Anionic graft polymerization of methyl methacrylate on starch and dextrin

The anionic graft polymerization of methyl methacrylate on the potassium alkoxide derivative of starch or dextrin in DMSO was studied. The effects of monomer and alkoxide concentrations as well as temperature were investigated. The yield of graft polymer increased with increasing alkoxide concentration. With increasing monomer concentration and with increasing temperature the extent of homopolymer formation increased. The composition of the graft polymers was found to depend on the reaction conditions. Graft polymers having about 10–40% poly(methyl methacrylate) were obtained. There were quantitative differences in yield of isolated graft polymer between starch and dextrin and these were ascribed to differences in the solubility properties of the carbohydrates. Evidence on the structure of the graft polymers and on the mechanism of the graft polymerization was obtained from acid hydrolysis of the graft polymers and determination of the molecular weights of the cleaved side chains.     

Dirichlet Series and Curious infinite Products

By number-theoretical methods we give a result generalizingthose of J. O. Shallit, one particular case of which reads asfollows: ...=2^–;, where a(n) is equal to 1 if the sum of the digits of n in basetwo is even, and – 1 if this sum is odd. Moreover we provea conjecture of Shallit concerning a way of approximating 2^–