Minimal Geodesics on Manifolds with Discontinuous Metrics

The paper describes some qualitative properties of minimizerson a manifold M endowed with a discontinuous metric. The discontinuityoccurs on a hypersurface disconnecting M. Denote by ₁ and₂ the open subsets of M such that M\ =₁₂. Assume that and are endowed with metrics ·, · ₍₁₎ and ·,·₍₂₎, respectively, such that (i=1, 2) is convex or concave. The existence of a minimizerof the length functional on curves joining two given pointsof M is proved. The qualitative properties obtained allows therefraction law in a very general situation to be described.     

On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian systems

We prove the existence of infinitely many homoclinic orbits on a Riemannian manifold (possibly non-compact), for a class of second order Hamiltonian systems of the form: $$D_t \dot x(t) + grad_x V(t,x(t)) = 0$$ where the potentialV isT-periodic in the time variable.     

ALS-associated mutant SOD1<Superscript>G93A</Superscript> causes mitochondrial vacuolation by expansion of the intermembrane space and by involvement of SOD1 aggregation and peroxisomes

Background  

Amyotrophic lateral sclerosis (ALS) is an age-dependent neurodegenerative disease that causes motor neuron degeneration, paralysis and death. Mutations in Cu, Zn superoxide dismutase (SOD1) are one cause for the familial form of this disease. Transgenic mice expressing mutant SOD1 develop age-dependent motor neuron degeneration, skeletal muscle weakness, paralysis and death similar to humans. The mechanism whereby mutant SOD1 induces motor neuron degeneration is not understood but widespread mitochondrial vacuolation has been observed during early phases of motor neuron degeneration. How this vacuolation develops is not clear, but could involve autophagic vacuolation, mitochondrial permeability transition (MPT) or uncharacterized mechanisms. To determine which of these possibilities are true, we examined the vacuolar patterns in detail in transgenic mice expressing mutant SOD1^G93A.     

Dichlorocarbene Addition to

In contrast to the terminal phosphinidene complex PhPW(CO)(5) (2), which adds to [5]metacyclophane (1) in a 1,4-fashion, dichlorocarbene preferentially adds in a 1,2-fashion to the formal "anti-Bredt" type double bond of the aromatic ring of 1 to afford the norcaradiene 11b, which immediately rearranges to the bridged cycloheptatriene 12b and further by a [1,5] sigmatropic chlorine migration to the isomeric 13b as the first observable product. More slowly, the latter isomerizes via a dissociative mechanism to give 15b. A computational study supports the notion that the [1,5] chlorine migration in the rearrangement 12b --> 13b, for which an activation barrier of 70.2 kJ mol(-)(1) was calculated, is essentially concerted with minor charge separation. In contrast, the analogous [1,5] chlorine migration in the flat model compound 7,7-dichlorocycloheptatriene (12a) displays features of a dissociative pathway.     

Bounce trajectories with one Bounce point

Summary In this paper we study the existence of bounce trajectories, under the action of a potential field, having only one bounce point and joining two prescribed points in a bounded regular domain ofR ^N.Work supported by M.P.I. and G.N.A.F.A.     

The dynamical behavior of homogeneous scalar-field spacetimes with general self-interaction potentials

The dynamics of homogeneous Robertson–Walker cosmological models with a self-interacting scalar field source is examined here in full generality, requiring only the scalar field potential to be bounded from below and divergent when the field diverges. In this way we are able to give a unified treatment of all the already studied cases—such as positive potentials which exhibit asymptotically polynomial or exponential behaviors—together with its extension to a much wider set of physically sensible potentials. Since the set includes potentials with negative inferior bound, we are able to give, in particular, the analysis of the asymptotically anti De Sitter states for such cosmologies.