INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Induced Modules for Affine Lie Algebras

We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence between a certain category of P-induced G-modules and the category of weight P-modules with injective action of the central element of G. In particular, the induction functor preserves irreducible modules. If P is a parabolic subalgebra with a finite-dimensional Levi factor then it defines a unique pseudo parabolic subalgebra P(ps), P subset of P(ps). The structure of P-induced modules in this case is fully determined by the structure of P(ps)-induced modules. These results generalize similar reductions in particular cases previously considered by V. Futorny, S. Konig, V. Mazorchuk [Forum Math. 13 (2001), 641-661], B. Cox [Pacific J. Math. 165 (1994), 269-294] and I. Dimitrov, V. Futorny, I. Penkov [Comm. Math. Phys. 250 (2004), 47-63].

Treatment of Osteomyelitis in the Feet of Diabetic Patients by Photodynamic Antimicrobial Chemotherapy

Objective: This article describes two inexpensive photodynamic antimicrobial chemotherapy (PACT) protocols to provide intensive local care on ulcerated feet of diabetic patients with osteomyelitis. Background Data: Patients with this condition generally have poor quality of life. The usual treatment consists of the administration of a cocktail of drugs including anti-inflammatories, promoters of blood circulation, and systemic antibiotics. However, depending on the conditions of the tissues, amputation may be required. Consequently, it is important to develop PACT protocols that can help avoid amputation. Materials and Methods: Two PACT protocols were applied to two diabetic patients with osteomyelitis. These protocols were based on several PACT sessions that consisted of: (1) local injection of mixtures of phenothiazines (2% in water) and Hypericum perforatum extract (10% in propylene glycol), and (2) illumination, lasting 10 min, applied to the lesion's interior and exterior using, respectively, an optical fiber and a non-coherent light source. The frequency of PACT was daily or every other day in the beginning, and weekly after tissue recovery begun. The patients were followed clinically and by radiographic testing. Results: Both PACT protocols helped cure these patients who were about to have amputation of their feet. Radiograms showed that bone had healed and that the bone's texture had improved. Conclusion: Here we have described efficient and affordable PACT protocols to treat osteomyelitis in the feet of diabetic patients. This treatment modality should be considered by vascular surgeons and by orthopedists to treat osteomyelitis that is resistant to conventional treatments.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

Mechanism and model of the oscillatory electro-oxidation of methanol

A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry (polynomial rings and ideal theory) revealing the occurrence of a Hopf and a saddle-node bifurcation. These analytical solutions are confirmed by numerical integration of the system of differential equations. (C) 2010 American Institute of Physics

Stability of biomass-derived black carbon in soils

Black carbon (BC) may play ail important role in the global C budget, due to its potential to act as a significant sink of atmospheric CO(2). In order to fully evaluate the influence of BC oil the global C cycle, in understanding of the stability of BC is required. The biochemical stability of BC was assessed in a chronosequence of high-BC-containing Anthrosols from the central Amazon, Brazil, using a range of spectroscopic and biological methods. Results revealed that the Anthrosols had 61-80% lower (P < 0.05) CO(2) evolution per unit C over 532 days compared to their respective adjacent soils with low BC contents. No significant (P > 0.05) difference in CO(2) respiration per unit C was observed between Anthrosols with contrasting ages of BC (600-8700 years BP) Lind soil textures (0.3-36% clay). Similarly, the molecular composition of the core regions of micrometer-sized BC particles quantified by synchrotron-based Near-Edge X-ray Fine Structure (NEXAFS) spectroscopy coupled to Scanning Transmission X-ray Microscopy (STXM) remained similar regardless of their ages and closely resembled the spectral characteristics or fresh BC. BC decomposed extremely slowly to ail extent that it was not possible to detect chemical changes between Youngest and oldest samples, as also confirmed by X-ray Photoelectron Spectroscopy (XPS). Deconvolution of NEXAFS spectra revealed greater oxidation oil the surfaces of BC particles with little penetration into the core of the particles. The similar C mineralization between different BC-rich soils regardless of soil texture underpins the importance of chemical recalcitrance for the stability of BC, in contrast to adjacent soils which showed the highest mineralization in the sandiest soil. However, the BC-rich Anthrosols had higher proportions (72-90%) of C in the more stable organo-mineral fraction than BC-poor adjacent soils (2-70%), Suggesting some degree of physical stabilization. (c) 2008 Elsevier Ltd. All rights reserved.

