Maximal Regularity for Perturbed Integral Equations on the Line

We characterize the existence and uniqueness of solutions for a perturbed linear integral equation with infinite delay in H?lder spaces. The method is based on the theory of operator-valued Fourier multipliers.     

On the Propagation of Regularity and Decay of Solutions to the k-Generalized Korteweg-de Vries Equation

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u ₀ ∈ H ^3/4+ (?) whose restriction belongs to H ^l ((b, ∞)) for some l ∈ ?⁺ and b ∈ ? we prove that the restriction of the corresponding solution u(·, t) belongs to H ^l ((β, ∞)) for any β ∈ ? and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves.     

Zeolites with Continuously Tuneable Porosity

Zeolites are important materials whose utility in industry depends on the nature of their porous structure. Control over microporosity is therefore a vitally important target. Unfortunately, traditional methods for controlling porosity, in particular the use of organic structure‐directing agents, are relatively coarse and provide almost no opportunity to tune the porosity as required. Here we show how zeolites with a continuously tuneable surface area and micropore volume over a wide range can be prepared. This means that a particular surface area or micropore volume can be precisely tuned. The range of porosity we can target covers the whole range of useful zeolite porosity: from small pores consisting of 8‐rings all the way to extra‐large pores consisting of 14‐rings.     

The kinetics laws for polymer collapse and biopolymer folding

We discuss some recent ideas relating to the folding and other conformational transitions of polymers. In particular we emphasize that it is possible to conceive the accompanying kinetic processes as a problem in non-equilibrium statistical mechanics. In this sense it should be possible to develop such methods to deduce the kinetic laws in the vicinity of various conformational transitions. To establish the ideas we first study the well known problem of the collapse transition of a homopolymer. We then turn to conformational transitions in periodic and random copolymers. We offer a brief survey of the status of these ideas in applications to biopolymeric conformational kinetics.     

Two Equivalent Reduction of Copper(I) Complexes; Evidence of an Anionic Copper Species

Reactive copper solutions have been prepared by a cold temperature, two equivalent lithium naphthalenide reduction of copper(I) complexes. One equivalent of organic halides react with one equivalent of the anionic copper to yield organocopper reagents.     

Improved Synthesis of Methyl 4,6-O-Benzylidene-3-cyano-2,3-dideoxy-α-D-erythro-hex-2-enopyranoside and Methyl 4,6-O-Benzylidene-2,3-dideoxy-3-C-formyl-α-D-erythro-hex-2-enopyranoside

Simple and efficient route to the title compounds by using diethyl aluminium cyanide in benzene for the epoxide ring opening and the electrophilic assistance of LiCIO₄ during the isomerization-elimination process.     

Projective resolutions up to bounded torsion and bounds for the orders of the finite subgroups

We prove that group (co)homology can be computed up to bounded torsion using certain generalized projective resolutions. We investigate the notion of dimension obtained using this kind of resolutions and its relationship with the existence of torsion in both ordinary and complete cohomology groups.     

Effects of alkyl chain lengths of gallates upon their distribution and reactivity towards diphenylpicryl hydracil radicals in Triton X‐100 micellar solutions

The reactivity of ethyl‐, propyl‐ and octylgallate towards diphenylpicryl hydracil radicals has been measured in homogeneous solution (ethanol) and in Triton X‐100 micellar solutions. Similar reactivities were measured in homogeneous solutions, indicating that the length of the alkyl chain does not influence the reactivity of the phenolic groups. On the other hand, different reactivities were measured in micellar solutions, particularly at low (5 mM) surfactant concentrations. Data obtained at different surfactant concentrations allow estimation of partitioning of the gallates and their intramicellar bimolecular rate constant. The values obtained indicate that all the observed differences in reactivity are attributable to differences in substrate partitioning between the micellar and aqueous pseudophases. In fact, similar values of the intramicellar rate constants were obtained, suggesting that the average location of the reactive groups inside the micelles is independent of the solute alkyl chain length. Copyright © 2009 John Wiley & Sons, Ltd.