Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant`s Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of finite W-algebras. The second main result is a parameterization of finite families of irreducible Gelfand-Tsetlin modules using Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for finite W-algebras. (C) 2009 Elsevier Inc. All rights reserved.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

A reduction of CETP activity, not an increase, is associated with modestly impaired postprandial lipemia and increased HDL-Cholesterol in adult asymptomatic women

Background: The relationship between CETP and postprandial hyperlipemia is still unclear. We verified the effects of varying activities of plasma CETP on postprandial lipemia and precocious atherosclerosis in asymptomatic adult women. Methods: Twenty-eight women, selected from a healthy population sample (n = 148) were classified according to three CETP levels, all statistically different: CETP deficiency (CETPd <= 4.5%, n = 8), high activity (CETPi >= 23.8, n = 6) and controls (CTL, CETP >= 4.6% and <= 23.7%, n = 14). After a 12 h fast they underwent an oral fat tolerance test (40 g of fat/m(2) of body surface area) for 8 hours. TG, TG-rich-lipoproteins (TRL), cholesterol and TRL-TG measurements (AUC, AUIC, AR, RR and late peaks) and comparisons were performed on all time points. Lipases and phospholipids transfer protein (PLTP) were determined. Correlation between carotid atherosclerosis (c-IMT) and postprandial parameters was determined. CETP TaqIB and I405V and ApoE-epsilon 3/epsilon 2/epsilon 4 polymorphisms were examined. To elucidate the regulation of increased lipemia in CETPd a multiple linear regression analysis was performed. Results: In the CETPi and CTL groups, CETP activity was respectively 9 and 5.3 higher compared to the CETPd group. Concentrations of all HDL fractions and ApoA-I were higher in the CETPd group and clearance was delayed, as demonstrated by modified lipemia parameters (AUC, AUIC, RR, AR and late peaks and meal response patterns). LPL or HL deficiencies were not observed. No genetic determinants of CETP deficiency or of postprandial lipemia were found. Correlations with c-IMT in the CETPd group indicated postprandial pro-atherogenic associations. In CETPd the regression multivariate analysis (model A) showed that CETP was largely and negatively predicted by VLDL-C lipemia (R(2) = 92%) and much less by TG, LDL-C, ApoAI, phospholipids and non-HDL-C. CETP (model B) influenced mainly the increment in ApoB-100 containing lipoproteins (R(2) = 85% negatively) and phospholipids (R(2) = 13%), at the 6(th)h point. Conclusion: The moderate CETP deficiency phenotype included a paradoxically high HDL-C and its sub fractions (as earlier described), positive associations with c-IMT, a postprandial VLDL-C increment predicting negatively CETP activity and CETP activity regulating inversely the increment in ApoB100-containing lipoproteins. We hypothesize that the enrichment of TG content in triglyceride-rich ApoB-containing lipoproteins and in TG rich remnants increases lipoproteins` competition to active lipolysis sites, reducing their catabolism and resulting on postprandial lipemia with atherogenic consequences.

[(13)C(2)]- Acetaldehyde Promotes Unequivocal Formation of 1,N(2)-Propano-2 `-deoxyguanosine in Human Cells

Acetaldehyde is an environmentally widespread genotoxic aldehyde present in tobacco smoke, vehicle exhaust and several food products. Endogenously, acetaldehyde is produced by the metabolic oxidation of ethanol by hepatic NAD-dependent alcohol dehydrogenase and during threonine catabolism. The formation of DNA adducts has been regarded as a critical factor in the mechanisms of acetaldehyde mutagenicity and carcinogenesis. Acetaldehyde reacts with 2`-deoxyguanosine in DNA to form primarily N(2)-ethylidene-2`-deoxyguanosine. The subsequent reaction of N(2)-ethylidenedGuo with another molecule of acetaldehyde gives rise to 1,N(2)-propano-2`-deoxyguanosine (1,N(2)-propanodGuo), an adduct also found as a product of the crotonaldehyde reaction with dGuo. However, adducts resulting from the reaction of more than one molecule of acetaldehyde in vivo are still controversial. In this study, the unequivocal formation of 1,N(2)-propanodGuo by acetaldehyde was assessed in human cells via treatment with [(13)C(2)]-acetaldehyde. Detection of labeled 1,N(2)-propanodGuo was performed by HPLC/MS/MS. Upon acetaldehyde exposure (703 mu M), increased levels of both 1,N(2)-etheno-2`-deoxyguanosine (1,N(2)-epsilon dGuo), which is produced from alpha,beta-unsaturated aldehydes formed during the lipid peroxidation process, and 1,N(2)-propanodGuo were observed. The unequivocal formation of 1,N(2)-propanodGuo in cells exposed to this aldehyde can be used to elucidate the mechanisms associated with acetaldehyde exposure and cancer risk.

