Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

Use of copper and gold electrodes as sensitive elements for fabrication of an electronic tongue: Discrimination of wines and whiskies

A low-cost method is proposed to classify wine and whisky samples using a disposable voltammetric electronic tongue that was fabricated using gold and copper substrates and a pattern recognition technique (Principal Component Analysis). The proposed device was successfully used to discriminate between expensive and cheap whisky samples and to detect adulteration processes using only a copper electrode. For wines, the electronic tongue was composed of copper and gold working electrodes and was able to classify three different brands of wine and to make distinctions regarding the wine type, i.e., dry red, soft red, dry white and soft white brands. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.

Effects of alloying elements on the cytotoxic response of titanium alloys

Titanium alloys, alloys, especially beta-type alloys containing beta-stabilizing elements, constitute a highly versatile category of metallic materials that have been under constant development for application in orthopedics and dentistry. This type of alloy generally presents a high mechanical strength-to-weight ratio, excellent corrosion resistance and low elastic modulus. The purpose of this study is to evaluate the cytotoxicity and adhesion of fibroblast cells on titanium alloy substrates containing Nb, Ta, Zr, Cu, Sn and Mo alloying elements. Cells cultured on polystyrene were used as controls. In vitro results with Vero cells demonstrated that the tested materials, except Cu-based alloy, presented high viability in short-term testing. Adhesion of cells cultured on disks showed no differences between the materials and reference except for the Ti-Cu alloy, which showed reduced adhesion attributed to poor metabolic activity. Titanium alloys with the addition of Nb, Ta, Zr, Sn and Mo elements show a promising potential for biomedical applications. (C) 2011 Elsevier B.V. All rights reserved.

Knowledge translation in Uganda : a qualitative study of Ugandan midwives' and managers' perceived relevance of the sub-elements of the context cornerstone in the PARIHS framework

BACKGROUND: A large proportion of the annual 3.3 million neonatal deaths could be averted if there was a high uptake of basic evidence-based practices. In order to overcome this 'know-do' gap, there is an urgent need for in-depth understanding of knowledge translation (KT). A major factor to consider in the successful translation of knowledge into practice is the influence of organizational context. A theoretical framework highlighting this process is Promoting Action on Research Implementation in Health Services (PARIHS). However, research linked to this framework has almost exclusively been conducted in high-income countries. Therefore, the objective of this study was to examine the perceived relevance of the subelements of the organizational context cornerstone of the PARIHS framework, and also whether other factors in the organizational context were perceived to influence KT in a specific low-income setting. METHODS: This qualitative study was conducted in a district of Uganda, where focus group discussions and semi-structured interviews were conducted with midwives (n = 18) and managers (n = 5) within the catchment area of the general hospital. The interview guide was developed based on the context sub-elements in the PARIHS framework (receptive context, culture, leadership, and evaluation). Interviews were transcribed verbatim, followed by directed content analysis of the data. RESULTS: The sub-elements of organizational context in the PARIHS framework--i.e., receptive context, culture, leadership, and evaluation--also appear to be relevant in a low-income setting like Uganda, but there are additional factors to consider. Access to resources, commitment and informal payment, and community involvement were all perceived to play important roles for successful KT. CONCLUSIONS: In further development of the context assessment tool, assessing factors for successful implementation of evidence in low-income settings--resources, community involvement, and commitment and informal payment--should be considered for inclusion. For low-income settings, resources are of significant importance, and might be considered as a separate subelement of the PARIHS framework as a whole.