Polar orthogonal representations of real reductive algebraic groups

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar orthogonal representations of real reductive algebraic groups which slightly generalizes some results of the structural theory of real reductive Lie algebras. (c) 2008 Elsevier Inc. All rights reserved.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.

NEW CHARACTERIZATIONS OF COMPLETE SPACELIKE SUBMANIFOLDS IN SEMI-RIEMANNIAN SPACE FORMS

In this paper we study n-dimensional complete spacelike submanifolds with constant normalized scalar curvature immersed in semi-Riemannian space forms. By extending Cheng-Yau`s technique to these ambients, we obtain results to such submanifolds satisfying certain conditions on both the squared norm of the second fundamental form and the mean curvature. We also characterize compact non-negatively curved submanifolds in De Sitter space of index p.

Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2. (C) 2008 Elsevier Inc. All rights reserved.

The Borsuk-Ulam theorem for homotopy spherical space forms

In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the types of these spaces which admit a free involution are characterized. The case of even-dimensional homotopy spherical space forms is basically known.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Dynamics of Dissolved Forms of Carbon and Inorganic Nitrogen in Small Watersheds of the Coastal Atlantic Forest in Southeast Brazil

Based on the fact that streamwater quality reflects landscape conditions, the objectives of this study were: to investigate nitrogen (N), carbon (C), and major ion concentrations in six streams crossing minimally disturbed Atlantic Forest areas, with similar geomorphological characteristics; to determine N and C fluxes in one of these pristine streams (Indaia); and assess the impact of human activity on the biogeochemistry of two other streams in the same region, crossing urbanized areas. The distribution pattern of carbon and inorganic nitrogen dissolved forms, as well as the major ion and biogenic gas concentrations in the streamwater, was similar in pristine streams, indicating that the C and N dynamics were determined by influence of some factors, such as climate, atmospheric deposition, geology, soil type, and land covering, which were analogous in the forested watersheds. The urban streams were significantly different from the pristine streams, showing low dissolved oxygen concentrations, high respiration rates, and high concentrations of carbon dioxide, dissolved inorganic nitrogen, dissolved inorganic carbon, and major ion. These differences were attributed to anthropogenic impact on water quality, especially domestic sewage discharge. Additionally, in the Indaia stream, it was possible to observe the importance of rainfall over temporal dynamics of dissolved carbon forms, and also, the obtained specific flux of dissolved inorganic nitrogen was relatively elevated (approximately 11 kg ha(-1) year(-1)). These results reveal the influence of human activity over the biogeochemistry of coastal streams and also indicate the importance N export of Atlantic Forest to the ocean.

Use of L-Proline and ATP Production by Trypanosoma cruzi Metacyclic Forms as Requirements for Host Cell Invasion

The process of host cell invasion by Trypanosoma cruzi depends on parasite energy. What source of energy is used for that event is not known. To address this and other questions related to T. cruzi energy requirements and cell invasion, we analyzed metacyclic trypomastigote forms of the phylogenetically distant CL and G strains. For both strains, the nutritional stress experienced by cells starved for 24, 36, or 48 h in phosphate-buffered saline reduced the ATP content and the ability of the parasite to invade HeLa cells proportionally to the starvation time. Inhibition of ATP production by treating parasites with rotenone plus antimycin A also diminished the infectivity. Nutrient depletion did not alter the expression of gp82, the surface molecule that mediates CL strain internalization, but increased the expression of gp90, the negative regulator of cell invasion, in the G strain. When L-proline was given to metacyclic forms starved for 36 h, the ATP levels were restored to those of nonstarved controls for both strains. Glucose had no such effect, although this carbohydrate and L-proline were transported in similar fashions. Recovery of infectivity promoted by L-proline treatment of starved parasites was restricted to the CL strain. The profile of restoration of ATP content and gp82-mediated invasion capacity by L-proline treatment of starved Y-strain parasites was similar to that of the CL strain, whereas the Dm28 and Dm30 strains, whose infectivity is downregulated by gp90, behaved like the G strain. L-Proline was also found to increase the ability of the CL strain to traverse a gastric mucin layer, a property important for the establishment of T. cruzi infection by the oral route. Efficient translocation of parasites through gastric mucin toward the target epithelial cells in the stomach mucosa is an essential requirement for subsequent cell invasion. By relying on these closely associated ATP-driven processes, the metacyclic trypomastigotes effectively accomplish their internalization.

