Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Dynamics on the Virasoro group, 2D gravity and hidden symmetries

We derive the action of 2D gravity from the two-cocycle of the Virasoro group by using a previously introduced method for constructing a dynamical system from a Lie group. A natural construction and explanation of the hidden SL(2, )-Kac-Moody symmetry, of general applicability, is provided. We also show how the proper quantization goes beyond the ordinary co-adjoint orbit method, and the possible connection with the Poisson-Lie groups.     

Synthesis of poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) by the competitive single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization in water

The synthesis of a block copolymer poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) is reported. This new material was synthesized by single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization (SET‐DTLRP) in two steps. First, a bifunctional macroinitiator of α,ω‐di(iodo)poly (butyl acrylate) [α,ω‐di(iodo)PBA] was synthesized by SET‐DTLRP in water at 25 °C. The macroinitiator was further reinitiated by SET‐DTLRP, leading to the formation of the desired product. This ABA block copolymer was synthesized with high initiator efficiency. The kinetics of the copolymerization reaction was studied for two PBA macroinitiators with number–average molecular weight of 10 k and 20 k. The relationship between the conversion and the number–average molecular weight was found to be linear. The dynamic mechanical thermal analysis suggests just one phase, indicating that copolymer behaves as a single material with no phase separation. This methodology provides the access to several block copolymers and other complex architectures that result from combinations of thermoplastics (PVC) and elastomers (PBA). From industrial standpoint, this process is attractive, because of easy experimental setup and the environmental friendly reaction medium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3001–3008, 2006     

Single electron transfer–degenerative chain transfer living radical polymerization of N‐butyl acrylate catalyzed by Na2S2O4 in water media

Living radical polymerization of n‐butyl acrylate was achieved by single electron transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionate. The plots of number–average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This methodology leads to the preparation of α,ω‐di(iodo) poly (butyl acrylate) (α,ω‐di(iodo)PBA) macroinitiators. The influence of polymerization degree ([monomer]/[initiator]), amount of catalyst, concentration of suspending agents and temperature were studied. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering (RALLS), a differential viscometer (DV), and refractive index (RI). The methodology studied in this work represents a possible route to prepare well‐tailored macromolecules made of butyl acrylate in an environmental friendly reaction medium. Moreover, such materials can be subsequently functionalized leading to the formation of different block copolymers of composition ABA. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2809–2825, 2006     

Determination of lithium in human serum by electrothermal atomic absorption spectrometry

An efficient method was developed for the determination of nanogram levels of lithium in biological samples. Serum samples from human subjects from southeastern Spain, treated or not treated with lithium carbonate, were analyzed by electrothermal atomic absorption spectrometry. The samples were previously treated with a matrix modifier consisting of 0.1% Triton X-100 and injected through a graphite tube with L'vov platform. The Li concentrations measured by the procedure described for the 3 certified reference samples used were not significantly different (p > 0.05) than certified levels. Sample recoveries and variability during several days, with coefficients of variation from 4.00 to 14.8%, demonstrated the reliability and accuracy of this technique. Mean Li concentration determined in the serum of individuals with psychiatric disorders treated with Li (n = 117, 5.077 +/- 1.795 microg Li/mL) was significantly higher (p < 0.001) than that in individuals not treated with Li (n = 24, 1.902 +/- 2.054 ng Li/mL).     

A LASER FLASH SPECTROSCOPY STUDY OF THE KINETICS OF ELECTRON TRANSFER FROM SPINACH PHOTOSYSTEM I TO SPINACH AND ALGAL FERREDOXINS

Laser flash absorption spectroscopy has been used to investigate the kinetics of electron transfer from P700 in Photosystem I (PSI)-enriched particles from spinach to the ferredoxins from spinach and the green alga Monoraphidium braunii. Very similar behavior for the interaction of both ferredoxins with the PSI complex was observed, although the algal ferredoxin appears to be slightly more effective as an electron acceptor. For both proteins, a non-linear protein concentration dependence of the rate constant for reduction was obtained, indicating complex formation preceding electron transfer. Estimates of 3 times 10⁷M^?1 s^?1 and 140–180 s^?l were obtained from these data for the second order rate constants for complex formation, and the limiting first order rate constants for electron transfer, respectively. At neutral pH, a biphasic dependence of the rate constant for ferredoxin reduction on the concentration of NaCl or MgCl₂ was observed. This was interpreted in terms of the electrostatic interactions which occur between ferredoxin and the PSI membrane. In addition, magnesium cations appear to play a specific role in the interaction between PSI and ferredoxin. Thus, the addition of these ions under optimal conditions induces a 6-f-old increase in the electron transfer reaction rate constant, compared with a 2-f-old increase in the presence of an optimal amount of NaCI. This cannot be explained as arising from ionic strength effects. To our knowledge, this is the first time that a direct measurement of the rate constant for the reduction of ferredoxin by the PSI complex has been reported.     

