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.     

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.     

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.     

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.     

A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature

We treat the time discretization of an initial-value problem for a homogeneous abstract parabolic equation by first using a representation of the solution as an integral along the boundary of a sector in the right half of the complex plane, then transforming this into a real integral on the finite interval , and finally applying a standard quadrature formula to this integral. The method requires the solution of a finite set of elliptic problems with complex coefficients, which are independent and may therefore be done in parallel. The method is combined with spatial discretization by finite elements.

     

Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation

Error estimates are shown for some spatially discrete Galerkin finite element methods for a non-linear heat equation. The approximation schemes studied are based on the introduction of the enthalpy as a new dependent variable, and also on the application of the Kirchhoff transformation and on interpolation of the non-linear coefficients into standard Lagrangian finite element spaces.     

Antibacterial activity of N-quaternary chitosan derivatives: Synthesis, characterization and structure activity relationship (SAR) investigations

Quaternary N-(2-(N,N,N-tri-alkyl ammoniumyl and 2-pyridiniumyl) acetyl) derivatives of chitosan polymer, chitooligomer, and glucosamine (monomer) were synthesized for the purpose of investigating the structure activity relationship (SAR) for the antibacterial effect. Novel methods were used in the synthesis. The final chitosan and chitooligomer derivatives could thus be obtained in two steps without prior protection of the hydroxyl groups. However, in order to obtain chitosan derivatives with the bulky N,N-dimethyl-N-dodecyl- and N,N-dimethyl-N-butyl side chains three steps were needed, starting from 3,6-O-di-tert-butyldimethylsilyl chitosan (3,6-O-di-TBDMS chitosan) as the key intermediate. The quaternary ammoniumyl acetyl derivatives of glucosamine were synthesized from glucosamine or tetra-O-acetylglucosamine. N,N,N-trimethyl chitosan (TMC) was used as reference compound for investigation of antibacterial activity. Clinical Laboratory Standard Institute (CLSI) protocols were used to determine MIC and MLC for activity against clinically important Gram-positive strains Staphylococcus aureus (ATCC 25923), and S. aureus (MRSA) (ATCC 43300), and Gram-negative strains of Escherichia coli (ATCC 25922), P. aeriginosa (ATCC 27853) and Enterococcus facialis (ATCC 29212). The MIC values for the compounds ranged from 8 to ?8192 mg/L. In general the N-(2-(N,N-dimethyl-N-dodecyl ammoniumyl) acetyl) derivatives of chitooligomer and glucosamine monomer were more active against bacteria than derivatives with shorter alkyl chains. In contrast the N-(2-(N,N-dimethyl-N-dodecyl ammoniumyl) acetyl) derivatives of chitosan were less active than derivatives with N-(2-N,N,N-trimetylammoniumyl) acetyl or N-(2-(N-pyridiniumyl) acetyl) quaternary moiety. N,N,N-trimethyl chitosan (TMC) was the most active compound in this study.     

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.