Random Classical Fidelity

We introduce a random perturbed version of the classical fidelity and we show that it converges with the same rate of decay of correlations, but not uniformly in the noise. This makes the classical fidelity unstable in the zero-noise limit.     

Surface and interfacial properties of PVDF/acrylic copolymer blends before and after UV exposure

Morphological and chemical properties of both the surface and interface of poly(vinylidene fluoride)/poly(methyl methacrylate)-co-poly(ethyl acrylate) (PVDF/PMMA-co-PEA) blend films have been investigated before and after the samples were exposed to ultraviolet (UV) irradiation using a xenon arc lamp at 50 °C and 9% relative humidity (RH) for 7 months. Surface and interfacial morphologies were studied by atomic force microscopy (AFM). Chemical composition information was obtained by confocal Raman microscopy, attenuated total reflection-FTIR spectroscopy (ATR-FTIR), X-ray photoelectron spectroscopy (XPS), and contact angle measurements. Results show an enrichment of the PVDF material at the air surface, while the acrylic copolymer enriches the interface. Blends having greater than 50% mass fraction of PVDF show little change in the surface morphology after UV exposure for 7 months. However, for a lower PVDF content, blends exhibit significant degradation of PMMA-co-PEA copolymer and a much rougher surface after UV exposure. Microstructural changes in the PVDF spherulites are also observed after UV degradation. It is found that the surface and interfacial morphologies are correlated with the chemical properties.     

Convenient preparation of 5-ethynyl-octaethylporphyrin free base and zinc complex

A method leading to the preparation of the free base or zinc meso-ethynyl functionalized octaethylporphyrin has been developed, which will open the access to various meso-ethynyl metalloporphyrins.     

A new, fast and efficient synthesis of 3-aryl indenones: intramolecular cyclization of 1,3-diarylpropynones in superacids

1,3-Diarylpropynones were cleanly converted to the corresponding 3-arylindenones in various superacidic media. This new, simple, one-pot reaction proved to be efficient (yields up to 95%) and very fast (reaction time less than 30 min).     

Latex particles bearing hydrophilic grafted hairs with controlled chain length and functionality synthesized by reversible addition–fragmentation chain transfer

A method is described for synthesizing latex particles with anchored hairs by the grafting of hydrophilic chains, synthesized by reversible addition–fragmentation chain transfer, onto functionalized latex particles. These have the potential to bind biologically active species. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1188–1195, 2003     

Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data

Lin and Zhang (J. Roy. Statist. Soc. Ser. B 61 (1999) 381) proposed the generalized additive mixed model (GAMM) as a framework for analysis of correlated data, where normally distributed random effects are used to account for correlation in the data, and proposed to use double penalized quasi-likelihood (DPQL) to estimate the nonparametric functions in the model and marginal likelihood to estimate the smoothing parameters and variance components simultaneously. However, the normal distributional assumption for the random effects may not be realistic in many applications, and it is unclear how violation of this assumption affects ensuing inferences for GAMMs. For a particular class of GAMMs, we propose a conditional estimation procedure built on a conditional likelihood for the response given a sufficient statistic for the random effect, treating the random effect as a nuisance parameter, which thus should be robust to its distribution. In extensive simulation studies, we assess performance of this estimator under a range of conditions and use it as a basis for comparison to DPQL to evaluate the impact of violation of the normality assumption. The procedure is illustrated with application to data from the Multicenter AIDS Cohort Study (MACS).     

Markovian Solutions of Inviscid Burgers Equation

For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller–Markov property (with respect to the space variable) at some time is conserved at later times, and an evolution equation is derived for the infinitesimal generator. Previously known explicit solutions such as Frachebourg–Martin's (white noise initial velocity) and Carraro–Duchon's Lévy process intrinsic-statistical solutions (including Brownian initial velocity) are recovered as special cases.     

Conversations on mind, matter, and mathematics

Conclusion  The debate between Jean-Pierre Changeux and Alain Connes is one of the most, interesting to take place in recent years. It re-frames in a very up-to-date context a whole series of traditional and difficult questions from the standpoint of the knowledge and experience of two of the leading protagonists of contemporary science. To the choice presented by the neurobiologist between a Platonist ontology and a neurocognitive psychology of mathematical activity, the mathematician replies with a conception that is objective (neither ontological nor psychological) of the thoroughly consistent universe of mathematical idealities. It is indeed in this three-sided arena that the major difficulties play themselves out. One of the great virtues of the book is to cast a spotlight on this confrontation.     

On the global structure of crystalline surfaces

We bound the number of plane segments in a crystalline minimal surface S in terms of its Euler characteristic, the number of line segments in its boundary, and a factor determined by the Wulff shapeW of its surface energy function. A major technique in the proofs is to quantize the Gauss map ofS based on the Gauss map ofW. One thereby bounds the number of positive-curvature corners and the interior complexity ofS. The support of the National Science Foundation and the Air Force Office of Scientific Research and the hospitality of Stanford University, where this paper was extensively rewritten, are gratefully acknowledged.