A note on the efficiency of the conjugate gradient method for a class of time‐dependent problems

We discuss the efficiency of the conjugate gradient (CG) method for solving a sequence of linear systems; Auⁿ⁺¹ = uⁿ, where A is assumed to be sparse, symmetric, and positive definite. We show that under certain conditions the Krylov subspace, which is generated when solving the first linear system Au¹ = u⁰, contains the solutions {uⁿ} for subsequent time steps. The solutions of these equations can therefore be computed by a straightforward projection of the right‐hand side onto the already computed Krylov subspace. Our theoretical considerations are illustrated by numerical experiments that compare this method with the order‐optimal scheme obtained by applying the multigrid method as a preconditioner for the CG‐method at each time step. Copyright © 2007 John Wiley & Sons, Ltd.     

Determining PCB desorption behaviour on sediments with SFE and investigating the dependency of selective fractions on sediment characteristics

A method for studying PCB desorption behaviour from sediments using supercritical fluid extraction (SFE) and pressurized liquid extraction (PLE) is presented. Four sediments were investigated and extracted with supercritical carbon dioxide employing increasingly harsher extraction conditions ranging from 40°C and 12?MPa to 100°C and 36.5?MPa. To ensure quantitative extractions, the remaining SFE residues were also extracted with PLE. Resulting profiles identified at least three different PCB fractions within the four sediments. Furthermore, a distinct fraction was obtained with extraction for 2?h at 40°C and 36.5?MPa. This fraction has previously been found to correlate well with bioavailable fractions. The dependency of this fraction on sediment total organic carbon (TOC) was investigated, both for sediments examined in this study as well as for previously reported values using the same extraction conditions. It was found that TOC does not correlate to selective SFE, which indicates that the use of TOC to predict bioavailability is questionable.     

Dynamics and energetics of the self-assembly of a hydrophobically modified polyelectrolyte: Naphthalene-labeled poly(acrylic acid)

Steady-state and time-resolved fluorescence studies were performed on aqueous solutions of poly(acrylic acid) hydrophobically modified with two very different levels of naphthalene (Np). It is demonstrated that unique information on association phenomena involving hydrophobe-modifed polymers can be obtained from an extended fluorescence study by using data for a less-modified polymer as a reference. For the more highly modified polymer, the presence of excited-state (as well as ground-state) dimers in addition to monomer emission due to locally excited naphthalene gives evidence for hydrophobic association between naphthalene groups. This association becomes, as expected, much less important at higher pH due to the electrostatic repulsion between different chain segments. However, it is noted that even at high pH there is a significant self-association. The coexistence of static and dynamic quenching phenomena of the Np monomer label was also revealed in the time-resolved fluorescence data. The data are compatible with the existence of two types of monomers and one excimer and suggest that the essential contribution to the monomer emission comes from isolated chromophores, whereas excimer formation arises from both a dynamic route (excited Np chromophores able to produce a dynamic excimer) and a static route (excitation of ground-state Np dimers). At room temperature, the dissociative reaction, excimer-to-monomer, can be neglected, and thus the rate constant for excimer formation and decay could be obtained with and without considering the influence of preformed dimers. Temperature has shown to induce different behavior in the polymer photophysics. In the case of the less-labeled polymer, the decays were found to be single-exponential with the fluorescence lifetime decreasing with increasing temperature. From the temperature dependence of the steady-state fluorescence data, the activation energy for excimer formation and the binding energy of the excimer were evaluated at different pH values, through the Stevens-Ban-type plots of the excimer-to-monomer intensity ratio. With the time-resolved data, measured in the temperature range of 5-60 degrees C, it was possible to extract the intrinsic activation energies for excimer formation. The thermodynamic driving force for the intrapolymeric association was found to be dependent on a balance between hydrophobic and electrostatic interactions, which are dependent on the pH, temperature, and hydrophobic content of the polymer.     

Intratumor heterogeneity in perfusion in human melanoma xenografts measured by contrast-enhanced magnetic resonance imaging

