7‐(2‐Oxoalkoxy)coumarins: Synthesis and Anti‐Inflammatory Activity of a Series of Substituted Coumarins

A series of 7‐(2‐oxoalkoxy)coumarins have been synthesized by conjugating substituted 7‐hydroxycoumarins with different chloroketones. The anti‐inflammatory properties of 7‐(2‐oxoalkoxy)coumarins were studied in LPS‐induced inflammatory response in J774 macrophages. Western blot was used to determine the expression of iNOS and COX‐2, NO was determined by measuring its metabolite nitrite by Griess reaction and IL‐6 was measured by ELISA. Seventeen of the studied compounds inhibited NO and IL‐6 production over 50% at 100 μM concentrations. IC₅₀ values of the best inhibitors were 21 μM/24 μM (NO/IL‐6) for compound 12 and 30 μM/10 μM (NO/IL‐6) for compound 20 . The main result was that the substitution with 7‐(2‐oxoalkoxy) group improved the anti‐inflammatory properties of most of the investigated 7‐hydroxycoumarins.     

Noncovalent complexation of glucosylthioureidocalix[4]arenes with carboxylates and their gas-phase characteristics: an ESI-FTICR mass spectrometric study

The noncovalent complexation of three glucosylcalix[4]arenes (1-3) towards 23 mono- and dicarboxylic acid anions were studied by ESI-FTICR mass spectrometry. Competitive complexation, collision-induced dissociation and gas-phase H/D-exchange experiments were performed to obtain information on selectivity of calixarenes towards carboxylates and characteristics of their complexes. The flexibility and number of glucose units of the host and the spatial disposition of the hydrogen bonding groups on the carboxylate guests were found to affect the selectivity of complexation strongly. The glucosylcalixarenes exhibited particular selectivity for dicarboxylic acid anions incorporating π-systems, and clear isomeric selectivity was observed for isophthalic among phthalic acid anions and for fumaric acid over maleic acid anion.     

Zero distribution of solutions of complex linear differential equations determines growth of coefficients

It is shown that the exponent of convergence λ(f) of any solution f of with entire coefficients A₀(z), …, A_k?2(z), satisfies λ(f) ? λ ∈ [1, ∞) if and only if the coefficients A₀(z), …, A_k?2(z) are polynomials such that for j = 0, …, k ? 2. In the unit disc analogue of this result certain intersections of weighted Bergman spaces take the role of polynomials. The key idea in the proofs is W. J. Kim’s 1969 representation of coefficients in terms of ratios of linearly independent solutions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On Interpolating Blaschke Products and?Blaschke-Oscillatory Equations

This research is partially a continuation of a 2007 paper by the author. Growth estimates for generalized logarithmic derivatives of Blaschke products are provided under the assumption that the zero sequences are either uniformly separated or exponential. Such Blaschke products are known as interpolating Blaschke products. The growth estimates are then proven to be sharp in a rather strong sense. The sharpness discussion yields a solution to an open problem posed by E. Fricain and J. Mashreghi in 2008. Finally, several aspects are pointed out to illustrate that interpolating Blaschke products appear naturally in studying the oscillation of solutions of a differential equation f″+A(z)f=0, where A(z) is analytic in the unit disc. In particular, a unit disc analogue of a 1988 result due to S. Bank on prescribed zero sequences for entire solutions is obtained, and a more careful analysis of a 1955 example due to B. Schwarz on the case A(z)=\frac1+4g²(1-z²)²A(z)=\frac{1+4\gamma^{2}}{(1-z^{2})^{2}} reveals that an infinite zero sequence is always a union of two exponential sequences.     

Non-Markovian thermalisation of a two-level atom

We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima-Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.     

A fast direct solver for elliptic problems with a divergence constraint

A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Toward the enantioselective total synthesis of lyngbyatoxin A: on the stereocontrolled introduction of the quaternary stereogenic centre

This paper deals with an approach to the enantioselective total synthesis of Lyngbyatoxin A, with focus on the stereocontrolled introduction of the quaternary stereogenic centre. The key step in the synthesis involves an enantiospecific Lewis-acid mediated rearrangement of chiral vinyl epoxides carrying a 7-substituted indole moiety.     

Nanoporous Network Channels from Self‐Assembled Triblock Copolymer Supramolecules

Supramolecular complexes of a poly(tert‐butoxystyrene)‐block‐polystyrene‐block‐poly(4‐vinylpyridine) triblock copolymers and less than stoichiometric amounts of pentadecylphenol (PDP) are shown to self‐assemble into a core–shell gyroid morphology with the core channels formed by the hydrogen‐bonded P4VP(PDP)complexes. After structure formation, PDP was removed using a simple washing procedure, resulting in well‐ordered nanoporous films that were used as templates for nickel plating.