Rankamaite from the Urubu pegmatite, Itinga, Minas Gerais, Brazil: Crystal chemistry and Rietveld refinement

A new occurrence of rankamaite is here described at the Urubu pegmatite, Itinga municipality, Minas Gerais, Brazil. The mineral forms cream-white botryoidal aggregates of acicular to fibrous crystals, intimately associated with simpsonite, thoreaulite, cassiterite, quartz, elbaite, albite, and muscovite. The average of six chemical analyses obtained by electron microprobe is (range in parentheses, wt%): Na(2)O 2.08 (1.95-2.13), K(2)O 2.61 (2.52-2.74), Al(2)O(3) 1.96 (1.89-2.00), Fe(2)O(3) 0.01 (0.00-0.03), TiO(2) 0.02 (0.00-0.06), Ta(2)O(5) 81.04 (79.12-85.18), Nb(2)O(5) 9.49 (8.58-9.86), total 97.21 (95.95-101.50). The chemical formula derived from this analysis is (Na(1.55)K(1.28))(Sigma 2.83)(Ta(8.45)Nb(1.64)Al(0.89)Fe(0.01)(3+)Ti(0.01))(Sigma 11.00)[O(25.02)(OH)(5.98)](Sigma 31.00). Rankamaite is an orthorhombic ""tungsten bronze"" (OTB), crystallizing in the space group Cmmm. Its unit-cell parameters refined from X-ray diffraction powder data are: a = 17.224(3), b = 17.687(3), c = 3.9361(7) angstrom, V = 1199.1(3) angstrom(3), Z = 2. Rietveld refinement of the powder data was undertaken using the structure of LaTa(5)O(14) as a starting model for the rankamaite structure. The structural formula obtained with the Rietveld analyses is: (Na(2.21)K(1.26))Sigma(3.37)(Ta(9.12)NB(1.30) Al(0.59))(Sigma 11.00)[O(26.29)(OH)(4.71)](Sigma 31.00). The tantalum atoms are coordinated by six and seven oxygen atoms in the form of distorted TaO(6) octahedra and TaO(2) pentagonal bipyramids, respectively. Every pentagonal bipyramid shares edges with four octahedra, thus forming Ta(5)O(14) units. The potassium atom is in an 11-fold coordination, whereas one sodium atom is in a 10-fold and the other is in a 12-fold coordination. Raman and infrared spectroscopy were used to investigate the room-temperature spectra of rankamaite.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Maximizing measures for endomorphisms of the circle

We study a given fixed continuous function phi : S(1) -> R and an endomorphism f : S(1)-> S(1), whose f-invariant probability measures maximize integral phi d mu. We prove that the set of endomorphisms having a f maximizing invariant measure supported on a periodic orbit is C(0) dense.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Lipid, fatty acid, protein, amino acid and ash contents in four Brazilian red algae species

Four species of marine benthic algae (Laurencia filiformis, L. intricata, Gracilaria domingensis and G. birdiae) that belong to the phylum Rhodophyta were collected in Espirito Santo State, Brazil and investigated concerning their biochemical composition (fatty acid, total lipid, soluble proteins, amino acid and ash). The total content of lipid (% dry weight) ranged from 1.1% to 6.2%: fatty acid from 0.7% to 1.0%: soluble protein from 4.6% to 18.3%, amino acid from 6.7% to 11.3% and ash from 22.5% to 38.4%. judging from their composition, the four species of algae appear to be potential sources of dietary proteins, amino acids, lipids and essential fatty acids for humans and animals. (C) 2009 Elsevier Ltd. All rights reserved.

Vanadium oxide-porphyrin nanocomposites as gas sensor interfaces for probing low water content in ethanol

Vanadium pentoxide xerogels (VXG) incorporating meso(3- and 4-pyridyl)porphyrin cobalt(III) species coordinated to four [Ru(bipy)(2)Cl](+) complexes were employed as gas sensing materials capable of detecting small amounts of water in commercial ethanol and fuel supplies. According to their X-ray diffraction data, the original VXG lamellar framework was maintained in the nanocomposite material, but the interlamellar distance increased from 11.7 to 15.2 angstrom, reflecting the intercalation of the porphyrin species into the vanadium pentoxide matrix. The films generated by direct deposition of the nanocomposite aqueous suspensions exhibited good electrical and electrochemical performance for application in resistive sensors. The analysis of water in ethanol and fuels was carried out successfully using an especially designed electric setup incorporating a laminar gas flow chamber and interdigitated gold electrodes coated with the nanocomposites. (C) 2010 Elsevier B.V. All rights reserved.

Polyaniline/layered zirconium phosphate nanocomposites: Secondary-like doped polyaniline obtained by the layer-by-layer technique

In the present work, nanocomposites of polyaniline (PANI) and layered alpha-Zr(HPO4)(2).H2O (alpha-ZrP) were prepared using two different approaches: (i) the in situ aniline polymerization in the presence of the layered inorganic material and (ii) the layer-by-layer (LBL) assembly using an aqueous solution of the polycation emeraldine salt (ES-PANI) and a dispersion of exfoliated negative slabs of alpha-ZrP. These materials were characterized spectroscopically using mainly resonance Raman scattering at four exciting radiations and electronic absorption in the UV-VIS-NIR region. Structural and textural characterizations were carried out using powder X-ray diffraction (XRD) and scanning electron microscopy (SEM). The polymer obtained by the in situ aniline polymerization is located primarily in the external surface of the inorganic material although aniline monomers were intercalated between alpha-ZrP interlayer regions before oxidative polymerization. Through resonance Raman spectroscopy, it was observed that the formed polymer has semiquinone units (ES-PANI) and also azo bonds (-N = N-), showing that this method results in a polymer with a different structure from the usual ""head-to-tail"" ES-PANI. The LBL assembly of pre-formed ES-PANI and exfoliated alpha-ZrP particles produces homogeneous films with reproducible deposition from layer to layer, up to 20 bilayers. Resonance Raman (lambda(0) = 632.8 nm) spectrum of PANI/ZrP LBL film shows an enhancement in the intensity of the polaronic band at 1333 cm(-1) (nu C-N center dot+) and the decrease of the band intensity at 1485 cm(-1) compared to bulk ES-PANI. Its UV-VIS-NIR spectrum presents an absorption tail in the NIR region assigned to delocalized free charge carrier. These spectroscopic features are characteristic of highly conductive secondary doped PANI suggesting that polymeric chains in PANI/ZrP LBL film have a more extended conformation than in bulk ES-PANI.

Characteristics and properties of carboxymethylchitosan

Four samples of N,O-carboxymethylchitosan (0.5 < <(DS)over bar> < 1.5) were prepared by reacting chitosan (<(DA)over bar> = 24%) with monochloroacetic acid in the presence of excess sodium hydroxide. The carboxymethylchitosan samples were soluble in a wider range of pH as compared to the parent chitosan and the X-ray diffraction showed that they adopt a less ordered arrangement. The carboxymethylation of chitosan decreased the thermal stability of the polymer as evaluated by thermogravimetry but no clear dependence of the activation energy on the average degree of substitution of carboxymethylchitosan was identified. However, the values of activation energy of carboxymethylchitosan issued from the isothermal study depended on the degree of conversion, suggesting the occurrence of a complex set of simultaneous reactions. (C) 2008 Published by Elsevier Ltd.