The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

Effects of photobioreactor configuration, nitrogen source and light intensity on the fed-batch cultivation of Arthrospira (Spirulina) platensis. Bioenergetic aspects

Bioenergetic analysis may be applied in order to predict microbial growth yields, based on the Gibbs energy dissipation and mass conservation principles of the overall growth reaction. The bioenergetics of the photoautotrophic growth of the cyanobacterium Arthrospira (Spirulina) platensis was investigated in different bioreactor configurations (tubular photobioreactor and open ponds) using different nitrogen sources (nitrate and urea) and under different light intensity conditions to determine the best growing conditions in terms of Gibbs energy dissipation, number of photons to sustain cell growth and phototrophic energy yields distribution in relation to the ATP and NADPH formation, and release of heat. Although an increase in the light intensity increased the Gibbs energy dissipated for cell growth and maintenance with both nitrogen sources, it did not exert any appreciable influence on the moles of photons absorbed by the system to produce one C-mol biomass. On the other hand, both bioenergetic parameters were higher in cultures with nitrate than with urea, likely because of the higher energy requirements needed to reduce the former nitrogen source to ammonia. They appreciably increased also when open ponds were substituted by the tubular photobioreactor, where a more efficient light distribution ensured a remarkably higher cell mass concentration. The estimated percentages of the energy absorbed by the cell showed that, compared with nitrate, the use of urea as nitrogen source allowed the system to address higher energy fractions to ATP production and light fixation by the photosynthetic apparatus, as well as a lower fraction released as heat. The best energy yields values on Gibbs energy necessary for cell growth and maintenance were achieved in up to 4-5 days of cultivation, indicating that it would be the optimum range to maintain cell growth. Thanks to this better bioenergetic situation, urea appears to be a quite promising low-cost, alternative nitrogen source for Arthrospira platensis cultures in photobioreactors. (C) 2011 Elsevier Ltd. All rights reserved.

BANACH SPACES WITHOUT MINIMAL SUBSPACES - EXAMPLES

We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11], by classifying them according to which side of the dichotomies they fall.

VCD to determine absolute configuration of natural product molecules: secolignans from Peperomia blanda

The absolute configuration and solution-state conformers of three peperomin-type secolignans isolated from Peperomia blanda (Piperaceae) are unambiguously determined by using vibrational circular dichroism (VCD) spectroscopy associated with density functional theory (DFT) calculations. Advantages of VCD over the electronic form of CD for the analysis of diastereomers are also discussed. This work extends our growing knowledge about secondary metabolites within the Piperaceae family species while providing a definitive and straightforward method to assess the absolute stereochemistry of secolignans.

Further monoterpene chromane esters from Peperomia obtusifolia: VCD determination of the absolute configuration of a new diastereomeric mixture

A reinvestigation of the monoterpene chromane ester enriched fraction from Peperomia obtusifolia using chiral chromatography led to the identification of a minor peak, which was elucidated by NMR and HRMS as fenchyl-3,4-dihydro-5-hydroxy-2,7-dimethyl-8-(3 ''-methyl-2 ''-butenyl)-2-(4'-methyl-1',3'-pentadienyl)-2H-1-benzopyran-6-carboxylate, the same structure assigned to two other fenchyl esters described previously, pointing out a stereoisomeric relationship among them. Further NMR analysis revealed that it was actually a mixture of two compounds, whose absolute configurations were determined by VCD measurements. Although, almost no vibrational transitions could be assigned to the chiral chromane, the experimental VCD spectrum was largely opposite to that obtained for the average experimental VCD [(2S,1'''R,2'''R,4'''S + 2R,1'''R,2'''R,4'''S)/2] for fenchol derivatives. These results allowed us to assign the putative compounds as a racemic mixture of the chiral chromane esterified with the monoterpene (1S,2S,4R)fenchol, which had not been identified in our early work. (C) 2012 Elsevier Ltd. All rights reserved.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Hypoellipticity in spaces of ultradistributions-Study of a model case

In this work we study C (a)-hypoellipticity in spaces of ultradistributions for analytic linear partial differential operators. Our main tool is a new a-priori inequality, which is stated in terms of the behaviour of holomorphic functions on appropriate wedges. In particular, for sum of squares operators satisfying Hormander's condition, we thus obtain a new method for studying analytic hypoellipticity for such a class. We also show how this method can be explicitly applied by studying a model operator, which is constructed as a perturbation of the so-called Baouendi-Goulaouic operator.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

U-Pb zircon in situ dating with LA-MC-ICP-MS using a mixed detector configuration

The LA-MC-ICP-MS method applied to U-Pb in situ dating is still rapidly evolving due to improvements in both lasers and ICP-MS. To test the validity and reproducibility of the method, 5 different zircon samples, including the standard Temora-2, ranging in age between 2.2 Ga and 246 Ma, were dated using both LA-MC-ICP-MS and SHRIMP. The selected zircons were dated by SHRIMP and, after gentle polishing, the laser spot was driven to the same site or on the same zircon phase with a 213 nm laser microprobe coupled to a multi-collector mixed system. The data were collected with a routine spot size of 25 μm and, in some cases, of 15 and 40 μm. A careful cross-calibration using a diluted U-Th-Pb solution to calculate the Faraday reading to counting rate conversion factors and the highly suitable GJ-1 standard zircon for external calibrations were of paramount importance for obtaining reliable results. All age results were concordant within the experimental errors. The assigned age errors using the LA-MC-ICP-MS technique were, in most cases, higher than those obtained by SHRIMP, but if we are not faced with a high resolution stratigraphy, the laser technique has certain advantages.

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.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

Structural stability of flexible lines in catenary configuration under torsion

Catenary risers can present during installation a very low tension close to seabed, which combined with torsion moment can lead to a structural instability, resulting in a loop. This is undesirable once it is possible that the loop turns into a kink, creating damage. This work presents a numerical methodology to analyze the conditions of loop formation in catenary risers. Stability criteria were applied to finite element models, including geometric nonlinearities and contact constraint due to riser-seabed interaction. The classical Greenhill's formula was used to predict the phenomenon and parametric analysis shows a “universal plot” able to predict instability in catenaries using a simple equation that can be applied for typical risers installation conditions and, generically, for catenary lines under torsion.

Gold ion implantation into alumina using an “inverted ion source” configuration.

We describe an approach to ion implantation in which the plasma and its electronics are held at ground potential and the ion beam is injected into a space held at high negative potential, allowing considerable savings both economically and technologically. We used an “inverted ion implanter” of this kind to carry out implantation of gold into alumina, with Au ion energy 40 keV and dose (3–9) × 1016 cm−2. Resistivity was measured in situ as a function of dose and compared with predictions of a model based on percolation theory, in which electron transport in the composite is explained by conduction through a random resistor network formed by Au nanoparticles. Excellent agreement is found between the experimental results and the theory.