2]pseudorotaxane formation with N-benzylanilinium axles and 24-crown-8 ether wheels

[reaction: see text] As a hybrid of the N,N-dibenzylammonium and 1,2-bis(pyridinium)ethane axles, various N-benzylanilinium cations were investigated as suitable axles for the formation of [2]pseudorotaxanes with the 24-membered crown ethers 24C8 and DB24C8. The effect of electron-donating OCH(3) and electron-withdrawing CF(3) groups on both the anilinium and benzyl aromatic rings was studied. Formation constants and structural details were compared to the [2]pseudorotaxanes formed by the two aforementioned dibenzylammonium and 1,2-bis(pyridinium)ethane axles.     

Thermal decomposition of some imidazole and N-methyl substituted imidazole complexes of palladium(II)

We describe in this paper the thermal decomposition in air of several complexes of palladium(II) chloride with imidazole and N-methylimidazole. Although the final process of the decomposition gives (PdCl₂)_n which then decomposes to pa ladium which oxidizes to PdO, there are interesting differences in the initial decomposition path. The reasons for these differences appear to be related to the trans-effect and to the presence in the imidazole complexes of hydrogen bonds which break down at temperatures of around 220.

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Zusammenfassung In diesem Beitrag wird die thermische Zersetzung verschiedener Komplexe des Palladium(II)chlorids mit Imidazol und N-Methylimidazol in Luft beschrieben. Obwohl der Endvorgang der Zersetzung (PdCl₂)_n ergibt, welches dann zu Palladium zersetzt und zu PdO oxidiert wird, bestehen interessante Unterschiede im Anfangsschritt der Zersetzung. Die Ursachen dieser Unterschiede scheinen mit dem Trans-Effekt und der Anwesenheit von Wasserstoffbindungen in den Imidazolkomplexen verbunden zu sein, welche bei Temperaturen um 220 zerstört werden.

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Résumé La décomposition thermique dans l'air de plusieurs complexes du chlorure de palladium(II) avec l'imidazole et le méthyl-4-imidazole est décrite. Bien que l'étape finale de la décomposition donne (PdCl₂)_n qui se décompose ensuite en palladium qui s'oxyde en PdO, des différences intéressantes apparaissent dans les étapes initiales de la décomposition. Les causes de ces différences sont en rapport avec l'effet trans et la présence, dans les complexes avec l'imidazole, de liaisons hydrogÊne qui se rompent vers 220.

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(II) -. (PdCl₂)_n, , PdO, . , - , 220.

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One of us (M.C. Navarro Ranninger) would like to thank the D.G.E.S.I. for a grant that allowed her to work on this research.     

Signatures andS-discrete lattice-ordered groups

The central theme of this article is the approximation of lattice-ordered groups (l-groups) first by Specker groups and, subsequently, by the so-calledS-discretel-groups. The sense of these approximations is made precise via the notion of a signature, defined below, and by that ofa ^*-subgroups. Sample result: ifG is a projectablel-group then it has anl-subgroupH which is Specker and for which the mapPPH defines a boolean isomorphism between the algebras of polars ofG andH.Presented by L. Fuchs.This article was written while this author was a Stouffer Visiting Professor at the University of Kansas. He wishes to thank the members of the Mathematics Department of that institution for their hospitality.     

Effect of film thickness on the electro-reduction of molecular oxygen on electropolymerized cobalt tetra-aminophthalocyanine films

We studied the electrocatalytic activity of cobalt tetra-aminophthalocyanine (CoTAPc) for the reduction of molecular oxygen (O₂) on adsorbed monomeric and on electropolymerized films of different thicknesses on glassy carbon (GC) electrode. The polymeric films, denoted poly-CoTAPc, were first characterized by electrochemical impedance spectroscopy and it appears that the types of phenomena revealed to be occurring depend less on the film thickness in basic than in acid media. For O₂ reduction, the results showed that poly-CoTAPc is more active than the monomeric CoTAPc adsorbed on GC. Indeed, rotating ring-disk electrode data showed that polymeric CoTAPc promotes the four-electron reduction of O₂ to water in parallel to a two-electron reduction to give peroxide. On monomeric and thin films of poly-CoTAPc, a two-electron reduction mechanism predominates. In basic media the activity increases very slightly with thickness, whereas in acid media this increase is more pronounced. This parallels the observed behavior revealed by electrochemical impedance spectroscopy.