End unit effect on the Tg of differentiated series of perfluoro-poly (oxymethylene-co-oxyethylene) oligomers

Twelve series of linear oligomers of four different degrees of polymerization (x_n = 8.77−41.55), having a common perfluorinated random copolymeric chain as molecular body and two equal foreign end units of one of the types listed in Table 1, have been synthesized by derivatization of base samples of one of them having a diolic---CH₂OH functionality. The glass transition temperature T_g of all the series was measured and thus examined as a function of x_n. A clear end unit effect is observed, dominantly determined in every series by chemical nature and structure of the end units, quantitatively expressed at any x_n by different positive or negative T_g deviations from the common asymptotic T_g∞ value. The results are also discussed in terms of copolymer end effect and of relation between T_g and end copolymeric composition.     

Hopf algebra actions

Finite groups acting on rings by automorphisms, and group-graded rings are instances of Hopf algebras H acting on H-module algebras A. We study such actions. Let A^H = {a ε A¦h · A = (h) a, all h ε H}, the ring of H-invariants, and form the smash product A # H. We study the ring extensions A^H A A # H. We prove a Maschke-type theorem for A # H-modules. We form an associated Morita context [A^H, A, A, A # H] and use these to get connections between the various rings.     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

Quasiperiodic motions in superquadratic time-periodic potentials

It is shown that for a large class of potentials on the line with superquadratic growth at infinity and with the additional time-periodic dependence all possible motions under the influence of such potentials are bounded for all time and that most (in a precise sense) motions are in fact quasiperiodic. The class of potentials includes, as very particular examples, the exponential, polynomial and much more. This extends earlier results and gives an answer to a problem posed by Littlewood in the mid 1960's. Along the way machinery is developed for estimating the action-angle transformation directly in terms of the potential and also some apparently new identities involving singular integrals are derived.     

Application of preparative high-speed counter-current chromatography for the separation of flavonoids from the leaves of Byrsonima crassa Niedenzu (IK)

The methanolic extract of the leaves of the medicinal plant Byrsonima crassa (Malpighiaceae) contain flavonoids with antioxidant activity. They were separated in a preparative scale using high-speed counter-current chromatography. The optimum solvent system used was composed of a mixture of ethyl acetate-n-propanol-water (140:8:80 (v/v/v)) and led to a successful separation between monoglucosilated flavonoids (quercetin-3-O-alpha-L-arabinoside, quercetin-3-O-beta-D-galactoside) and the biflavonoid amentoflavone in only 3.5 h. The purities of quercetin-3-O-alpha-L-arabinoside (95 mg), quercetin-3-O-beta-D-galactoside (16 mg) and the biflavonoid amentoflavone (114 mg) were all isolated at purity over 95%. Identification was performed by 1H NMR, 13C NMR and UV analyses.