Soil Carbon Turnover Measurement by Physical Fractionation at a Forest-to-Pasture Chronosequence in the Brazilian Amazon

The effect of conversion from forest-to-pasture upon soil carbon stocks has been intensively discussed, but few studies focus on how this land-use change affects carbon (C) distribution across soil fractions in the Amazon basin. We investigated this in the 20 cm depth along a chronosequence of sites from native forest to three successively older pastures. We performed a physicochemical fractionation of bulk soil samples to better understand the mechanisms by which soil C is stabilized and evaluate the contribution of each C fraction to total soil C. Additionally, we used a two-pool model to estimate the mean residence time (MRT) for the slow and active pool C in each fraction. Soil C increased with conversion from forest-to-pasture in the particulate organic matter (> 250 mu m), microaggregate (53-250 mu m), and d-clay (< 2 mu m) fractions. The microaggregate comprised the highest soil C content after the conversion from forest-to-pasture. The C content of the d-silt fraction decreased with time since conversion to pasture. Forest-derived C remained in all fractions with the highest concentration in the finest fractions, with the largest proportion of forest-derived soil C associated with clay minerals. Results from this work indicate that microaggregate formation is sensitive to changes in management and might serve as an indicator for management-induced soil carbon changes, and the soil C changes in the fractions are dependent on soil texture.

Simulation of Soil Carbon Dynamics under Sugarcane with the CENTURY Model

Currently there is a trend for the expansion of the area cropped with sugarcane (Saccharum officinarum L.), driven by an increase in the world demand for biofuels, due to economical, environmental, and geopolitical issues. Although sugarcane is traditionally harvested by burning dried leaves and tops, the unburned, mechanized harvest has been progressively adopted. The use of process based models is useful in understanding the effects of plant litter in soil C dynamics. The objective of this work was to use the CENTURY model in evaluating the effect of sugarcane residue management in the temporal dynamics of soil C. The approach taken in this work was to parameterize the CENTURY model for the sugarcane crop, to simulate the temporal dynamics of soil C, validating the model through field experiment data, and finally to make predictions in the long term regarding soil C. The main focus of this work was the comparison of soil C stocks between the burned and unburned litter management systems, but the effect of mineral fertilizer and organic residue applications were also evaluated. The simulations were performed with data from experiments with different durations, from 1 to 60 yr, in Goiana and Timbauba, Pernambuco, and Pradopolis, Sao Paulo, all in Brazil; and Mount Edgecombe, Kwazulu-Natal, South Africa. It was possible to simulate the temporal dynamics of soil C (R(2) = 0.89). The predictions made with the model revealed that there is, in the long term, a trend for higher soil C stocks with the unburned management. This increase is conditioned by factors such as climate, soil texture, time of adoption of the unburned system, and N fertilizer management.

Functional specialization of Eucalyptus fine roots: contrasting potential uptake rates for nitrogen, potassium and calcium tracers at varying soil depths

1. Little is known about the role of deep roots in the nutrition of forest trees and their ability to provide a safety-net service taking up nutrients leached from the topsoil. 2. To address this issue, we studied the potential uptake of N, K and Ca by Eucalyptus grandis trees (6 years of age - 25 m mean height), in Brazil, as a function of soil depth, texture and water content. We injected NO(3)(-)- (15)N, Rb(+) (analogue of K(+)) and Sr(2+) (analogue of Ca(2+)) tracers simultaneously in a solution through plastic tubes at 10, 50, 150 and 300 cm in depth in a sandy and a clayey Ferralsol soil. A complete randomized design was set up with three replicates of paired trees per injection depth and soil type. Recently expanded leaves were sampled at various times after tracer injection in the summer, and the experiment was repeated in the winter. Soil water contents were continuously monitored at the different depths in the two soils. 3. Determination of foliar Rb and Sr concentrations and (15)N atom % made it possible to estimate the relative uptake potential (RUP) of tracer injections from the four soil depths and the specific RUP (SRUP), defined as RUP, per unit of fine root length density in the corresponding soil layer. 4. The highest tracer uptake rates were found in the topsoil, but contrasting RUP distributions were observed for the three tracers. Whilst the RUP was higher for NO(3)(-)- (15)N than for Rb(+) and Sr(2+) in the upper 50 cm of soil, the highest SRUP values for Sr(2+) and Rb(+) were found at a depth of 300 cm in the sandy soil, as well as in the clayey soil when gravitational solutions reached that depth. 5. Our results suggest that the fine roots of E. grandis trees exhibit contrasting potential uptake rates with depth depending on the nutrient. This functional specialization of roots might contribute to the high growth rates of E. grandis trees, efficiently providing the large amounts of nutrients required throughout the development of these fast-growing plantations.

Preliminary studies of laser-induced breakdown spectrometry for the determination of Ba, Cd, Cr and Pb in toys

The performance of laser-induced breakdown spectrometry (LIBS) for the determination of Ba, Cd, Cr and Pb in toys has been evaluated by using a Nd:YAG laser operating at 1064 nm and an Echelle spectrometer with intensified charge-coupled device detector. Samples were purchased in different cities of Sao Paulo State market and analyzed directly without sample preparation. Laser-induced breakdown spectrometry experimental conditions (number of pulses, delay time. integration time gate and pulse energy) were optimized by using a Doehlert design. Laser-induced breakdown spectrometry signals correlated reasonably well with inductively coupled plasma optical emission spectrometry (ICP OES) concentrations after microwave-assisted acid digestion of selected samples. Thermal analysis was used for polymer identification and scanning electron microscopy to Visualize differences in crater geometry of different polymers employed for toy fabrication. Results indicate that laser-induced breakdown spectrometry can be proposed as a rapid screening method for investigation of potentially toxic elements in toys. The unique application of laser-induced breakdown spectrometry for identification of contaminants in successive layers of ink and polymer is also demonstrated. (C) 2009 Elsevier B.V. All rights reserved.

