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 classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S-2. The model possesses exact soliton solutions with nontrivial Hopf topological charges and an infinite number of local conserved currents. We show that the Poisson bracket algebra of the corresponding charges is isomorphic to that of the area-preserving diffeomorphisms of the sphere S-2. We also show that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group of diffeomorphisms. We indicate possible generalizations of the model.

Salt-induced sphere-to-disk transition of octadecyltrimethylammonium bromide micelles

We have used surface tension measurements, differential scanning calorimetry (DSC), dynamic light scattering (DLS), and cryo-transmission electron microscopy (cryo-TEM) to investigate the dynamic and structural behavior of octadecyltrimethylammonium bromide (C(18)TAB) micelles in water and NaBr solution. The surface tension data for fixed C(18)TAB concentrations of 25 mM and varied NaBr additions (0-50 mM) shows that the critical micelle concentration (cmc) increases after an initial decrease at 0.5 mM NaBr. This unusual effect has been explained using results from DSC and DLS. At low salt concentrations (below ca. 25 mM) the relaxation time distribution is bimodal with a dominant fast mode due to spherical micelles. Above ca. 35 mM NaBr disklike structures are favored and the relaxation time distribution is more closely unimodal. The postulated sphere-to-disk transition is supported by cryo-TEM micrographs. A pronounced increase in the micellar effective hydrodynamic radius (R-H) is observed as the NaBr concentration is increased above about 35 mM; below 35 mM the R-H of the spherical micelles changes Little with ionic strength.

Morphology and topography analysis of mesoporous titania templated by micrometric latex sphere arrays

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

Sphere of influence and gravitational capture radius: a dynamical approach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Composition of the first coordination sphere of Ni2+ in concentrated aqueous NiBr2 solutions by x-ray diffraction

Two concentrated solutions of NiBr2 have been examined by x-ray diffraction. The Fourier transformed scattering data indicate inner complex formation between Ni2 + and Br- ions. Average numbers of bonded bromide ions per nickel atom have been determined for each solution and the reliability of the complexation numbers as well as of the other structural parameters has been critically examined. © 1985 American Institute of Physics.

Bifundamental fuzzy 2-Sphere and fuzzy killing spinors

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.

Shvo's catalyst in chemoenzymatic dynamic kinetic resolution of amines-inner or outer sphere mechanism?

Evidence is provided for the inner-sphere mechanism with actual metal coordination of the racemic amine in the crucial hydrogen transfer step promoted by Shvo's catalyst of the chemoenzymatic dynamic kinetic resolution (DKR) of amines. Key intermediates involved in this H-transfer step were intercepted and continuously monitored by electrospray ionization mass spectrometry (ESI-MS) and characterized by their dissociation chemistries via ESI-MS/MS. © 2013 The Royal Society of Chemistry.

The production of statistical data and information in the Caribbean: proposals for increasing efficiency in this sphere

Includes bibliography

COINCIDENCES OF FIBREWISE MAPS BETWEEN SPHERE BUNDLES OVER THE CIRCLE

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

Contesting Sphere Boundaries Online: Private/Technical/Public Discourses in Polycystic Ovarian Syndrome Discussion Groups

The internet is fast becoming a means for people to obtain information, creating a unique forum for the intersection of the public, technical, and private spheres. To ground my research theoretically, I used Jürgen Habermas’s sphere theory. Habermas (1987) explains that the technical sphere colonizes the private sphere, which decreases democratic potential. In particular, the internet is a place for altering technical colonization of the private and public spheres. My research focuses on women’s health because it is a particularly useful case study for examining sphere tensions. Historically, the biomedical health establishment has been a powerful agent of colonization, resulting in detrimental effects for women and their health. The purpose of this study is to examine how the internet encourages expert and female patient deliberation, which empowers women to challenge the experts and, thus, make conversations between the private/technical spheres more democratic. I used PCOS (Polycystic Ovarian Syndrome) as a case to observe the changing sphere boundaries by studying the discourse that took place on multiple patient and doctor websites over a four-year period. Through my research, I found that the PCOS women challenge the biomedical model by appropriating medical language. By understanding the medical talk, the women are able to feel confident when discussing their health conditions with the doctor and with each other. The PCOS women also become lay-experts who have personal and medical experience with PCOS, reducing private sphere colonization. This case study exemplifies how female empowerment can influence expert culture, challenging our conventional understanding of democracy.

Morphology and topography analysis of mesoporous titania templated by micrometric latex sphere arrays

In this work, mesoporous titania is prepared by templating latex sphere arrays with four different sphere diameters at the micrometric scale (phi > 1 mu m). The mesoporous titania homogeneously covers the latex spheres and substrate, forming a thin coating characterized by N-2 adsorption isotherm, small angle X-rays scattering, atomic force, field emission and transmission electronic microscopies. Mesoporous titania has been templated into different shapes such as hollow particles and monoliths according to the amount of sol used to fill the voids of the close packed latex spheres. Titania topography strongly depends on the adsorption of polymeric segments over latex spheres surface, which could be decreased by changing the dimensions of latex spheres (phi = 9.5 mu m) generating a lamellar architecture. Thus, micrometric latex sphere arrays can be used to achieve new surface patterns for mesoporous materials via a fast and inexpensive chemical route for construction of functional devices in different technological fields such as energy conversion, inclusion chemistry and biomaterials. (C) 2011 Elsevier Inc. All rights reserved.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.