The perfusion in tumors shows substantial spatial heterogeneity compared to that in normal tissues. The aim of the present study was to evaluate the intratumor heterogeneity in perfusion in tumors of two amelanotic human melanoma xenograft lines, A-07 and R-18, grown intradermally in Balb/c nu/nu mice. A non-invasive contrast-enhanced magnetic resonance imaging method yielding results in absolute values was applied. The perfusion was determined in manually defined regions of interest, corresponding to a whole tumor or to subregions of a tumor. The mean perfusion and the intertumor heterogeneity in perfusion were similar for the two tumor lines. For whole A-07 tumors, the perfusion ranged from 0.089 mL/(g . min) to 0.20 mL/(g . min) [mean: 0.15 mL/(g . min)], and for whole R-18 tumors, from 0.030 mL/(g . min) to 0.17 mL/(g . min) [mean: 0.13 mL/(g . min)]. The intratumor heterogeneity, on the other hand, was estimated to be 6.4 times larger in A-07 tumors than in R-18 tumors. The highest perfusion values, up to 0.69 mL/(g . min), were found in subregions of A-07 tumors. The intratumor heterogeneity was substantially larger than the intertumor heterogeneity in A-07 tumors, whereas in R-18 tumors, the intratumor heterogeneity was similar to the intertumor heterogeneity. These observations imply that measurements of mean tumor perfusion may have limited value as a predictive assay for outcome of treatment.     

The Blow-up Rate of Solutions to Boundary Blow-up Problems for the Complex Monge–Ampère Operator

A regularity result for solutions to boundary blow-up problems for the complex Monge–Ampère operator in balls in is proved. For certain boundary blow-up problems on bounded, strongly pseudoconvex domains in with smooth boundary an estimate of the blow-up rate of solutions are given in terms of the distance to the boundary and the product of the eigenvalues of the Levi form.     

Explicit limits for nonperiodic homogenization and reduction of dimensionLimites explicites pour l'homogénéisation non-périodique et la réduction de dimension

The aim of this Note is to give explicit limit expressions, for diffusion equations involving a small parameter ε, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials. To cite this article: B. Gustafsson, J. Mossino, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 977–982.     

Mechanistic investigation of the 2,5-diphenylpyrrolidine-catalyzed enantioselective alpha-chlorination of aldehydes

The mechanism for the 2,5-diphenylpyrrolidine-catalyzed enantioselective alpha-chlorination of aldehydes with electrophilic halogenation reagents has been investigated by using experimental and computational methods. These studies have led us to propose a mechanism for the reaction that proceeds through an initial N-chlorination of the chiral catalyst-substrate complex, followed by a 1,3-sigmatropic shift of the chlorine atom to the enamine carbon atom. The suggested reaction course is different from previously proposed mechanisms for organocatalytic enamine reactions, in which the carbon-electrophile bond is formed directly. Furthermore, the rate-determining step in the overall reaction was determined and the presence of nonlinear effects was probed.     

Electrophoretic properties of complexes between DNA and the cationic surfactant cetyltrimethylammonium bromide

We use agarose gel electrophoresis to characterize how the monovalent catioinic surfactant cetyltrimethylammonium bromide (CTAB) compacts double-stranded DNA, which is detected as a reduction in electrophoretic DNA velocity. The velocity reaches a plateau at a ratio R = 1.8 of CTAB to DNA-phosphate charges, i.e., above the neutralization point, and the complexes retain a net negative charge at least up to R = 200. Condensation experiments on a mixture of two DNA sizes show that the complexes formed contain only one condensed DNA molecule each. These CTAB-DNA globules were further characterized by time-resolved measurements of their velocity inside the gel, which showed that CTAB does not dissociate during the migration but possibly upon entry into the gel. Using the Ogston-model for electrophoresis of spherical particles, the measured in-gel velocity of the globule is quantitatively consistent with CTAB having two opposite effects, reduction of both the electrophoretic charge and DNA coil size. In the case of CTAB the two effects nearly cancel, which can explain why opposite velocity shifts (globule faster than uncomplexed DNA) have been observed with some catioinic condensation agents. Dissociation of the complexes by addition of anionic surfactants was also studied. The DNA release from the globule was complete at a mixing ratio between anionic and cationic surfactants equal to 1, in agreement with equilibrium studies. Circular DNA retained its supercoiling, and this demonstrates a lack of DNA nicking in the compaction-release cycle which is important in DNA transfection and purification applications.     

Synthesis of Glycosylated Amino Acids for Use in Solid Phase Glycopeptide Synthesis,Part 2: N-(9-Fluorenylmethyloxycarbonyl)-3-0-[2,4,6-TRI-0-Acetyl-3-0-(2,3,4-TRI-0-Acetyl-α-D-Xylopyranosyl)-β-D-Glucopyranosyl]-L-Serine

Abstract

FMOC-serine phenacylester was glycosylated with a derivative of the disaccharide α-D-Xylp-(1→3)-β-D-Glcp, and the product was treated with zinc to remove the phenacyl group. The title derivative is useful for synthesis of blood clotting factor IX glycopeptide fragments by the solid-phase approach.