Total absolute horospherical curvature of submanifolds in hyperbolic space

We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in 3-space and the horospherical Fenchel and Fary-Milnor`s theorems.

Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Cloning, expression, purification and characterization of recombinant glutathione-S-transferase from Xylella fastidiosa

Xylella fastidiosa is an important pathogen bacterium transmitted by xylem-feedings leafhoppers that colonizes the xylem of plants and causes diseases on several important crops including citrus variegated chlorosis (CVC) in orange and lime trees. Glutathione-S-transferases (GST) form a group of multifunctional isoenzymes that catalyzes both glutathione (GSH)-dependent conjugation and reduction reactions involved in the cellular detoxification of xenobiotic and endobiotic compounds. GSTs are the major detoxification enzymes found in the intracellular space and mainly in the cytosol from prokaryotes to mammals, and may be involved in the regulation of stress-activated signals by suppressing apoptosis signal-regulating kinase 1. In this study, we describe the cloning of the glutathione-S-transferase from X. fastidiosa into pET-28a(+) vector, its expression in Escherichia coli, purification and initial structural characterization. The purification of recombinant xfGST (rxfGST) to near homogeneity was achieved using affinity chromatography and size-exclusion chromatography (SEC). SEC demonstrated that rxfGST is a homodimer in solution. The secondary and tertiary structures of recombinant protein were analyzed by circular dichroism and fluorescence spectroscopy, respectively. The enzyme was assayed for activity and the results taken together indicated that rxfGST is a stable molecule, correctly folded, and highly active. Several members of the GST family have been extensively studied. However, xfGST is part of a less-studied subfamily which yet has not been structurally and biochemically characterized. In addition, these studies should provide a useful basis for future studies and biotechnological approaches of rxfGST. (C) 2008 Elsevier Inc. All rights reserved.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim