HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

Determination of catechins in green tea infusions by reduced flow micellar electrokinetic chromatography

A sulfated-beta-cyclodextrin (s-beta-CD) modified reduced flow micellar electrokinetic chromatography (RF-MEKC) method was developed and validated for the determination of catechins in green tea. The optimal electrolyte consisted of 0.2% triethylamine, 50 mmol/L SDS and 0.8% s-beta-CD (pH = 2.9), allowing baseline separation of five catechins in 4 min. The samples and standards were injected at 0.6 psi for 5 s under constant voltage of -30 kV. Sample preparation simply involved extraction of 2 g of tea with 200 mL water at 95 C under constant stirring for 5 min. The method demonstrated excellent performance, with limits of detection (LOD) and quantification (LOQ) of 0.02-0.1 and 0.1-0.5 mu g/mL, respectively, and recovery percentages of 94-101%. The method was applied to six samples of Brazilian green tea infusions. Epigallocatechin gallate (23.4-112.4 mu g/mL) was the major component, followed by epigallocatechin (18.4-78.9 mu g/mL), epicatechin gallate (5.6-29.6 mu g/mL), epicatechin (4.6-14.5 mu g/mL) and catechin (3.2-8.2 mu g/mL). (C) 2011 Elsevier Ltd. All rights reserved.

The effect of hydrophobic and hydrophilic fumed silica on the rheology of magnetorheological suspensions

We investigate magnetorheological fluids (MRFs) prepared with carbonyl iron powder and different types of hydrophobic and hydrophilic fumed silica. The rheological properties of the MRF suspensions were investigated with and without an applied magnetic field. The MRF samples prepared with hydrophobic silicas presented a more pronounced thixotropic effect and a higher recovery rate than those prepared with hydrophilic silicas. The application of a magnetic field to all the MRFs samples investigated leads to an increase in the viscosity and the thixotropic effect. MRF prepared with hydrophobic silicas presented smaller values of the viscosity than those prepared with hydrophilic silicas. At low applied magnetic fields, the type of the silica used to prepare the MRF leads to noticeable differences in the shear stress. However, these differences disappear at high magnetic fields. The results obtained showed that MRF samples prepared with the hydrophobic silica with the biggest particle diameter presented better characteristics for magnetorheological fluids, with higher values of yield stress, recovery rate, and elastic modulus. (C) 2009 The Society of Rheology. [DOI: 10.1122/1.3086870]

A selective conductive polymer-based sensor for volatile halogenated organic compounds (VHOC)

A novel poly(p-xylylene), PPX, derivative bearing alkoxyphenyl side groups was electrochemically synthesized in 87% yield. The polymer, poly(4`-hexyloxy-2,5-biphenyleneethylene) (PHBPE), presented a fraction (92%) soluble in common organic solvents. It showed to be thermally resistant up to 185 degrees C. UV-vis analysis revealed an E-gap of 3.5 eV Gas sensors made from thin films of 10-camphorsulfonic acid-doped PHBPE deposited on interdigitated electrodes exhibited significant changes in electrical conductance upon exposure to five VHOCs: 1,2-dichloroethane, bromochloromethane, trichloromethane, dichloromethane and tetrachloromethane. The conductance decreased after exposure to tetrachloromethane and increased after exposure to all the other VHOCs. Three-dimensional plots of relative response versus time of half response versus time of half recovery showed good discrimination between the five VHOCs tested. (c) 2008 Elsevier B.V. All rights reserved.