Diblock copolymers based on allyl methacrylate: Synthesis,characterization, and chemical modification

Different diblock copolymers constituted by one segment of a monomer supporting a reactive functional group, like allyl methacrylate (AMA), were synthesized by atom transfer radical polymerization (ATRP). Bromo‐terminated polymers, like polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(butyl acrylate) (PBA) were employed as macroinitiators to form the other blocks. Copolymerizations were carried out using copper chloride with N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) as the catalyst system in benzonitrile solution at 70 °C. At the early stage, the ATRP copolymerizations yielded well‐defined linear block copolymers. However, with the polymerization progress a change in the macromolecular architecture takes place due to the secondary reactions caused by the allylic groups, passing to a branched and/or star‐shaped structure until finally yielding gel at monomer conversion around 40% or higher. The block copolymers were characterized by means of size exclusion chromatography (SEC), ¹H NMR spectroscopy, and differential scanning calorimetry (DSC). In addition, one of these copolymers, specifically P(BA‐b‐AMA), was satisfactorily modified through osmylation reaction to obtain the subsequent amphiphilic diblock copolymer of P(BA‐b‐DHPMA), where DHPMA is 2,3‐dihydroxypropyl methacrylate; demonstrating the feasibility of side‐chain modification of the functional obtained copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3538–3549, 2007     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

Optical properties of in situ doped and undoped titania nanocatalysts and doped titania sol-gel nanofilms

In this paper we present spectroscopic properties of doped and undoped titanium dioxide (TiO₂) as nanofilms prepared by the sol-gel process with rhodamine 6G doping and studied by photoacoustic absorption, excitation and emission spectroscopy. The absorption spectra of TiO₂ thin films doped with rhodamine 6G at very low concentration during their preparation show two absorption bands, one at 2.3 eV attributed to molecular dimmer formation, which is responsible for the fluorescence quenching of the sample and the other at 3.0 eV attributed to TiO₂ absorption, which subsequently yields a strong emission band at 600 nm. The electronic band structure and optical properties of the rutile phase of TiO₂ are calculated employing a fully relativistic, full-potential, linearized, augmented plane-wave (FPLAPW) method within the local density approximation (LDA). Comparison of this calculation with experimental data for TiO₂ films prepared for undoped sol-gels and by sputtering is performed.     

Infima and complements in the lattice of quasi-uniformities

We show that the infimum of any family of proximally symmetric quasi-uniformities is proximally symmetric, while the supremum of two proximally symmetric quasi-uniformities need not be proximally symmetric. On the other hand, the supremum of any family of transitive quasi-uniformities is transitive, while there are transitive quasi-uniformities whose infimum with their conjugate quasi-uniformity is not transitive. Moreover we present two examples that show that neither the supremum topology nor the infimum topology of two transitive topologies need be transitive. Finally, we prove that several operations one can perform on and between quasi-uniformities preserve the property of having a complement.     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Stable products of spheres in the non-linear coupling of oscillators or quasi-periodic motions

For generic families of vector fields or transformations, normally hyperbolic invariant products of spheres appear near partially elliptic rest points. To cite this article: M. Kammerer-Colin de Verdière, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.