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.

Static and dynamic bimolecular fluorescence quenching of porphyrin dendrimers in solution

The fluorescence quenching kinetics of two porphyrin dendrimer series (GnTPPH(2) and GnPZn) by different type of quenchers is reported. The microenvironment surrounding the core in GnPZn was probing by core-quencher interactions using benzimidazole. The dependence of quencher binding constant (K(a) ) on generation indicates the presence of a weak interaction between branches and the core of the porphyrin dendrimer. The similar free volume in dendrimers of third and fourth generation suggests that structural collapse in high generations occurs by packing of the dendrimer peripheral layer. Dynamic fluorescence quenching of the porphyrin core by 1,3-dicyanomethylene-2-methyl-2-pentyl-indan (PDCMI) in GnTPPH(2) is a distance dependent electron transfer process with an exponential attenuation factor beta=0.33 angstrom(-1). The quenching by 1,2-dibromobenzene occurs by diffusion process of the quencher toward to the porphyrin core, and its rate constant is practically independent of dendrimer generation.

Hexagonal mesoporous silica modified with 2-mercaptothiazoline for removing mercury from water solution

A method for the attachment of 2-mercaptothiazoline (MTZ) to modified silica gel has been developed. In the first step, a new silylant agent was synthesized, named SiMTZ, by the reaction between MTZ molecule and chloropropyltrimethoxysilane (SiCl). SiMTZ and tetraethylortosilicate were co-condensed in the presence of n-dodecylamine, a neutral surfactant template, to produce a modified ordered hexagonal mesoporous silica named HMTZ. The modified material contained 0.89 +/- 0.03 mmol of 2-mercaptothiazoline per gram of silica. FT-IR, FT-Raman, Si-29- and C-13-NMR spectra were in agreement with the proposed structure of the modified mesoporous silica in the solid state. HMTZ material has been used for divalent mercury adsorption from aqueous solution at 298 I K. The series of adsorption isotherms were adjusted to a modified Langmuir equation. The maximum number of moles of mercury adsorbed gave 2.34 +/- 0.09 mmol/g of material. The same interaction was followed by calorimetric titration on an isoperibol calorimeter. The HMTZ presented a high capacity for the removal of the contaminant mercury from water. The Delta H and Delta G values for the interaction were determined to be -56.34 +/- 1.07 and -2.14 +/- 0.11 kJ mol(-1). This interaction process was accompanied by a decrease of entropy value (- 182 J mol(-1) K-1). Thus, the interaction between mercury and HMTZ resulted in a spontaneous thermodynamic system with a high favorable exothermic enthalpic effect. (c) 2007 Elsevier B.V. All rights reserved.

A General Solution of the Fokker-Planck Equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

On the energy transported by exact plane gravitational-wave solutions

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

Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential

In this work we consider the effect of a spatially dependent mass over the solution of the Klein-Gordon equation in 1 + 1 dimensions, particularly the case of inversely linear scalar potential, which usually presents problems of divergence of the ground-state wave function at the origin, and possible nonexistence of the even-parity wave functions. Here we study this problem, showing that for a certain dependence of the mass with respect to the coordinate, this problem disappears. (c) 2006 Elsevier B.V. All rights reserved.

Correlation of reactivity with structural factors in a series of Fe(II) substituted cobalt ferrites

A series of powdered cobalt ferrites, CoxFe3-xO4 with 0.66 <= x< 1.00 containing different amounts of Fe-II, were synthesized by a mild procedure, and their Fe and Co site occupancies and structural characteristics were explored using X-ray anomalous scattering and the Rietveld refinement method. The dissolution kinetics, measured in 0.1 M oxalic acid aqueous solution at 70 degrees C, indicate in all cases the operation of a contracting volume rate law. The specific rates increased with the Fell content following approximately a second-order polynomial expression. This result suggests that the transfer of Fe-III controls the dissolution rate, and that the leaching of a first layer of ions Co-II and Fe-II leaves exposed a surface enriched in slower dissolving octahedral Fe-III ions. Within this model, inner vicinal lattice Fe-II accelerates the rate of Fe-III transfer via internal electron hopping. A chain mechanism, involving successive electron transfers, fits the data very well. (C) 2006 Elsevier B.V. All rights reserved.

