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.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS)

Time-dependent fluctuations in surface-enhanced Raman scattering (SERS) intensities were recorded from a roughened silver electrode immersed in diluted solutions of rhodamine 6G (R6G) and congo red (CR). These fluctuations were attributed to a small number of SERS-active molecules probing regions of extremely high electromagnetic field (hot spots) at the nanostructured surface. The time-dependent distribution of SERS intensities followed a tailed statistics at certain applied potentials, which has been linked to single-molecule dynamics. The shape of the distribution was reversibly tuned by the applied voltage. Mixtures of both dyes, R6G and CR, at low concentrations were also investigated. Since R6G is a cationic dye and CR is an anionic dye, the statistics of the SERS intensity distribution of either dye in a mixture were independently controlled by adjusting the applied potential. The potential-controlled distribution of SERS intensities was interpreted by considering the modulation of the surface coverage of the adsorbed dye by the interfacial electric field. This interpretation was supported by a two-dimensional Monte Carlo simulation that took into account the time evolution of the surface configuration of the adsorbed species and their probability to populate a hypothetical hot spot. The potential-controlled SERS dynamics reported here is a first step toward the spectroelectrochemical investigation of redox processes at the single-molecule level by SERS.

Mass transport effects in the borohydride oxidation reaction-Influence of the residence time on the reaction onset and faradaic efficiency

The borohydride oxidation reaction (BOR) was studied on Pt and Au electrodes by cyclic voltammetry in dilute alkaline borohydride solutions (0.1 M NaOH + 10(-3) mol L(-1) NaBH(4)). More specifically, the electrodes were considered as either Vulcan XC72-supported Pt or Au (noted as Pt/C and Au/C, respectively) active layers or smooth Pt or Au surfaces, the latter possibly being covered by a layer of (non-metalized) Vulcan XC72 carbon powder. The BOR onset potential and the number of electrons (n(e-)) exchanged per BH(4)(-) anion (faradaic efficiency) were investigated for these electrodes, to determine whether the residence time of reaction intermediates (at the electrode surface or inside the porous layer) does influence the overall reaction pathway/completion. For the carbon-supported platinum, n(e-) strongly depends on the thickness of the active layer. While thin (ca. 0.5 mu m-thick) Pt/C active layers yield n(e-) < 4, thick layers (approximately 3 mu m) yield n(e-)approximate to 8, which can be ascribed to the sufficient residence time of the molecules formed within the active layer (H(2), by heterogeneous hydrolysis, or BOR intermediates) enabling further (near-complete) oxidation. This puts into evidence that not only the nature of the electrocatalyst is important to reach high BOR efficiency, but also the structure/thickness of the active layer. The same trend applies for Au/C active layers and for smooth Pt or Au surfaces covered with a layer of (inactive) Vulcan XC72. In addition, the BOR onset usually shifts negative when the reaction intermediates are trapped, which suggests that some of the intermediates are more easily oxidized than BH(4)(-) itself; based on literature data, BH(3)OH(-) species is a likely candidate. (C) 2011 Elsevier B.V. All rights reserved.

Evaluation of Postpolymerization as a Function of the Storage Time of Triethylene Glycol Dimethacrylate/2,2-Bis[4-(2-Hydroxy-3-Methacryloxy-Prop-1-Oxy)-Phenyl]-propane Bisphenyl-alpha-Glycidyl Ether Dimethacrylate Copolymers Used in Dental Resins by Differential Scanning Calorimetry and Dynamic Mechanical Analysis

The aim of this work was to evaluate the effect of the storage time on the thermal properties of triethylene glycol dimethacrylate/2,2-bis[4-(2-hydroxy-3-methacryloxy-prop-1-oxy)-phenyl]propane bisphenyl-alpha-glycidyl ether dimethacrylate (TB) copolymers used in formulations of dental resins after photopolymerization. The TB copolymers were prepared by photopolymerization with an Ultrablue IS light-emitting diode, stored in the dark for 160 days at 37 degrees C, and characterized with differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and Fourier transform infrared spectroscopy with attenuated total reflection. DSC curves indicated the presence of an exothermic peak, confirming that the reaction was not completed during the photopolymerization process. This exothermic peak became smaller as a function of the storage time and was shifted at higher temperatures. In DMA studies, a plot of the loss tangent versus the temperature initially showed the presence of two well-defined peaks. The presence of both peaks confirmed the presence of residual monomers that were not converted during the photopolymerization process. (C) 2009 Wiley Periodicals, Inc. J Appl Polym Sci 112: 679-684, 2009