Ultrasensitive Simultaneous Quantification of 1,N(2)-Etheno-2 `-deoxyguanosine and 1,N(2-)Propano-2 `-deoxyguanosine in DNA by an Online Liquid Chromatography-Electrospray Tandem Mass Spectrometry Assay

Exocyclic DNA adducts produced by exogenous and endogenous compounds are emerging as potential tools to study a variety of human diseases and air pollution exposure. A highly sensitive method involving online reverse-phase high performance liquid chromatography with electrospray tandem mass spectrometry detection in the multiple reaction monitoring mode and employing stable isotope-labeled internal standards was developed for the simultaneous quantification of 1,N(2)-etheno-2`-deoxyguanosine (1,N(2)-epsilon dGuo) and 1,N(2)-propano-2`-deoxyguanosine (1,N(2)-propanodGuo) in DNA. This methodology permits direct online quantification of 2`-deoxyguanosine and ca. 500 amol of adducts in 100 mu g of hydrolyzed DNA M the same analysis. Using the newly developed technique, accurate determinations of 1,N(2)-etheno-2`-deoxyguanosine and 1,N2-propano-2`-deoxyguanosine levels in DNA extracts of human cultured cells (4.01 +/- 0.32 1,N(2)-epsilon dGuo/10(8) dGuo and 3.43 +/- 0.33 1,N(2)-propanodGuo/10(8) dGuo) and rat tissue (liver, 2.47 +/- 0.61 1,N(2)-epsilon dGuo/10(8) dGuo and 4.61 +/- 0.69 1,N(2)-propanodGuo/108 dGuo; brain, 2.96 +/- 1.43,N(2)-epsilon dGuo/10(8) dGuo and 5.66 +/- 3.70 1,N(2)-propanoclGuo/10(8) dGuo; and lung, 0,87 +/- 0.34 1,N(2)-edGuo/ 10(8) dGuo and 2.25 +/- 1.72 1,N(2)-propanodGuo/10(8) dGuo) were performed. The method described herein can be used to study the biological significance of exocyclic DNA adducts through the quantification of different adducts in humans and experimental an with pathological conditions and after air pollution exposure.

Flow injection analysis of ethyl xanthate by gas diffusion and UV detection as CS(2) for process monitoring of sulfide ore flotation

A sensitive and robust analytical method for spectrophotometric determination of ethyl xanthate, CH(3)CH(2)OCS(2)(-) at trace concentrations in pulp solutions from froth flotation process is proposed. The analytical method is based on the decomposition of ethyl xanthate. EtX(-), with 2.0 mol L(-1) HCl generating ethanol and carbon disulfide. CS(2). A gas diffusion cell assures that only the volatile compounds diffuse through a PTFE membrane towards an acceptor stream of deionized water, thus avoiding the interferences of non-volatile compounds and suspended particles. The CS(2) is selectively detected by UV absorbance at 206 nm (epsilon = 65,000 L mol(-1) cm(-1)). The measured absorbance is directly proportional to EtX(-) concentration present in the sample solutions. The Beer`s law is obeyed in a 1 x 10(-6) to 2 x 10(-4) mol L(-1) concentration range of ethyl xanthate in the pulp with an excellent correlation coefficient (r = 0.999) and a detection limit of 3.1 x 10(-7) mol L(-1), corresponding to 38 mu g L. At flow rates of 200 mu L min(-1) of the donor stream and 100 mu L min(-1) of the acceptor channel a sampling rate of 15 injections per hour could be achieved with RSD < 2.3% (n = 10, 300 mu L injections of 1 x 10(-5) mol L(-1) EtX(-)). Two practical applications demonstrate the versatility of the FIA method: (i) evaluation the free EtX(-) concentration during a laboratory study of the EtX(-) adsorption capacity on pulverized sulfide ore (pyrite) and (ii) monitoring of EtX(-) at different stages (from starting load to washing effluents) of a flotation pilot plant processing a Cu-Zn sulfide ore. (C) 2010 Elsevier By. All rights reserved.

