Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then 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, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

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.

Mycoplasmal lipid-associated membrane proteins and Mycoplasma arthritidis mitogen recognition by serum antibodies from patients with rheumatoid arthritis

Mycoplasmal lipid-associated membrane proteins (LAMPs) and Mycoplasma arthritidis mitogen (MAM superantigen) are potent stimulators of the immune system. The objective of this work was to detect antibodies to MAM and LAMPs of Mycoplasma hominis and M. fermentans in the sera of patients affected by rheumatoid arthritis (RA) and systemic lupus erythematosus (SLE) to identify mycoplasmal products that can be involved in the etiopathogenesis of these autoimmune diseases. Serum samples from female RA and SLE patients and controls, recombinant MAM, and LAMPs of M. hominis PG21 and M. fermentans PG18 were used in Western blot assays. A similar frequency of sera from patients and controls reactive to MAM was detected. A larger number of M. hominis and M. fermentans LAMPs were recognized by sera from RA patients than controls, but no differences were detected between sera from SLE patients and controls. Among the LAMPs recognized by IgG antibodies from RA patients, proteins of molecular masses in a range of < 49 and a parts per thousand yen20 KDa (M. hominis) and < 102 and a parts per thousand yen58 KDa (M. fermentans) were the most reactive. These preliminary results demonstrate the strong reactivity of antibodies of RA patients with some M. hominis and M. fermentans LAMPs. These LAMPs could be investigated as mycoplasmal antigens that can take part in the induction or amplification of human autoimmune responses.

The genotoxic effects of DNA lesions induced by artificial UV-radiation and sunlight

Solar radiation sustains and affects all life forms on Earth. The increase in solar UV-radiation at environmental levels, due to depletion of the stratospheric ozone layer, highlights serious issues of social concern. This becomes still more dramatic in tropical and subtropical regions where radiation-intensity is still higher. Thus, there is the need to evaluate the harmful effects of solar UV-radiation on the DNA molecule as a basis for assessing the risks involved for human health, biological productivity and ecosystems. In order to evaluate the profile of DNA damage induced by this form of radiation and its genotoxic effects, plasmid DNA samples were exposed to artificial-UV lamps and directly to sunlight. The induction of cyclobutane pyrimidine dimer photoproducts (CPDs) and oxidative DNA damage in these molecules were evaluated by means of specific DNA repair enzymes. On the other hand, the biological effects of such lesions were determined through the analysis of the DNA inactivation rate and mutation frequency, after replication of the damaged pCMUT vector in an Escherichia coli MBL50 strain. The results indicated the induction of a significant number of CPDs after exposure to increasing doses of UVC, UVB, UVA radiation and sunlight. Interestingly, these photoproducts are those lesions that better correlate with plasmid inactivation as well as mutagenesis, and the oxidative DNA damages induced present very low correlation with these effects. The results indicated that DNA photoproducts play the main role in the induction of genotoxic effects by artificial UV-radiation sources and sunlight. (C) 2010 Elsevier B.V. All rights reserved.

Determinants of Accelerated Small Intestinal Transit in Alcohol-Related Chronic Pancreatitis

Patients with chronic pancreatitis may have abnormal gastrointestinal transit, but the factors underlying these abnormalities are poorly understood. Gastrointestinal transit was assessed, in 40 male outpatients with alcohol-related chronic pancreatitis and 18 controls, by scintigraphy after a liquid meal labeled with (99m)technetium-phytate. Blood and urinary glucose, fecal fat excretion, nutritional status, and cardiovascular autonomic function were determined in all patients. The influence of diabetes mellitus, malabsorption, malnutrition, and autonomic neuropathy on abnormal gastrointestinal transit was assessed by univariate analysis and Bayesian multiple regression analysis. Accelerated gastrointestinal transit was found in 11 patients who showed abnormally rapid arrival of the meal marker to the cecum. Univariate and Bayesian analysis showed that diabetes mellitus and autonomic neuropathy had significant influences on rapid transit, which was not associated with either malabsorption or malnutrition. In conclusion, rapid gastrointestinal transit in patients with alcohol-related chronic pancreatitis is related to diabetes mellitus and autonomic neuropathy.

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.