Optimal Domains for <Emphasis Type="Italic">L</Emphasis><Superscript>0</Superscript>-valued Operators Via Stochastic Measures

We study extension of operators T: E→ L⁰([0, 1]), where E is an F–function space and L⁰([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic measures and the corresponding spaces of integrable functions. Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain).     

Solving the Gleason problem on linearly convex domains

Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions . Received: 2 July 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

Synthesis and optical properties of a poly(p‐phenylenevinylene) derivative and polyfluorenes with bipolar groups along the main chain

A poly(p‐phenylenevinylene) derivative (PPV–TPA)] and a series of statistical copolyfluorenes (PF–TPA)] containing oxadiazole and triphenylamine segments along the main chain were synthesized by the Heck reaction and nickel‐mediated coupling, respectively. The PF–TPA copolyfluorenes with relatively low contents of oxadiazole and triphenylamine units were readily soluble in common organic solvents, whereas the other copolyfluorenes displayed lower solubility. PPV–TPA showed excellent solubility in solvents such as tetrahydrofuran (THF), dichloromethane, chloroform, and toluene. Thin films of the polymers absorbed light in the range of 375–396 nm and had optical band gaps of 2.76–2.98 eV. They emitted blue‐green light with a maximum at 414–522 nm. The fluorescence quantum yields in THF solutions were 0.08–0.53. The copolyfluorene PF–TPA thin films with high contents of oxadiazole and triphenylamine moieties emitted pure blue light that remained stable even after annealing at 150 °C for 4 h in air. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3556–3566, 2006     

Atom transfer radical polymerization directly from poly(vinylidene fluoride): Surface and antifouling properties

The direct preparation of grafting polymer brushes from commercial poly (vinylidene fluoride) (PVDF) films with surface‐initiated atom transfer radical polymerization (ATRP) is demonstrated. The direct initiation of the secondary fluorinated site of PVDF facilitated grafting of the hydrophilic monomers from the PVDF surface. Homopolymer brushes of 2‐(N,N‐dimethylamino)ethyl methacrylate (DMAEMA) and poly (ethylene glycol) monomethacrylate (PEGMA) were prepared by ATRP from the PVDF surface. The chemical composition and surface topography of the graft‐functionalized PVDF surfaces were characterized by X‐ray photoelectron spectroscopy, attenuated total reflectance/Fourier transform infrared spectroscopy, and atomic force microscopy. A kinetic study revealed a linear increase in the graft concentration of poly[2‐(N,N‐dimethylamino)ethyl methacrylate] (PDMAEMA) and poly[poly(ethylene glycol) monomethacrylate] (PPEGMA) with the reaction time, indicating that the chain growth from the surface was consistent with a controlled or living process. The living chain ends were used as macroinitiators for the synthesis of diblock copolymer brushes. The water contact angles on PVDF films were reduced by the surface grafting of DMAEMA and PEGMA. Protein adsorption experiments revealed a substantial antifouling property of PPEGMA‐grafted PVDF films and PDMAEMA‐grafted PVDF films in comparison with the pristine PVDF surface. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3434–3443, 2006     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Sobolev Spaces with only Trivial Isometries

We will give some conditions for Sobolev spaces on bounded Lipschitz domains to admit only trivial isometries.     

Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions

We answer a problem of Liao [S.T. Liao, Standard systems of differential equations and obstruction sets—from linearity to perturbations, in: System Researches, Proceedings Dedicated to the 85th Anniversary of Qian Xue-Sen, Zhejiang Education Press, Hangzhou, China, 1996, pp. 279-290 (in Chinese)]: A C¹ vector field or a C¹ diffeomorphism on an n-dimensional manifold has equal entropy with that of its bundle extensions. We also prove that each ergodic probability with simple Lyapunov spectrum has at most n²n! covering probabilities on each bundle extension.     

Synchronized picosecond pulse generation with a synchronously pumped dye laser and a compressed Nd: YAG laser for non-degenerate transient grating experiments

We have set up a laser system which simultaneously provides synchronized picosecond pulses in the visible and at a wavelength of 1.06 m with a repetition rate of 76 MHz. The set-up consists of a dye laser synchronously pumped by the second harmonic of a cw mode-locked Nd:YAG laser and a fiber-grating compressor for the fundamental wavelength of the Nd;YAG laser. Crosscorrelation measurments reveal the time jitter between the two pulse trains to be less than 10 ps. As a first application we have performed non-degenerate transient grating experiments in semiconductors. The non-degenerate technique allows to use excitation energies well above the bandgap energy and to separate non-linear refractive index effects from photoinduced absorption or transmission changes.     

蛋白质—四氯苯醌荷移反应的分光光度研究

本文用分光光度法研究了蛋白质—四氯苯醌荷移反应。通过对影响反应各因素的研究,确立了以四氯苯醌形成荷移络合物的方法测定蛋白质的最佳条件,测定了最大结合数及反应平衡常数。     

Asymmetric Baeyer—Villiger oxidation: control of stereoelectronic demand

The recent development of asymmetric Baeyer—Villiger oxidation of prochiral and racemic ketones is briefly summarized, focusing on the regio- and stereocontrol of the oxidation attained by regulating the stereoelectronic demand in the step of rearrangement of the Criegee intermediate.Based on the report presented at the International Conference Modern Trends in Organoelement and Polymer Chemistry dedicated to the 50th anniversary of the A. N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences (Moscow, May 30–June 4, 2004).Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1784–1794, September, 2004.