The intramolecular charge transfer in a donor-pi-acceptor dianion probed by resonance Raman spectroscopy and quantum chemical calculations

The dideprotonation of 4-(4-nitrophenylazo)resorcinol generates an anionic species with substantial electronic pi delocalization. As compared to the parent neutral species, the anionic first excited electronic transition, characterized as an intramolecular charge transfer (ICT) from the CO(-) groups to the NO(2) moiety, shows a drastic red shift of ca. 200 nm in the lambda(max) in the UV-vis spectrum, leading to one of the lowest ICT energies observed (lambda(max) = 630 nm in dimethyl sulfoxide (DMSO)) in this class of push-pull molecular systems. Concomitantly, a threefold increase in the molar absorptivity (epsilon(max)) in comparison to the neutral species is observed. The resonance Raman enhancement profiles reveal that in the neutral species the chromophore involves several modes, as nu(C-N), nu(N=N), nu(C=C) and nu(s)(NO(2)), whereas in the dianion, there is a selective enhancement of the NO(2) vibrational modes. The quantum chemical calculations of the electronic transitions and vibrational wavenumbers led to a consistent analysis of the enhancement patterns observed in the resonance Raman spectra. Copyright (C) 2009 John Wiley & Sons, Ltd.

Effects of a high fat diet on liver mitochondria: increased ATP-sensitive K(+) channel activity and reactive oxygen species generation

High fat diets are extensively associated with health complications within the spectrum of the metabolic syndrome. Some of the most prevalent of these pathologies, often observed early in the development of high-fat dietary complications, are non-alcoholic fatty liver diseases. Mitochondrial bioenergetics and redox state changes are also widely associated with alterations within the metabolic syndrome. We investigated the mitochondrial effects of a high fat diet leading to non-alcoholic fatty liver disease in mice. We found that the diet does not substantially alter respiratory rates, ADP/O ratios or membrane potentials of isolated liver mitochondria. However, H(2)O(2) release using different substrates and ATP-sensitive K(+) transport activities are increased in mitochondria from animals on high fat diets. The increase in H(2)O(2) release rates was observed with different respiratory substrates and was not altered by modulators of mitochondrial ATP-sensitive K(+) channels, indicating it was not related to an observed increase in K(+) transport. Altogether, we demonstrate that mitochondria from animals with diet-induced steatosis do not present significant bioenergetic changes, but display altered ion transport and increased oxidant generation. This is the first evidence, to our knowledge, that ATP-sensitive K(+) transport in mitochondria can be modulated by diet.

Wettability of Aqueous Rhamnolipids Solutions Produced by Pseudomonas aeruginosa LBI

The wetting behavior of rhamnolipids produced by Pseudomonas aeruginosa LBI strain grown on waste oil substrate and sodium dodecyl sulfate (SDS) on glass, polyethylene terephthalate (PET), poly(vinyl chloride) (PVC), poly(epsilon-caprolactone) (PCL) and polymer blend (PVC-PCL) was investigated by the measuring contact angle of sessile drops, to determine the wetting characteristics of rhamnolipids. The comparison of the wetting profiles showed that at low SDS and rhamnolipid concentrations, the contact angle increased and when the concentration of the surfactant increased further, the contact angle decreased. The blend surface (PVC-PCL) showed better wettability than the homopolymers themselves and the blend changed the surface hydrophobicity of the polymer, making it more hydrophilic. The rhamnolipids produced by the LBI strain exhibited superior wetting abilities than the chemical surfactant SDS one. This is the first work that evaluates the wetting properties of rhamnolipids on polymer blends.

