Neoproterozoic geodynamic evolution of SW-Gondwana: a southern African perspective

Our current understanding of the tectonic history of the principal Pan-African orogenic belts in southwestern Africa, reaching from the West Congo Belt in the north to the Lufilian/Zambezi, Kaoko, Damara, Gariep and finally the Saldania Belt in the south, is briefly summarized. On that basis, possible links with tectono-stratigraphic units and major structures on the eastern side of the Rio de la Plata Craton are suggested, and a revised geodynamic model for the amalgamation of SW-Gondwana is proposed. The Rio de la Plata and Kalahari Cratons are considered to have become juxtaposed already by the end of the Mesoproterozoic. Early Neoproterozoic rifting led to the fragmentation of the northwestern (in today`s coordinates) Kalahari Craton and the splitting off of several small cratonic blocks. The largest of these ex-Kalahari cratonic fragments is probably the Angola Block. Smaller fragments include the Luis Alves and Curitiba microplates in eastern Brazil, several basement inliers within the Damara Belt, and an elongate fragment off the western margin, named Arachania. The main suture between the Kalahari and the Congo-So Francisco Cratons is suspected to be hidden beneath younger cover between the West Congo Belt and the Lufilian/Zambezi Belts and probably continues westwards via the Cabo Frio Terrane into the Goias magmatic arc along the Brasilia Belt. Many of the rift grabens that separated the various former Kalahari cratonic fragments did not evolve into oceanic basins, such as the Northern Nosib Rift in the Damara Belt and the Gariep rift basin. Following latest Cryogenian/early Ediacaran closure of the Brazilides Ocean between the Rio de la Plata Craton and the westernmost fragment of the Kalahari Craton, the latter, Arachania, became the locus of a more than 1,000-km-long continental magmatic arc, the Cuchilla Dionisio-Pelotas Arc. A correspondingly long back-arc basin (Marmora Basin) on the eastern flank of that arc is recognized, remnants of which are found in the Marmora Terrane-the largest accumulation of oceanic crustal material known from any of the Pan-African orogenic belts in the region. Corresponding foredeep deposits that emerged from the late Ediacaran closure of this back-arc basin are well preserved in the southern areas, i.e. the Punta del Este Terrane, the Marmora Terrane and the Tygerberg Terrane. Further to the north, present erosion levels correspond with much deeper crustal sections and comparable deposits are not preserved anymore. Closure of the Brazilides Ocean, and in consequence of the Marmora back-arc basin, resulted from a change in the Rio de la Plata plate motion when the Iapetus Ocean opened between the latter and Laurentia towards the end of the Ediacaran. Later break-up of Gondwana and opening of the modern South Atlantic would have followed largely along the axis of the Marmora back-arc basin and not along major continental sutures.

SRTM resample with short distance-low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60 degrees north latitude and 56 degrees south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc-second (similar to 30m) for areas within the USA and at 3 arc-second (similar to 90m) resolution for the rest of the world. A resolution of 90m can be considered suitable for the small or medium-scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3"" to 1"". We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1"" model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1"" NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1"" surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline-interpolated surface still presented some noise and linear artifacts, which were removed by kriging.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Instability of equilibrium points of some Lagrangian systems

In this work we show that, if L is a natural Lagrangian system such that the k-jet of the potential energy ensures it does not have a minimum at the equilibrium and such that its Hessian has rank at least n - 2, then there is an asymptotic trajectory to the associated equilibrium point and so the equilibrium is unstable. This applies, in particular, to analytic potentials with a saddle point and a Hessian with at most 2 null eigenvalues. The result is proven for Lagrangians in a specific form, and we show that the class of Lagrangians we are interested can be taken into this specific form by a subtle change of spatial coordinates. We also consider the extension of this results to systems subjected to gyroscopic forces. (C) 2008 Elsevier Inc. All rights reserved.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Extensions of homogeneous polynomials ON c(0)(l(2)(i))

We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c(0)(l(2)(i)).

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (c) 2008 Elsevier Inc. All rights reserved.

Hypercentral unit groups and the hyperbolicity of a modular group algebra

We classify groups G such that the unit group U-1 (ZG) is hypercentral. In the second part, we classify groups G whose modular group algebra has hyperbolic unit groups U-1 (KG).

