A simple ionic triphenylene receptor for catecholamines, serotonin and D-glucosamine in buffered water

The combination of hydrophobic effects and ionic pairing within a triphenylene-based receptor were exploited for the binding of biological phenylethylamines, serotonin and D-glucosamine in phosphate buffered water.     

The two spin states of an end-on copper(II)-superoxide mimic

The reaction of nitrosobenzene with copper(I) complexes of a tetradentate ligand led to two novel species that are best described as copper(II) complexes of an O-bonded nitrosobenzyl radical anion, in either the singlet or the triplet spin-state. Both states were characterized by crystal structures, magnetic measurements and DFT calculations.     

Euclidean algorithms are Gaussian

We obtain a central limit theorem for a general class of additive parameters (costs, observables) associated to three standard Euclidean algorithms, with optimal speed of convergence. We also provide very precise asymptotic estimates and error terms for the mean and variance of such parameters. For costs that are lattice (including the number of steps), we go further and establish a local limit theorem, with optimal speed of convergence. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various other techniques: Dirichlet series, Perron's formula, quasi-powers theorems, and the saddle-point method. Such dynamical analyses had previously been used to perform the average-case analysis of algorithms. For the present (dynamical) analysis in distribution, we require estimates on transfer operators when a parameter varies along vertical lines in the complex plane. To prove them, we adapt techniques introduced recently by Dolgopyat in the context of continuous-time dynamics (Ann. Math. 147 (1998) 357).     

Nitroxide‐mediated homo‐ and block copolymerization of styrene and multifunctional acryl‐ and methacryl derivatives

The ability of different alkoxyamines ( I1 , I2 , I3 , I4 , and I5 ) to initiate controlled radical polymerization of styrene was evaluated. Among them, 2‐hydroxymethyl‐2‐[(2‐methyl‐1‐phenyl‐propyl)‐(1‐phenyl‐ethoxy)‐amino]‐propane‐1,3‐diol ( I5 ) gave the highest polymerization rate of styrene, and the best control over the molecular weight and the molecular weight distribution of polystyrene. Kinetic studies confirmed that with initiator I5 the polymerization of styrene proceeded in a controlled way. The controlled radical homopolymerization of multifunctional acryl‐ and methacryl derivatives using initiator I5 could not be realized as demonstrated by the high polydispersities (PD) obtained. However, it was possible to polymerize multifunctional acryl‐ and methacryl derivatives using a polystyrene macroinitiator ( Pst ) and, thus, novel amphiphilic block copolymers with a narrow molecular weight distribution were obtained. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1873–1882, 2005     

Synthesis and spectroscopic properties of monocyclic and bicyclic erbium phtalocyanines

Bimacrocyclic and monomacrocyclic erbium phtalocyanines have been synthesized and their luminescence spectra and lifetimes have been studied. The bi-planar structure of ErPc₂ complexes, although interesting at first sight, is non-luminescent because of a strong absorption band near 1.5 μm. However, the luminescence of the erbium ion can be recovered after oxidation or reduction of the macrocycle. Monomacrocyclic erbium phtalocyanines exhibit a strong luminescence of erbium as a result of the energy transfer between the excited phtalocyanine macrocycle and the erbium ion. With a perchlorinated phtalocyanine and a perdeuterated axial ligand in a deuterated solvent, the luminescence lifetime reaches 5 μs, which is the maximum lifetime found for conventional perdeutarated ligands. The large absorption cross-section of phtalocyanine in the red may counterbalance the fast luminescence lifetime, allowing the hope for a new all-organic integrated optical amplifier device.     

Uniquely solvable quadratic boolean equations

Quadratic boolean equations with a unique solution are characterized. A linear-time algorithm is proposed to recognize them.     

General order Newton-Padé approximants for multivariate functions

Summary Padé approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off(x ₁, ...,x _p ). Therefore multivariate Newton-Padé approximants are introduced; their computation will only use the value off at some points. In Sect. 1 we shall repeat the univariate Newton-Padé approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Padé approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that forp=1 the classical Newton-Padé approximants for a univariate function are obtained.