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.