Electrical characterization of lead zirconate titanate prepared by organic solution route

Two series of lead zirconate titanate (PZT) ceramics with composition Zr/Ti approximate to 53/47 have been prepared by the organic solution route. The effects on the electrical properties of calcination temperature in one series and of sintering time period in the other were examined. Dielectric constant, electrical conductivity and impedance spectroscopy results differed from one series to the other, probably due to differences in structure of the precursor powders, as seen by X-ray diffraction. Tetragonal and rhombohedral phases predominate in the powders used, respectively, in the calcined and sintered series. Physical and electrical behavior of ceramics prepared from predominantly rhombohedral powder suggests the evaporation of PbO. The presence of two semi-circles in impedance plots leads to the association of the low frequency semi-circle to the presence of PbO, which, apparently, was not eliminated from ceramics prepared from predominantly tetragonal powder. (C) 2001 Elsevier B.V. Ltd and Techna S.r.l. All rights reserved.

Aqueous solution behavior of thermosensitive (N-isopropylacrylamide-acrylic acid-ethyl methacrylate) terpolymers

A series of N-isopropylacrylamide (NIPAM)-acrylic acid-ethyl methacrylate terpolymers with varied monomer compositions was prepared by radical polymerization. The solution behavior of these polymers was studied in dilute aqueous solution using spectrophotometry, fluorescence spectroscopy and high-sensitivity differential scanning calorimetry. The results obtained revealed that the lower critical solution temperatures depend strongly on the copolymer composition, solution pH and ionic strength. At a high pH, the ionization of acrylic acid (AA) units leads to an increase in solution cloud points (T-c). Solutions of polymers containing 10% or less of AA display a constant T-c for pH above 5.5, with 15% there is a continuous increase in T-c with pH and, for higher AA contents, no clouding was observed within the studied temperature range. Fluorescence probe studies were conducted by following the I (1)/I (3) ratio of pyrene vibronic bands and the emission of anilinonaphtalene sulfonic acid, sodium salt (ANS), both approaches revealing the existence of hydrophobic domains for polymers with higher ethyl methacrylate content at temperatures lower than T-c, suggesting some extent of aggregation and/or a coil-to-globule transition. Scanning calorimetry measurements showed an endothermic transition at temperatures agreeing with the previously detected cloud points. Moreover, the transition curves became broader and with a smaller transition enthalpy, as both the AA content and the solution pH were increased. These broader transitions were interpreted to be the result of a wider molecular distribution upon polymer ionization, hence, displaying varied solution properties. The decrease in transition enthalpy was rationalized as a consequence of reminiscent hydration of NIPAM units, even after phase separation, owing to the presence of electric charges along the polymer chain.

ITERATIVE NUMERICAL-SOLUTION OF SCATTERING PROBLEMS

An iterative Neumann series method, employing a real auxiliary scattering integral equation, is used to calculate scattering lengths and phase shifts for the atomic Yukawa and exponential potentials. For these potentials the original Neumann series diverges. The present iterative method yields results that are far better, in convergence, stability and precision, than other momentum space methods. Accurate result is obtained in both cases with an estimated error of about 1 in 10(10) after some 8-10 iterations.

Bayesian L-optimal exact design of experiments for biological kinetic models

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

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

In vitro susceptibility of oral Candida albicans strains to different pH levels and calcium hydroxide saturated aqueous solution

Candida albicans is present in the oral cavity and in the whole digestive tract of humans and other animals, being frequently related to endodontic treatment failure. The present study determined the incidence of C. albicans in the oral cavity and the susceptibility of isolates to different pH values and saturated calcium hydroxide aqueous solution at pH 12.5. Sixty-five patients attending the Endodontic Clinic at the Sagrado Coração University participated in the study. The collected samples were cultivated in selective media for C. albicans and the isolates were tested in terms of resistance to both alkaline pH and saturated aqueous solution of calcium hydroxide. In relation to time variables, yeast viability was assessed by the Sabouraud's agar culture and fluorescein diacetate and ethidium bromide fluorescent staining method. Results from the different pHs and experimental times, including those from different techniques measuring fungal viability, were compared using the chi-square and Fisher's exact tests (α=0.05). The yeasts became completely inviable after 48 h of contact with the calcium hydroxide solution. On the other hand, when exposed to the alkaline culture broth, the yeasts were found to be viable at pHs 9.5 and 10.5 for up to 7 days. In conclusion, C. albicans can only be completely inhibited by direct contact with saturated calcium hydroxide aqueous solution after 48 h of exposure.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.