A “Multiplicative Coboundary” theorem for some sequences of random matrices

Schmidt(¹⁰) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products.     

Ferrocene studies. IV. Some furan containing derivatives of ferrocene

The condensation of ferrocenecarboxyhydrazide, ferrocenecarboxaldehyde and acetylferrocene with a number of furan derivatives is reported. The reaction of chalcones containing both the furan and the ferrocene nucleus with Phenylhydrazine and hydrazine proceeds to yield pyrazolines.     

Design of Supramolecular Cyclodextrin Complex Sensors for Ion and Molecule Recognition in Water

The design and function of novel supramolecular fluoroionophore/cyclodextrin (CyD) complex sensors for ion and molecule recognition in water are reviewed. For the crown ether fluoroionophore/-CyD complex, the dimerization of the fluoroionophore inside the -CyD is found to be selectively promoted by alkali metal ion binding, thereby resulting in metal-ion-selective pyrene dimer emission in water. This supramolecular function is successfully utilized in the design of a podand fluoroionophore/-CyD complex for sensing toxic lead ion in water. The boronic acid fluoroionophore/-CyD complex binds sugars and produces increased fluorescence emission in water. The response mechanism appears to be due to the suppression of the photoinduced electron transfer (PET) from pyrene donor to trigonal phenylboronic acid acceptor. This is a novel emission function provided by the boronic acid fluoroionophore/-CyD complex sensors in water.     

Synthesis and properties of monodisperse oligofluorene-functionalized truxenes: highly fluorescent star-shaped architectures

This paper describes the strategy toward novel monodisperse, well-defined, star-shaped oligofluorenes with a central truxene core and from monofluorene to quaterfluorene arms. Introduction of solubilizing n-hexyl groups at both fluorene and truxene moieties results in highly soluble, intrinsically two-dimensional nanosized macromolecules T1-T4. The radius for the largest oligomer of ca. 3.9 nm represents one of the largest known star-shaped conjugated systems. Cyclic voltammetry experiments reveal reversible or quasi-reversible oxidation and reduction processes (Eox = +0.74 to 0.80 V, Ered = -2.66 to 2.80 eV vs Fc/Fc+), demonstrating excellent electrochemical stability toward both p- and n-doping, while the band gaps of the oligomers are quite high (EgCV = 3.20-3.40 eV). Close band gaps of 3.05-3.29 eV have been estimated from the electron absorption spectra. These star-shaped macromolecules demonstrate good thermal stability (up to 400-420 degrees C) and improved glass transition temperatures with an increase in length of the oligofluorene arms (from Tg = 63 degrees C for T1 to 116 degrees C for T4) and show very efficient blue photoluminescence (lambdaPL = 398-422 nm) in both solution (PhiPL = 70-86%) and solid state (PhiPL = 43-60%). Spectroelectrochemical experiments reveal that compounds T1-T4 are stable electrochromic systems which change their color reversibly from colorless in the neutral state (approximately 340-400 nm) to colored (from red to purple color; approximately 500-600 nm) in the oxidized state.