A quantum chemical study on a set of non-imidazole H(3) antihistamine molecules

Molecular orbital calculations were carried out on a set of 28 non-imidazole H(3) antihistamine compounds using the Hartree-Fock method in order to investigate the possible relationships between electronic structural properties and binding affinity for H3 receptors (pK(i)). It was observed that the frontier effective-for-reaction molecular orbital (FERMO) energies were better correlated with pK(i) values than highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy values. Exploratory data analysis through hierarchical cluster (HCA) and principal component analysis (PCA) showed a separation of the compounds in two sets, one grouping the molecules with high pK(i) values, the other gathering low pK(i) value compounds. This separation was obtained with the use of the following descriptors: FERMO energies (epsilon(FERMO)), charges derived from the electrostatic potential on the nitrogen atom (N(1)), electronic density indexes for FERMO on the N(1) atom (Sigma((FERMO))c(i)(2)). and electrophilicity (omega`). These electronic descriptors were used to construct a quantitative structure-activity relationship (QSAR) model through the partial least-squares (PLS) method with three principal components. This model generated Q(2) = 0.88 and R(2) = 0.927 values obtained from a training set and external validation of 23 and 5 molecules, respectively. After the analysis of the PLS regression equation and the values for the selected electronic descriptors, it is suggested that high values of FERMO energies and of Sigma((FERMO))c(i)(2), together with low values of electrophilicity and pronounced negative charges on N(1) appear as desirable properties for the conception of new molecules which might have high binding affinity. 2010 Elsevier Inc. All rights reserved.

Comparação estratigráfica e isotópica (Sm-Nd) das regiões do Cerro Morado e La Torre, bacia de Ischigualasto-Villa Unión, noroeste argentino

A bacia de Ischigualasto-Villa Unión (Stipanicic e Bonaparte, 1972), que consiste de uma bacia alongada no sentido NW-SE e preenchida por rochas sedimentares Triássicas, foi gerada durante o Eo-Triássico pela reativação de descontinuidades crustais pré-existentes, associadas ao Gondwanides, na região central andina. Esta limitada a oeste, pelo vale do Rio Bermejo, no qual se encontra a zona de sutura do Vale Fértil, que se caracteriza pela borda ativa da bacia. Aqui, apresentar-se-á uma revisão da estratigrafia da bacia de Ischigualasto-Villa Unión, detalhando-se duas áreas chaves do registro estratigráfico inferior da bacia, na região do Cerro Morado e La Torre. Nestas áreas utilizou-se de técnicas estratigráficas e isotópicas (Sm-Nd em rocha total), com o objetivo de estabelecer uma correlação entre seus registros estratigráficos e suas áreas-fonte, além de caracterizar o comportamento tectônico. Ambos os perfis apresentam na porção inferior o preenchimento por um sistema aluvial-fluvial (Formação Tarjados sensu Romer & Jensen, 1966), subdividido em 4 associações de fácies: leques aluviais, canais fluviais, barras longitudinais e planície de inundação; e, na porção superior, o preenchimento por um sistema lacustre-deltáico (Formação Los Chañares sensu Frenguelli, 1944, no Cerro Morado e, Formação Lomas Blancas sensu Bossi e Herbst, 1968, em La Torre), subdividido em 4 associações de fácies: lacustre, pró delta, frente deltáica e planicie deltáica. Sobre as últimas unidades ocorre um lacólito de diabásio (Formação Los Baldecitos) A formação Tarjados apresenta as maiores idades TDM na região do Cerro Morado, variando entre 1,33 e 1,60 Ga, enquanto que em La Torre os valores oscilam entre 1,03 e 1,30 Ga. Isso é interpretado aqui como uma variação da área fonte entre as duas regiões na época de sua sedimentação, cujas regiões poderiam estar compartimentadas em termos tectônicos a época de sua deposição. A formação Los Chañares possui idades TDM variando entre 0,90 e 1,36 Ga, e a formação Lomas Blancas possui idades TDM entre 0,99 e 1,35 Ga, com dominância de valores próximos a 1 Ga nos dois blocos. Os diabásios da formação Los Baldecitos possuem idades TDM entre 0,51 e 0,33 Ga, cujo dado é interpretado com uma extração mantélica próxima a 130 Ma de um manto modificado pela orogenia do Ciclo Gondwânico, ou até mesmo pelo processo de slab break-off da crosta oceânica consumida pela colisão do micro-continente Cuyania com a proto-margem do Gondwana (Ramos, 1999). Todas as rochas dessa formação obtiveram valores de Epsilon Nd positivos. A integração dos dados estratigráficos e isotópicos nos permite interpretar as duas áreas como meio-grábens distintos na etapa inicial de preenchimento, em função da discrepância entre as idades TDM entre as áreas. A partir da transgressão lacustre as áreas-fonte são uniformizadas e o alto estrutural pré-existente é transgredido.

Nonautonomous difference equations with applications

This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation. In the second part we present some concrete models that are used in ecology/biology and economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models. One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter space of the autonomous Ricker competition model. Since the dynamics of the Ricker competition model is similar to the logistic competition model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results. Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.