HYPERBOLICITY OF SEMIGROUP ALGEBRAS II

In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Z-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Electroluminescent devices based on rare-earth tetrakis beta-diketonate complexes

In this paper the synthesis, photo luminescence and electroluminescence investigation of the novel tetrakis beta-diketonate of rare-earth complexes such as M[Eu(dbM)(4)] and M[Tb(acac)(4)] with a variety of cationic ligands, M=Li(+), Na(+) and K(+) have been investigated. The emission spectra of the Eu(3+) and Tb(3+) complexes displayed characteristic narrow bands arising from intraconfigurational transitions of trivalent rare-earth ions and exhibited red color emission for the Eu(3+) ion ((5)D(0) -> F(J), J=0-6) and green for the Tb(3+) ion ((5)D(4) -> (7)F(J), J = 6-0). The lack of the broaden emission bands arising from the ligands suggests the efficient intramolecular energy transfer from the dbm and acac ligands to Eu(3+) and Tb(3+) ions, respectively. In accordance to the expected, the values of PL quantum efficiency (eta) of the emitting (5)D(0) state of the tetrakis(beta-diketonate) complexes of Eu(3+) were higher compared with those tris-complexes. Therefore, organic electroluminescent (EL) devices were fabricated with the structure as follows: indium tin oxide (ITO)/hole transport layer (HTL) NPB or MTCD/emitter layer M[RE(beta-diketonate)(4)] complexes)/Aluminum (Al). All the films were deposited by thermal evaporation carried out in a high vacuum environment system. The OLED light emission was independent of driving voltage, indicating that the combination of charge carriers generates excitons within the M[RE(beta-diketonate)(4)] layers, and the energy is efficiently transferred to RE(3+) ion. As a best result, a pure red and green electroluminescent emission was observed from the Eu(3+) and Tb(3+) devices, confirmed by (X,Y) color coordinates. (C) 2008 Elsevier B.V. All rights reserved.

Luminescent nanoparticles of MgAl(2)O(4):Eu, Dy prepared by citrate sol-gel method

MgAl(2)O(4):Eu, Dy nanoparticles were prepared by citrate sol-gel method and thermally treated at 600, 700, 800 and 900 degrees C. The trivalent europium ion is partially reduced to the divalent state at 700 and 800 degrees C. Infrared spectra of the phosphors showed bands around 700 and 520 cm(-1) corresponding to the AlO(6) groups. X-ray diffraction patterns present sharp reflections of samples heated from 700 to 900 degrees C indicating the MgAl(2)O(4) spinel phase. Grain size in the range 20-30 nm were observed by measurement of transmission electron microscopy (TEM). The emission spectra of the phosphors show a broadened band at 480 nm assigned to the 4f(G)5d -> 4f(7) ((8)S(7/2)) transition of Eu(2+) ion overlapped to the (4)F(9/2) -> (6)H(15/2) transition of the Dy(3+) ion. Besides, the (4)F(9/2) -> (6)H(13/2) transition (579 nm) of Dy(3+) ion is overlapped with the (5)D(0) -> (7)F(0) (578 nm) and (5)D(0) -> (7)F(1) (595 nm) transitions from the Eu(3+) ion. Excitation spectra of the sample heated at 900 degrees C monitoring the excitation at 615 nm of (5)D(0) -> (7)F(2) transition of Eu(3+) ion exhibit a broad band assigned to the O -> Eu(3+) ligand-to-metal charge-transfer states (LMCT) around 280 nm. The samples present green persistent luminescence after exposure to UV radiation. The chromaticity coordinates were obtained from the luminescence emission spectrum. (C) 2008 Elsevier B.V. All rights reserved.

Oxorhenium(V) Complexes with 2,3-Dihydroxynaphthalene

2,3-Dihydroxynaphthalene (H(2)dhn) reacts with [ReOCl(3)-(PPh(3))(2)] or [ReOBr(3)(PPh(3))(2)] in a 1:1 molar ratio with formation of the isostructural complexes [ReOCl(2)(PPh(3))(2)(Hdhn)] (4) and [ReOBr(2)-(PPh(3))(2)(Hdhn)] (5). They have distorted octahedral coordination spheres with the halide and the triphenylphosphine ligands arranged in equatorial trans positions to each other. The Hdhn-ligand coordinates monodentately in trans position to the oxo ligand. Intramolecular hydrogen bonds between the Hdhn and the halogeno ligands stabilize this coordination mode. The products represent the first examples of oxorhenium(V) complexes with monodentate catecholate-type ligands.