ON THE COMPOSITE OF THREE IRREDUCIBLE MORPHISMS IN THE FOURTH POWER OF THE RADICAL

We study here the nonzero composite of three irreducible morphisms between indecomposable modules lying in the fourth power of the radical.

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Birkhoffian Systems in Infinite Dimensional Manifolds

We generalize the theory of Kobayashi and Oliva (On the Birkhoff Approach to Classical Mechanics. Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo, 2003) to infinite dimensional Banach manifolds with a view towards applications in partial differential equations.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

Stacked central configurations for the spatial six-body problem

In this paper we show the existence of three new families of stacked spatial central configurations for the six-body problem with the following properties: four bodies are at the vertices of a regular tetrahedron and the other two bodies are on a line connecting one vertex of the tetrahedron with the center of the opposite face. (c) 2009 Elsevier B.V. All rights reserved.

Cys mutants in functional regions of Sticholysin I clarify the participation of these residues in pore formation

Experimental evidence shows that the mechanism of pore formation by actinoporins is a multistep process, involving binding of the water-soluble monomer to the membrane and subsequent oligomerization on the membrane surface, leading to the formation of a functional pore. However, as for other eukaryotic pore-forming toxins, the molecular details of the mechanism of membrane insertion and oligomerization are not clear. In order to obtain further insight with regard to the structure-function relationship in sticholysins, we designed and produced three cysteine mutants of recombinant sticholysin I (rStI) in relevant functional regions for membrane interaction: StI E2C and StI F15C (in the N-terminal region) and StI R52C (in the membrane binding site). The conformational characterization derived from fluorescence and CD spectroscopic studies of StI E2C, StI F15C and StI R52C suggests that replacement of these residues by Cys in rStI did not noticeably change the conformation of the protein. The substitution by Cys of Arg(52) in the phosphocholine-binding site, provoked noticeable changes in rStI permeabilizing activity; however, the substitutions in the N-terminal region (Glu(2), Phe(15)) did not modify the toxin`s permeabilizing ability. The presence of a dimerized population stabilized by a disulfide bond in the StI E2C mutant showed higher pore-forming activity than when the protein is in the monomeric state, suggesting that sticholysins pre-ensembled at the N-terminal region could facilitate pore formation. (C) 2011 Elsevier Ltd. All rights reserved.

Total phenolic content and free radical scavenging activities of methanolic extract powders of tropical fruit residues

Methanolic extract powders of acerola, passion fruit and pineapple industrial residues, including pulp, seeds and peel, altogether (except for acerola) devoid of seeds, were screened for antioxidant capacity. The total phenolic contents (TPCs) of the extract powders were compared with their radical-scavenging activities (RSA) against both DPPH(center dot) and superoxide anion (O(2)(center dot-)) radicals, and their protective effect against liposome peroxidation, triggered by peroxyl radical. Lipid peroxidation was followed by the fluorescence decay of the probe, 4,4-difluoro-5-(4-phenyl-1,3-butadienyl)-4-bora-3a,4a-diaza-s-indacene-3-undecanoic acid (C(11)-BODIPY(581/591)). The TPCs of acerola, passion fruit and pineapple extract powders were (94.6 +/- 7.4); (41.2 +/- 4.2) and (9.1 +/- 1.3) mg of gallic acid equivalents g(-1) of dry extract, respectively. Acerola showed the best RSA-DPPH(center dot) scores, whereas passion fruit was more protective on the RSA-O(2)(center dot-) system. Together with the protective effects against lipid peroxidation (rate of BODIPY decay) which, were similar for acerola and passion fruit extracts, these data suggest that the methanolic extracts of acerola and passion fruit residues may be useful as antioxidant supplements, particularly the acerola extract, due to its high phenolic content. (C) 2008 Elsevier Ltd. All rights reserved

Useful Strategies for Algal Volatile Analysis

The production of volatile organic compounds (VOC) by plants is well known. However, few scientific groups have studied VOC produced by green, brown and red algae. Headspace collection of volatiles and solid phase microextraction, as well as the traditional extraction by hydrodistillation combined with analytical chromatographic techniques (i.e., GC-MS), have significantly improved the investigation of VOC from plants and algae. The major volatile compounds found in seaweeds are hydrocarbons, terpenes, phenols, alcohols, aldehydes, ketones, esters, fatty acids and halogen or sulfur-containing compounds. This article presents an overview of VOC isolated from and identified in marine macro-algae. Focus is given to non-halogenated and non-sulfur volatile compounds, as well as strategies to analyze and identify algal VOC by GC-MS.

Biochemical composition of two red seaweed species grown on the Brazilian coast

BACKGROUND: Algae species have been used as an important source of food because they are highly nutritive considering their vitamin, protein, mineral, fiber, essential fatty acid and carbohydrate contents. However, a large number of seaweeds have been poorly studied, especially Brazilian species. Two red macroalgae species from the Brazilian coast (Plocamium brasiliense and Ochtodes secundiramea) were assessed with respect to their total lipid, fatty acid, total nitrogen, protein, amino acid and total carbohydrate contents. RESULTS: The total lipid contents (dry weight) were 36.3 and 35.4 g kg(-1); fatty acid contents were 9.3 and 12.1 g kg(-1); total nitrogen contents were 37.4 and 24.9 g kg(-1); protein contents were 157.2 and 101.0 g kg(-1); amino acid contents were 127.5 and 91.4 g kg(-1); and total carbohydrate contents were 520.3 and 450.7 g kg(-1) for P. brasiliense and O. secundiramea, respectively. CONCLUSION: Considering these compositions, both algae species were determined to have sources of protein, essential amino acids and carbohydrates similar to the edible seaweeds Laminaria japonica and Palmaria palmata. (C) 2011 Society of Chemical Industry

Alteration of purinergic P2X(4) and P2X(7) receptor expression in rats with temporal-lobe epilepsy induced by pilocarpine

Although ATP and P2X receptor activity have been lately associated with epilepsy, little is known regarding their exact roles in epileptogenesis. Temporal-lobe epilepsy (TLE) in rat was induced by pilocarpine in order to study changes of hippocampal P2X(2), P2X(4) and P2X(7) receptor expression during acute, latent or chronic phases of epilepsy. During acute and chronic phases increased P2X(7) receptor expression was principally observed in glial cells and glutamatergic nerve terminals, suggesting participation of this receptor in the activation of inflammatory and excitotoxic processes during epileptogenesis. No significant alterations of hippocampal P2X(2) and P2X(4) receptor expression was noted during the acute or latent phase when compared to the control group, indicating that these receptors are not directly involved with the initiation of epilepsy. However, the reduction of hippocampal P2X(4) receptor immunostaining in the chronic phase could reflect neuronal toss or decreased GABAergic signaling. (C) 2008 Elsevier B.V. All rights reserved.