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.

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.

A novel physiological property of snake bradykinin-potentiating peptides-Reversion of MK-801 inhibition of nicotinic acetylcholine receptors

The first naturally occurring angiotensin-converting enzyme (ACE) inhibitors described are pyroglutamyl proline-rich oligopeptides, found in the venom of the viper Bothrops jararaca, and named as bradykinin-potentiating peptides (BPPs). Biochemical and pharmacological properties of these peptides were essential for the development of Captopril, the first active site-directed inhibitor of ACE, currently used for the treatment of human hypertension. However, a number of data have suggested that the pharmacological activity of BPPs could not only be explained by their inhibitory action on enzymatic activity of somatic ACE. In fact, we showed recently that the strong and long-lasting anti-hypertensive effect of BPP-10c [

Effect of polyol excess on the electrical property of vegetable-polyurethane film

Freestanding castor oil-based polyurethane (PU) film was obtained using spin-coating method. The effect of polyol content was analysed by means of thermally stimulated depolarisation current and AC dielectric measurements techniques. Two relaxation peaks were observed in the temperature range of -40 to 60 degrees C for PU with different polyol contents. The presence of polyol excess provides a shift to lower temperature of the a relaxation and the decrease in the activation energy of the transition in this region might be attributed to the plasticising effect of the polyol. The peak at higher temperature is due to the Maxwell-Wagner-Sillars relaxation, which also shifts in the low temperature direction as the polyol content is increased.