A Characterisation of Strong Wave Tails in Curved Space-Times

A characterisation of when wave tails are strong is proposed. The existence of a curvature induced tail (i.e. a Green's function term whose support includes the interior of the light-cone) is commonly understood to cause backscattering of the field governed by the relevant wave equation. Strong tails are characterised as those for which the purely radiative part of the field is backscattered. With this definition, it is shown that electromagnetic waves in asymptotically flat space-times and fields governed by tail-free propagation have weak tails, but minimally coupled scalar fields in a cosmological scenario have strong tails.Comment: 17 pages, Revtex, to appear in Classical and Quantum Gravit

The 3-dimensional cored and logarithm potencials: Periodic orits

Agraïments: The first author is partially supported by CNPq grant 201802/2012-0.We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (1+x2 +(y2 +z2)/q2)1/2, and H(x, y, z, px, py, pz) = (p2x +p2y +p2z/q)/2+ (log(1+x2 +(y2 + z2)/q2))/2, with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ε, we show that both systems give essentially the same set of equations of motion up to first order in ε. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ε, apply equally to both systems in every energy level H = h > 0. The averaging method used proves the existence of at most three periodic orbits, for ε small enough, and gives an analytic approximation for the initial conditions of these periodic orbits

Novel colorectal endoscopic in vivo imaging and resection practice: a short practice guide for interventional endoscopists

Colorectal cancer remains a leading cause of cancer death in the UK. With the advent of screening programmes and developing techniques designed to treat and stage colorectal neoplasia, there is increasing pressure on the colonoscopist to keep up to date with the latest practices in this area. This review looks at the basic principles behind endoscopic mucosal resection and forward to the potential endoscopic tools, including high-magnification chromoscopic colonoscopy, high-frequency miniprobe ultrasound and confocal laser scanning endomicroscopic colonoscopy, that may soon become part of routine colorectal cancer management