Nanogravimetric study of the complex voltammetric response in the electro-oxidation of methanol on platinum

Instead of a time-invariant voltammetric profile, many electrochemical systems display a cycle-dependent current-potential response. This phenomenon has been referred to as complex voltammetric response and it has been observed during the electro-oxidation of several molecules such as methanol, ethanol, propanol and hydrogen. There are currently two explanations for the surface mechanism underlying this behavior. In one scenario, the complex voltammogram would result from the specific kinetic pathway taken during the forward sweep. In the other explanation, the phenomenon is discussed in terms of the interplay among the surface roughening and subsequent relaxation, and the ohmic drop coupled to a negative differential resistance. We report in this paper a nanogravimetric investigation of the complex voltammetric response in the electro-oxidation of methanol on platinum electrode in both acidic and alkaline media. Different periodic patterns composed of intercalated small and large hysteresis cycles were observed as a function of the applied voltage and the series resistance between the working electrode and the potentiostat. Independently, nanogravimetric results indicated no detectable difference in the delta-frequency versus voltage profile between small and large hysteresis cycles. These findings were interpreted as experimental evidence of the secondary, if any, role played by the very electrochemical reaction on the emergence of complex voltammetric response. (C) 2009 Elsevier Ltd. All rights reserved.

Computational study of the step size parameter of the subgradient optimization method

The subgradient optimization method is a simple and flexible linear programming iterative algorithm. It is much simpler than Newton's method and can be applied to a wider variety of problems. It also converges when the objective function is non-differentiable. Since an efficient algorithm will not only produce a good solution but also take less computing time, we always prefer a simpler algorithm with high quality. In this study a series of step size parameters in the subgradient equation is studied. The performance is compared for a general piecewise function and a specific p-median problem. We examine how the quality of solution changes by setting five forms of step size parameter.

Investigation of the drying process of linseed oil using FTIR and ToF-SIMS

The drying process of linseed oil, oxidized at 80 oC, has been investigated with rheology measurements, Fourier transformation infrared spectroscopy (FTIR), and time of flight secondary ion mass spectrometry (ToF-SIMS). The drying process can be divided into three main steps: initiation, propagation and termination. ToF-SIMS spectra show that the oxidation is initiated at the linolenic (three double bonds) and linoleic fatty acids (two double bonds). ToF-SIMS spectra reveal peaks that can be assigned to ketones, alcohols and hydroperoxides. In this article it is shown that FTIR in combination with ToF-SIMS are well suited tools for investigations of various fatty acid components and reaction products of linseed oil.

The time consistency of the Friedman rule

We consider the problem of time consistency of the Ramsey monetary and fiscal policies in an economy without capital. Following Lucas and Stokey (1983) we allow the government at date t to leave its successor at t + 1 a profile of real and nominal debt of all maturities, as a way to influence its decisions. We show that the Ramsey policies are time consistent if and only if the Friedman rule is the optimal Ramsey policy.

The Predation of Artemia Nauplii by the Larvae of the Amazon River Prawn, Macrobrachium amazonicum (Heller, 1862), is Affected by Prey Density, Time of Day, and Ontogenetic Development

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of the season of year, stage of lactation and milking time on the chloride content in bovine milk

From January to October 1995, chloride content determinations were accomplished in 2,218 samples of milk collected from 67 quarters of 17 lactating cows, in initial, middle and final stages of lactation, in the morning and afternoon milking. The highest means of chloride contents were observed among the milk samples collected in the final stage of lactation (0,203 gC1/100ml), in the summer (0,212 gC1/100ml) and in the morning milking (0,189 g C1/100ml). The differences observed between the chloride contents in the samples obtained in the different stages of lactation and the seasons of the year were statistically significant (P<0.0001). The gratest occornce of chloride at rates superior to 0.22 gC1100ml was observed in the final stge of lactation (31.4%), summer (44.2%) and after the morning milking (27.8%). These results evidentiate the influence of physiological and external factors (stage of lactation and season of the year) on the concentration of chloride of milk.

Analysis of the Influence of Sparkout Time on Grinding Using Several Lubrication/Cooling Methods

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)