Under induction‐period conditions, the simulations confirm the validity of the quasi‐steady‐state assumption (QSSA) for the Mayo dimer in this regime; however, after the induction period, the QSSA for the dimer is not valid, and this brings into question the scientific basis of the well‐known expression k_th[M]³ (where [M] is the monomer concentration and k_th is the kinetic constant of autoinitiation) for the autoinitiation rate in styrene polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6962‐6979, 2006     

Capillary zone electrophoresis for analysis of phytochelatins and other thiol peptides in complex biological samples derivatized with monobromobimane

A new method to improve the analysis of phytochelatins and their precursors (cysteine, gamma-Glu-Cys, and glutathione) derivatized with monobromobimane (mBrB) in complex biological samples by capillary zone electrophoresis is described. The effects of the background electrolyte pH, concentration, and different organic additives (acetonitrile, methanol, and trifluoroethanol) on the separation were studied to achieve optimum resolution and number of theoretical plates of the analyzed compounds in the electropherograms. Optimum separation of the thiol peptides was obtained with 150 mM phosphate buffer at pH 1.60. Separation efficiency was improved when 2.5% v/v methanol was added to the background electrolyte. The electrophoretic conditions were 13 kV and capillary dimensions with 30 cm length from the inlet to the detector (38 cm total length) and 50 microm inner diameter. The injection was by pressure at 50 mbar for 17 s. Under these conditions, the separation between desglycyl-peptides and phytochelatins was also achieved. We also describe the optimum conditions for the derivatization of biological samples with mBrB to increase electrophoretic sensitivity and number of theoretical plates. The improved method was shown to be simple, reproducible, selective, and accurate in measuring thiol peptides in complex biological samples, the detection limit being 2.5 microM glutathione at a wavelength of 390 nm.     

Introduction of heteroatom-based substituents into 1,4-dihydropyridines by means of a halogen-mediated, oxidative protocol: diamination, sulfonylation, sulfinylation, bis-sulfanylation, and halo-phosphonylation processes

The natural tendency of 1,4-dihydropyridines to undergo "biomimetic" oxidation to afford pyridinium salts can be switched off and, through the use of reagents that interact electrophilically with the enamine moiety present in the heterocyclic system, it is possible to promote alternative oxidations. In this way, efficient regio- and stereocontrolled synthetic methods have been developed that lead to diversely substituted di- and tetrahydropyridines. These include iodoazidation, diamination, bis-sulfonamidation, sulfonylation, sulfinylation, thiocyanation, sulfanylation, bis-sulfanylation, and halo-phosphonylation processes.     

Hydrodynamic equations for attractive particle systems on ℤ

Hydrodynamic properties for a class of nondiffusive particle systems are investigated. The method allows one to study local equilibria for a class of asymmetric zero-range processes, and applies as well to other models, such as asymmetric simple exclusion and misanthropes. Attractiveness is an essential ingredient. The hydrodynamic equations present shock wave phenomena. Preservation of local equilibrium is proven to hold away from the shocks. The problem of breakdown of local ergodicity at the shocks, which was investigated by D. Wick in a particular model, remains open in this more general setup.