Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds I: Resolvent construction at high energy

This is the first in a series of papers in which we investigate the resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds with applications to the restriction theorem, spectral multiplier results and Strichartz estimates. In this first paper, we use semiclassical Lagrangian distributions and semiclassical intersecting Lagrangian distributions, along with Mazzeo-Melrose 0-calculus, to construct the high energy resolvent on general non- trapping asymptotically hyperbolic manifolds, generalizing the work due to Melrose, Sa Barreto and Vasy. We note that there is an independent work by Y. Wang which also constructs the high-energy resolvent.Comment: 49 page

The Inverse-Compton And Extragalactic Components Of The Diffuse Gamma-Ray Emission

We present spectra of the inverse-Compton and extragalactic components of the high-energy gamma-radiation based on an analysis of the emission at high galactic latitudes ($\vert$b$\vert$ $\geq$ $30\deg$). We correlate the gamma-ray intensity with a model consisting of an isotropic component, a component proportional to the 408 MHz synchrotron radiation, and a component proportional to atomic hydrogen (H I) column density with different emissivities in eight galactic octants. The spectrum of gamma-radiation that is correlated with the H I column density indicates that this component originates in cosmic-ray/matter interactions. The cosmic-ray electrons which produce the 408 MHz radio continuum emission also produce gamma-radiation through inverse-Compton interactions with interstellar photons. By correlating the gamma-radiation with the 408 MHz continuum, we measure the spectrum and absolute intensity of the IC emission. The isotropic component gives us the spectrum and intensity of the extragalactic gamma-radiation. We discuss interpretation of the extragalactic spectrum.Comment: 21 page Postscript file, 10 Postscript figure

How China's Palm Oil Imports Impact Its Soybean Oil Imports

International Relations/Trade,