R-matrix methods for studying nuclear effects in μCF

Properties ofR-matrix theory that are useful for studying muon-catalyzed fusion reactions are reviewed, and applications to the dt system are discussed, using both improved adiabatic and non-adiabatic (variational) wave functions. We give complex eigenvalues and - sticking fractions for the (L, v)=(0,0) and (0, 1) states of dt using variational Hamiltonian matrix elements that have been properly symmetrized by means of the Block operator. Expressions for the fusion rate and - sticking fraction are developed from a time-dependent theory that uses the complex-energy states corresponding to the poles of the systemS-matrix. These are shown to reduce with the appropriate approximations to the expressions and values commonly used. Additional nuclear effects on these quantities can easily be studied within the framework developed, but they are not expected to be large.     

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^–