Resonance Identities for Closed Characteristics on Compact Star-shaped Hypersurfaces in R2n{\bf R}^{2n}

Resonance relations among periodic orbits on given energy hypersurfaces are very important for getting deeper understanding of the dynamics of the corresponding Hamiltonian systems. In this paper, we establish two new resonance identities for closed characteristics on every compact star-shaped hypersurface $\Sigma$ in ${\bf R}^{2n}$ when the number of geometrically distinct closed characteristics on $\Sigma$ is finite, which extend those identities established by C. Viterbo in 1989 for star-shaped hypersurfaces assuming in addition that all the closed characteristics and their iterates are non-degenerate, and that by W. Wang, X. Hu and Y. Long in 2007 for strictly convex hypersurfaces in ${\bf R}^{2n}$.Comment: arXiv admin note: substantial text overlap with arXiv:math/0701608. To appear in Journal of Functional Analysis, this is the final versio

SOUND SCATTERING OF AN OBSTACLE PLACED NEAR A NON-LOCALLY REACTING GROUND

The Boundary Element Method (BEM) is widely used in outdoor sound scattering prob-lems due to its computational efficiency when compared to the FEM (FEM) for certain propagation geometries. The advantage of the BEM is apparent for problem geometries where the scattering surface is much smaller than the computational domain of the prob-lem. The Green\u27s function can be used in the BEM formulation to represent a non-locally reacting porous ground surface. The Weyl Van der Pol formula is often used to accurately calculate the Green\u27s functions above a locally reacting surface. However, the Green’s function representation for the sound field above and below a non-locally reacting ground has not yet been established. Nevertheless, the steepest descent method can be used to derive these functions

Electron Transfer Activity of Mitochondria Neet-Proteins

Mitochondrial NEET proteins are recently discovered iron-sulfur proteins that are localized within mitochondria. There are three NEET proteins: mitoNEET, a type II diabetes drug pioglitazone binding target, a mitoNEET related protein 1 (Miner1 or NAF-1), and a mitoNEET-related protein 2 (Miner2). While both mitoNEET and Miner1 are mitochondrial outer membrane proteins, Miner2 is a mitochondrial matrix protein. All three NEET proteins bind at least one [2Fe-2S] cluster via CDGSH (Cys-Asp-Gly-Ser-His) motif. In this work, we have investigated the electron transfer activity of mitoNEET, and found that the CDGSH-type [2Fe-2S] clusters of mitoNEET can be reduced by the reduced flavin mononucleotide (FMNH2) under anaerobic or aerobic conditions in vitro. We have also found that the reduced mitoNEET [2Fe-2S] clusters can be oxidized by ubiquinone or oxygen. Further studies have demonstrated that the type II diabetes medication pioglitazone may compete for the FMNH2 binding site of mitoNEET, and inhibit the reduction of the mitoNEET [2Fe-2S] clusters by FMNH2. We have also described the inhibitory effect of nitric oxide on the electron transfer activity of the mitochondrial matric protein Miner2. We have found that nitric oxide can bind to the reduced Miner2 [2Fe-2S] clusters without disruption of the cluster, and that visible light excitation can quickly release nitric oxide from the nitric oxide-bound cluster in Miner2. Binding of nitric oxide effectively inhibits the electron transfer activity of the Miner2 [2Fe-2S] clusters. The results suggest that mitochondrial NEET-proteins may play a novel role in energy metabolism in cells, and that nitric oxide may regulate the electron transfer activity of the NEET-proteins and modulate the energy metabolism in mitochondria via directly binding to the [2Fe-2S] clusters in the proteins