A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.     

A study of random Weyl trees

We study binary search trees constructed from Weyl sequences {nθ}, n≥1, where θ is an irrational and {·} denotes “mod 1.” We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of θ. If H_n is the height of the tree with n nodes when θ is chosen at random and uniformly on [0, 1], then we show that in probability, H_n∼(12/π²)log n log log n. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 271–295, 1998     

Synthesis of 7-(E)-alkenyl-4-amino-3-quinolinecarbonitriles via Pd-mediated Heck, Stille, and Suzuki reactions

A regio- and stereoselective synthesis of 7-(E)-alkenyl-4-amino-3-quinolinecarbonitriles via Pd-mediated coupling reactions was developed. The comparison and optimization of stereoselectivity of the Heck, Stille, and Suzuki reactions of 7-bromo or 7-triflate-3-quinolinecarbonitrile are described. Compound 7 and 10 were potent inhibitors of Src kinase and Raf/Mek activity, respectively.     

Strong CH⋅⋅⋅Halide Hydrogen Bonds from 1,2,3‐Triazoles Quantified Using Pre‐Organized and Shape‐Persistent Triazolophanes

The structures associated with halide (F^?, Cl^?, Br^?) complexation inside CH hydrogen‐bonding macrocyclic receptors, called triazolophanes, are characterized using density functional theory (DFT). The associated binding energies in the gas and solution phases are evaluated. The ruffles in the empty triazolophane become smoothed‐out upon Cl^?‐ and Br^?‐ion binding directly into the middle of the cavity. The largely pre‐organized cavity morphs into an elliptical shape to facilitate shorter hydrogen bonds in the north and south regions and longer ones west and east. The smaller F^? ion sits in, and flattens‐out, only the north (or south) region. The 1,2,3‐triazoles show shorter CH???Cl^? contacts than for the phenylenes. Both Cl^? and Br^? show the same binding geometries but Cl^? has a larger binding energy consistent with its stronger Lewis basicity. Model triads were used to decompose the overall binding energy into those of its components. In the course of this triad analysis, anion polarization was identified and its contribution to the triad???Cl^? binding energy estimated. Consequently, the binding energies for the individual aryl units within the comparatively non‐polarized triazolophanes were estimated. The 1,2,3‐triazoles are twice as strong as the phenylenes thus contributing most of the interaction energy to Cl^?‐ion binding. Therefore, the 1,2,3‐triazoles appear to approach the hydrogen bond strengths of the NH donors of pyrrole units.     

New ceramic microfiltration membranes from mineral coal fly ash

This work aims to develop a new mineral porous tubular membrane based on mineral coal fly ash. Finely ground mineral coal powder was calcinated at 700 °C for about 3 h. The elaboration of the mesoporous layer was performed by the slip casting method using a suspension made of the mixture of fly ash powder, water and PVA. The obtained membrane was submitted to a thermal treatment which consists in drying at room temperature for 24 h then a sintering at 800 °C. SEM photographs indicated that the membrane surface was homogeneous and did not present any macro defects (cracks, etc.). The average pore diameter of the active layer was 0.25 μm and the thickness was around 20 μm. The membrane permeability was 475 l/h m² bar.This membrane was applied to the treatment of the dying effluents generated by the washing baths in the textile industry. The performances in term of permeate flux and efficiency were determined and compared to those obtained using a commercial alumina microfiltration membrane. Almost the same stabilised permeate flux was obtained (about 100 l/h m²). The quality of permeate was almost the same with the two membranes: the COD and color removal was 75% and 90%, respectively.     

Supramolecular self-assembly of dendronized polymers: reversible control of the polymer architectures through acid-base reactions

Acid-base switchable supramolecular dendronized polyacetylenes (DPAs) with increasing steric bulk on going from generation one [G1] to three [G3], were constructed using multiple self-assembly processes between Fréchet-type [G1]-[G3]-dendritic dialkylammonium salts and a dibenzo[24]crown-8-containing polymer. The formation of the supramolecular systems is acid-base switchable to either an ON (rodlike dendronized polymers) or an OFF (flexible polymers) state. Thus, by controlling the superstructures of the supramolecular polymers with the [G1]-[G3] dendrons, it is possible to induce conformational changes within the polymer backbones. The supramolecular dendronized polymers, as well as their threading-dethreading properties, were characterized by (1)H NMR and UV absorption spectroscopies, gel permeation chromatography (GPC) and light scattering (LS). Independent measures of molecular weight (GPC, LS) indicate that DPAs behave as increasingly rigid macromolecules with each generation in solution. Molecular dynamics simulations of each DPA suggest that the lengths of the polymer backbones increase accordingly. Atomic force microscopy of the [G3]-dendronized polystyrene (DPS), as well as the DPAs, reveal surface morphologies indicative of aggregated superstructures.     

Electric field-induced isomerization of azobenzene by STM

The electric field applied between the tip of a scanning tunneling microscope and a metallic surface is shown to induce the reversible trans-cis isomerization of single azobenzene derivatives adsorbed on a Au(111) surface. The investigated molecule is symmetrically equipped with four tert-butyl groups, which decouple the azobenzene core from the metallic surface, facilitating the formation of highly ordered islands. Due to the spatial extension of the electric field, it is possible to switch many molecules within the same island simultaneously.     

Shape persistence delivers lock-and-key chloride binding in triazolophanes

Triazolophanes have recently surfaced as a new class of shape-persistent macrocycles that bind anions. Bearing only triazole- and phenyl-derived CH hydrogen bond donors, these receptors have shown extraordinary Cl(-) binding strengths (>10(6) M(-1), CH(2)Cl(2)). The attributes of the triazolophane that are responsible are presented herein alongside recent literature accounts that have utilized similar strategies in new and exciting supramolecular systems. This review describes how triazolophanes leverage the structural pre-organization characteristic of spherands to take advantage of non-traditional hydrogen bonds originating from extrinsic CH donors.