The structure of strongly stationary systems

Motivated by a problem in ergodic Ramsey theory, Furstenberg and Katznelson introduced the notion of strong stationarity, showing that certain recurrence properties hold for arbitrary measure preserving systems if they are valid for strongly stationary ones. We construct some new examples and prove a structure theorem for strongly stationary systems. The building blocks are Bernoulli systems and rotations on nilmanifolds.     

On the nature of the BOLD fMRI contrast mechanism

Since its development about 15 years ago, functional magnetic resonance imaging (fMRI) has become the leading research tool for mapping brain activity. The technique works by detecting the levels of oxygen in the blood, point by point, throughout the brain. In other words, it relies on a surrogate signal, resulting from changes in oxygenation, blood volume and flow, and does not directly measure neural activity. Although a relationship between changes in brain activity and blood flow has long been speculated, indirectly examined and suggested and surely anticipated and expected, the neural basis of the fMRI signal was only recently demonstrated directly in experiments using combined imaging and intracortical recordings. In the present paper, we discuss the results obtained from such combined experiments. We also discuss our current knowledge of the extracellularly measured signals of the neural processes that they represent and of the structural and functional neurovascular coupling, which links such processes with the hemodynamic changes that offer the surrogate signal that we use to map brain activity. We conclude by considering applications of invasive MRI, including injections of paramagnetic tracers for the study of connectivity in the living animal and simultaneous imaging and electrical microstimulation.     

Observation of discrete solitons in optically induced real time waveguide arrays

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered (pi out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.     

Anion recognition by functionalized single wall carbon nanotubes

Amidoferrocenyl-functionalised single wall carbon nanotubes (Fc-SWNT) are efficient exoreceptors for the redox recognition of H2PO4-.     

Behavior of the solution of a random semilinear heat equation

We consider a semilinear heat equation in one space dimension, with a random source at the origin. We study the solution, which describes the equilibrium of this system, and prove that, as the space variable tends to infinity, the solution becomes a.s. asymptotic to a steady state. We also study the fluctuations of the solution around the steady state.     

Synthesis and optical properties of green‐light‐emitting copolymers containing side‐chain oxadiazole units

Atom transfer radical polymerization was used to prepare well‐defined vinyl polyoxadiazole homomacromonomers with a properly modified α‐dicarboxylic acid methyl ester as the initiator. Macromonomers of various molecular weights with narrow polydispersities in some cases were obtained, as proved by gel permeation chromatography (GPC). The structures of the obtained macromonomers were then identified with ¹H NMR spectroscopy. These macromonomers were subsequently copolymerized with a dihydroxy anthracene based monomer by a polycondensation technique, and this resulted in polymacromonomers. Coil–rod–coil copolymers containing side‐chain anthracene and oxadiazole units were also synthesized by atom transfer radical polymerization. The resulting copolymers combined an anthracene derivative as the rigid block with a random copolymer of the desired anthracene‐ and/or oxadiazole‐based monomers as the flexible block. These copolymers were primarily characterized with GPC and ¹H NMR techniques. Additionally, the optical properties of all these copolymers were investigated in detail, and they suggested energy transfer from the oxadiazole to the anthracene chromophores, which became much more efficient in the solid state. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1049–1061, 2005     

Linear pentablock quintopolymers (l‐SIDMV) with five incompatible blocks: Polystyrene,polyisoprene‐1,4, poly(dimethylsiloxane), poly(tert‐butyl methacrylate), and poly(2‐vinylpyridine)

Three linear pentablock quintopolymers (l‐SIDMV), where S is polystyrene (PS), I polyisoprene‐1,4 (PI), D poly(dimethylsiloxane) (PDMS), M poly(tert‐butyl methacrylate) (PtBuM), and V poly(2‐vinylpyridine) (P2VP), were synthesized by anionic polymerization high vacuum techniques. The approach involves the following: (a) The synthesis of living triblock terpolymer PS‐b‐PI‐b‐PDMSLi and diblock copolymer P2VP‐b‐PtBuMK by sequential polymerizations of the corresponding monomers with sec‐BuLi and benzyl potassium, respectively; and (b) The selective linking of the living triblock terpolymer with the chlorosilane group of 2‐(chloromethylphenyl)ethyldimethylchlorosilane (CMPDMS), followed by linking of the living block copolymer with the remaining chloromethyl group of CMPDMS. Molecular characterization carried out by size exclusion chromatography, membrane osmometry, solution (in CDCl₃ or d₈‐toluene) and solid‐state ¹H‐NMR spectroscopy indicated a high degree of molecular and compositional homogeneity. Differential scanning calorimetry results on the precursors and final polymers were discussed. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3938–3946, 2008     

Polymerization of higher α‐olefins using a Cs‐symmetry hafnium metallocene catalyst. Kinetics of the polymerization and microstructural analysis

The C_s‐symmetry hafnium metallocene [(p‐Et₃Si)C₆H₄]₂C(2,7‐di‐tert‐BuFlu)(C₅H₄)Hf(CH₃)₂ and tetrakis(pentafluorophenyl) borate dimethylanilinium salt ([B(C₆F₅)₄]^?[Me₂NHPh]⁺) were used as the catalytic system for the polymerization of higher α‐olefins (from hexene‐1 to hexadecene‐1) in toluene at 0 °C. The evolution of the polymerization was studied regarding the variation of the molecular weight, molecular weight distribution and yield with time. The effect of the monomer structure on the polymerization kinetics was established. The role of trioctylaluminum in accelerating the polymerization was investigated. ¹³C NMR spectroscopy was used to study the microstructure of the poly(α‐olefins) by the determination of the pentad monomer sequences. The thermal properties of the polymers were obtained by differential scanning calorimetry, DSC. The results were discussed in connection with the polymer microstructure. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4314–4325, 2009     

Electrochemical Impedance Spectroscopy and Cyclic Voltammetry of <Emphasis Type="Italic">cis</Emphasis>-[Cr(bipy)<Subscript>2</Subscript>(SCN)<Subscript>2</Subscript>]I (where bipy: 2,2′-Bipyridine) in Polar Solvents

Cyclic voltammetric studies (CV) on the complex cis-bis(2,2′-bipyridine)bis(thiocyanate)chromium(III) iodide [Cr(bipy)₂(SCN)₂]I (where bipy: 2,2′-bipyridine, C₁₀H₈N₂) were recorded on platinum (Pt) and glassy carbon (GC) electrodes in either acetonitrile (ACN) or acetone (ACE) solvent media including n-tetrabutylammonium hexafluorophosphate (NBu₄PF₆) as supporting electrolyte, at scan rates (v) ranging from 0.05 to 0.12 V⋅s⁻¹. In addition, electrochemical impedance spectroscopic (EIS) measurements in the frequency (f) range from 0.1 Hz to 50 kHz were carried out on GC and Pt electrodes. The half-wave potential (E _1/2) of the redox couple Cr(III)/Cr(II) was determined as −0.84 V and −0.79 V (versus Ag/AgCl) in ACN and ACE, respectively. The heterogeneous electron transfer rate constant (k _s) corresponding to the couple Cr(III)/Cr(II) was found to be greater on GC compared to the Pt electrode. The nature of the solvent medium also affects the kinetics of the investigated couple, to be exact, k _s increases remarkably upon replacement of ACE by ACN. The EIS results indicate that the GC electrode is a better capacitor and provides the smaller charge transfer resistance in ACN.