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.}     

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     

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.     

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.     

Nitric oxide photorelease from ruthenium salen complexes in aqueous and organic solutions

The complexes [Ru(salen)(NO)Cl] and [Ru(salen)(NO)(H(2)O)](+) were shown to release the nitrosyl ligand as nitric oxide upon exposure to visible light in organic and aqueous solutions respectively, by means of UV-visible, EPR, and FTIR spectroscopies. The former was prepared by a new synthetic route and had its structure determined by single-crystal X-ray diffraction. A crystal of the dichloromethane solvate is orthorhombic, space group Fdd2 (No. 43) and formula C(16)H(14)ClN(3)O(3)Ru.CH(2)Cl(2), with Z = 16 and cell parameters a = 25.489(4), b = 33.435(4), and c = 9.3716(9) A. The electronic absorption spectra of the complexes were calculated using the INDO/S method. The water-soluble complex is a potential drug for antitumoral phototreatment.     

Mathematical Models for Unstable Quantum Systems and Gamow States

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.     

Lossless Medical Image Compression by Using Difference Transform

This paper introduces a new method of compressing digital images by using the Difference Transform applied in medical imaging. The Difference Transform algorithm performs the decorrelation process of image data, and in this way improves the encoding process, achieving a file with a smaller size than the original. The proposed method proves to be competitive and in many cases better than the standards used for medical images such as TIFF or PNG. In addition, the Difference Transform can replace other transforms like Cosine or Wavelet.     

Green Extraction Techniques as Advanced Sample Preparation Approaches in Biological,Food, and Environmental Matrices: A Review

Green extraction techniques (GreETs) emerged in the last decade as greener and sustainable alternatives to classical sample preparation procedures aiming to improve the selectivity and sensitivity of analytical methods, simultaneously reducing the deleterious side effects of classical extraction techniques (CETs) for both the operator and the environment. The implementation of improved processes that overcome the main constraints of classical methods in terms of efficiency and ability to minimize or eliminate the use and generation of harmful substances will promote more efficient use of energy and resources in close association with the principles supporting the concept of green chemistry. The current review aims to update the state of the art of some cutting-edge GreETs developed and implemented in recent years focusing on the improvement of the main analytical features, practical aspects, and relevant applications in the biological, food, and environmental fields. Approaches to improve and accelerate the extraction efficiency and to lower solvent consumption, including sorbent-based techniques, such as solid-phase microextraction (SPME) and fabric-phase sorbent extraction (FPSE), and solvent-based techniques (μQuEChERS; micro quick, easy, cheap, effective, rugged, and safe), ultrasound-assisted extraction (UAE), and microwave-assisted extraction (MAE), in addition to supercritical fluid extraction (SFE) and pressurized solvent extraction (PSE), are highlighted.