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

ECAP of Fe. Experiments and simulations of the in-elbow textures

The study of deformation properties of low carbon steels is of particular interest because of their many technological applications. Obtaining fine grained Fe based materials can be approached by one of the several available Severe Plastic Deformation (SPD) techniques. The current paper shows experimental data and simulations of the deformation process of iron samples by Equal Channel Angular Extrusion (ECAE). The samples were extruded in a 120 degrees channel die either by one or a few passes. The heterogeneity and local development of the deformation on the elbow of the channel has been studied by X-ray measuring and simulation of the texture evolution. The Self Consistent models used for simulation allowed the calculation of the spin of the main texture components which agreed pretty well with the experiments.

Characterization of nickel-niobium composite electrocoatings

The electrodeposition of nickel based composites is been performed in order to improve properties of nickel layers, such as hardness, wear resistance, lubrication, corrosion resistance and catalytic activity. In the present work Nb powders (20 mu m average size) and Ni were codeposited on 1020 carbon steel by galvanostatic electrolysis of Watts bath, using 10, 20 and 40 mA/cm(2) cathodic current density and 240, 400 and 550 rpm electrolyte stirring rate. The morphology and texture of the coatings, Nb incorporated volume fraction, microhardness, adhesion to the substrate and corrosion behavior were evaluated. The Ni-Nb composite layers presented a rough morphology with randomly oriented Ni grains, whereas pure Ni coatings were smooth and showed highly preferred orientation in the [110] or [100] direction. The volume fraction of Nb in the composites determined by image analysis ranged from 8.5 to 19%. The 400 rpm stirring rate led to the highest Nb content (16 to 19016) for all current densities investigated The microhardness of the composite layers was higher than that of pure Ni coatings due to refining of Ni grains induced by incoporation of Nb particles. The adhesion of the coatings estimated qualitatively by bend test was found satisfactory. The Ni-Nb composites presented lower corrosion rate than Ni coatings in both 3% NaCl and 20% H2SO4 solutions.

Compositional and textural properties of milkfat-soybean oil enzymatic interesterification

Milkfat-soybean oil blends were enzymatically interesterified (EIE) by Aspergillus niger lipase immobilized on SiO(2)-PVA hybrid composite in a solvent free system. An experimental mixture design was used to study the effects of binary blends of milkfat-soybean oil (MF:SBO) at different proportions (0:100; 25:75; 33:67; 50:50; 67:33; 75:25; 100:0) on the compositional and textural properties of the EIE products, considering, as response variables, the interesterification yield (IY), consistency and hardness. Lipase-catalysed interesterification reactions increased the relative proportion of TAGs` C(46)-C(52) and decreased the TAGs` C(40)-C(42) and C(54) concentrations. The highest IY was attained (10.8%) for EIE blend of MF:SBO 67:33 resulting in a more spreadable material at refrigerator temperature in comparison with butter, milkfat or non-interesterified (NIE) blend. In this case, consistency and hardness values were at least 32% lower than values measured for butter. Thus, using A. niger lipase immobilized on SiO(2)-PVA improves the textural properties of milkfat and has potential for development of a product incorporating unsaturated and essential fatty acids from soybean oil. (C) 2010 Elsevier Ltd. All rights reserved.

Magnetostriction of melt-spun Fe(85)Ga(15), Fe(78)Ni(7)Ga(15) and Fe(78)Co(7)Ga(15) stacked ribbon samples

A set of stacked ribbon samples with the compositions Fe(85)Ga(15), Fe(78)Ni(7)Ga(15) and Fe(78)Co(7)Ga(15) were prepared. XRD on these ribbons show that the binary Fe(85)Ga(15) ribbon exhibits the disordered A2 structure where as the addition of Co and Ni leads to the appearance of an additional ordered DO(3) structure. A comparison of the ratio of the XRD-line intensities gave strong evidence of a (100) texture perpendicular to the ribbon surface. The optical studied microstructure supports these results because it shows a columnar grain growth parallel to the solidification direction-which is parallel to ribbon thickness. The highest magnetostriction was found for Fe(78)Ni(7)Ga(15) (370 ppm), while the Fe(78)Co(7)Ga(15) a smaller magnetostriction of 270 ppm was found. The enhancement of the magnetostriction is attributed to the (100) texture in these ribbons. (C) 2009 Elsevier B.V. All rights reserved.