A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

We consider the discretization in time of an inhomogeneous parabolicequation in a Banach space setting, using a representation ofthe solution as an integral along a smooth curve in the complexleft half-plane which, after transformation to a finite interval,is then evaluated to high accuracy by a quadrature rule. Thisreduces the problem to a finite set of elliptic equations withcomplex coefficients, which may be solved in parallel. The paperis a further development of earlier work by the authors, wherewe treated the homogeneous equation in a Hilbert space framework.Special attention is given here to the treatment of the forcingterm. The method is combined with finite-element discretizationin spatial variables.     

Equisingular Deformations of Sandwiched Singularities

We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough.     

Antibacterial activity of methylated chitosan and chitooligomer derivatives: Synthesis and structure activity relationships

The purpose of this study was to synthesize series of methylated chitosaccharide derivatives, possessing various degree of methylation, and to determine their structure activity relationship (SAR) with regard to their antibacterial effect against Staphylococcus aureus. Chitosan polymer and chitooligomers were used as starting materials and were methylated by reaction with methyl iodide. Depending on the reaction conditions the degree of N-quaternization ranged from 0% to 74%, with varying degree of N,N-dimethylation, N-monomethylation and O-methylation. More selective N-quaternization could be obtained with protection group strategy. At pH 5.5 the chitosaccharide polymers and their methylated derivatives were active against S. aureus with minimal inhibitory concentration (MIC) ranging from 16 to 512 μg/mL. At pH 7.2 the non-quaternized derivatives were inactive but their highly N-quaternized derivatives showed MIC as low as 8 μg/mL. The chitooligomers, as well as their derivatives, were inactive at both pH’s. The SAR studies revealed that N-quaternization was mainly responsible for the antibacterial effects at pH 7.2, whereas it did not contribute to the antibacterial activity under acidic conditions.     

Metabolism of Carotenoids in Salmonids. Part 3. Metabolites of astaxanthin and canthaxanthin in the skin of atlantic salmon (salmo salar,L.)

Diets supplemented with astaxanthin and canthaxanthin, respectively, and a control diet without carotenoid additions, were fed to 1½-year-old Atlantic salmon (Salmo salar, L.) for one year. The integuments were investigated as to their quantitative and qualitative carotenoid composition. Astaxanthin and canthaxanthin deposited in the skin amounted to 20 and 14% of the total carotenoids only. Seventy % must be considered as metabolites of astaxanthin and canthaxanthin and 10% as basic xanthophylls also present in the control groups. Astaxanthin apparently underwent the following metabolic pathway: astaxanthin→idoxanthin→adonixanthin→zeaxanthin→zeaxanthin 5,6-epoxides. Reduction of the 4′-carbonyl group was stereospecific leading to the (4′R)-idoxanthin. Canthaxanthin was obviously converted to β,β-carotene via 4′-hydroxyechinenone, echinenone, and 4-hydroxy-β,β-carotene.     

Reduction of chromium in ethylene polymerisation using bis(imido)chromium(VI) catalyst precursors

Hybrid density functional calculations on [Cr(NR)2C3H7(C2H4)]+ (R = H, tBu) have revealed a facile reductive elimination reaction involving beta-hydrogen transfer from the alkyl chain, suggesting that the active species in ethylene polymerisation with bis(imido)chromium(VI) precursors contains a reduced chromium atom.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

Cyclic Ketones in Spiroannulation

Conversion of a cyclic carbonyl carbon into a quaternary carbon has been effected by a Wittig–Horner reaction with diethyl (N-benzyliden)aminomethylphosphonate and a subsequent alkylation with a protected vinyl ketone. The product was a substrate for spiroannulation after initial hydrolysis. The reaction sequence was carried out as a one-pot reaction.     

Synthesis and characterization of new selective Zn fluorescent probes for functionalization: in vitro Cell imaging applications

Herein the synthesis and characterization of new, lipophilic highly Zn²⁺-selective fluorescent probes are reported. High affinity for zinc (K_d 1.1–8.0 nM) over other biologically relevant metals and mixtures of metals was observed. Excitation at 360 nm afforded an emission spectrum with maximum at 530 nm for the zinc bound complex. The linear relationship between fluorescence intensity and zinc concentration indicates that FZnA-probes can be used for quantification. The probes have been synthesized in 28–45% overall yield and the feasibility for further functionalization with biologically relevant side chains has been demonstrated. In vitro studies using PC12 cells and 10 μM of one of the novel probes (FZnA-Ada) visualized endogenous labile Zn²⁺ after 45 min incubation time.     

Total Synthesis of the Anti‐inflammatory and Pro‐resolving Lipid Mediator MaR1n−3 DPA Utilizing an sp3–sp3 Negishi Cross‐Coupling Reaction

The first total synthesis of the lipid mediator MaR1_{n?3 DPA} ( 5 ) has been achieved in 12 % overall yield over 11 steps. The stereoselective preparation of 5 was based on a Pd‐catalyzed sp³–sp³ Negishi cross‐coupling reaction and a stereocontrolled Evans–Nagao acetate aldol reaction. LC‐MS/MS results with synthetic material matched the biologically produced 5 . This novel lipid mediator displayed potent pro‐resolving properties stimulating macrophage efferocytosis of apoptotic neutrophils.     

Notes on Euler’swork on divergent factorial series and their associated continued fractions

Factorial series which diverge everywhere were first considered by Euler from the point of view of summing divergent series. He discovered a way to sum such series and was led to certain integrals and continued fractions. His method of summation was essentialy what we call Borel summation now. In this paper, we discuss these aspects of Euler’s work from the modern perspective.