Fonsecaea pedrosoi infection induces differential modulation of costimulatory molecules and cytokines in monocytes from patients with severe and mild forms of chromoblastomycosis

The host defense mechanism in chromoblastomycosis has not been thoroughly investigated. It has been suggested that cell- mediated immunity in patients with long- standing chromoblastomycosis is somehow impaired. As a result, these individuals became unable to develop an efficient immune reaction. Many studies have shown that monocyte- derived macrophages exhibit critical activities in immunity to microorganisms. Moreover, the ability of cells from the monocytic lineage to process and present antigens, to produce cytokines, and to provide costimulatory signals confirms their pivotal role in the initiation of specific immune responses. In the present study, it was observed that monocytes from patients with a severe form of disease had a higher production of IL- 10 and a lower expression of HLA- DR and costimulatory molecules when stimulated with specific antigen or LPS. Immune modulation with recombinant IL- 12 or anti- IL- 10 can restore the antigen- specific Th1- type immune response in chromoblastomycosis patients by up- regulating HLA- DR and costimulatory molecules in monocytes. Therefore, our data show that monocytes from patients with different clinical forms of chromoblastomycosis present distinct phenotypic and functional profiles. This observation suggests possible mechanisms that control the T cell response and influence their role in the development of pathology.

Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model

In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function lambda(t), t >= 0. This rate function also depends on some parameters that need to be estimated. Two forms of lambda(t), t >= 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright (C) 2007 John Wiley & Sons, Ltd.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

Mixture of changing uniaxial micellar forms in lyotropic biaxial nematics

Lyotropic nematics consisting of surfactant-cosurfactant water solutions may present a biaxial phase or direct U(+) <-> U(-) transitions, in different regions of the temperature-relative concentration phase diagram, for different systems and compositions. We propose that these may be related to changes of uniaxial micellar form, which may occur either smoothly or abruptly. Smooth change of cylinder-like into disc-like shapes requires a distribution of Maier-Saupe interaction constants and we consider two limiting cases for the distribution of forms: a single Gaussian and a double Gaussian. Alternatively, an abrupt change of form is described by a discontinuous distribution of interaction constants. Our results show that the dispersive distributions yield a biaxial phase, while an abrupt change of shape leads to coexistence of uniaxial phases. Fitting the theory to the experiment for the ternary system KL/decanol/D2O leads to transition lines in very good agreement with experimental results. In order to rationalise the results of the comparison, we analyse temperature and concentration form dependence, which connects micellar and experimental macroscopic parameters. Physically consistent variations of micellar asymmetry, amphiphile partitioning and volume are obtained. To the best of the authors` knowledge, this is the first truly statistical microscopic approach that is able to model experimentally observed lyotropic biaxial nematic phases.

Irreducible morphisms of categories of complexes

We study irreducible morphisms of complexes. In particular, we show that the irreducible morphisms having one (finite) irreducible submorphism fall into three canonical forms and we give necessary and sufficient conditions for a given morphism of that type to be irreducible. Our characterization of the above mentioned type of irreducible morphisms of complexes characterizes also some class of irreducible morphisms of the derived category D(-)(A) for A a finite dimensional k-algebra, where k is a field. (C) 2009 Published by Elsevier Inc.

On automorphisms of split metacyclic groups

Let D( m, n; k) be the semi-direct product of two finite cyclic groups Z/m = < x > and Z/n = < y >, where the action is given by yxy(-1) = x(k). In particular, this includes the dihedral groups D(2m). We calculate the automorphism group Aut (D(m, n; k)).