Convex Sobolev inequalities and spectral gap

This note is devoted to the proof of convex Sobolev (or generalized Poincar\'{e}) inequalities which interpolate between spectral gap (or Poincar\'{e}) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities with constants which are uniformly bounded in the limit approaching the logarithmic Sobolev inequalities. We recover the case of the logarithmic Sobolev inequalities as a special case

Stark quenching of rovibrational states of H2+ due to motion in a magnetic field

The motional electric field experienced by an H2+ ion moving in a magnetic field induces an electric dipole, so that one-photon dipole transitions between rovibrational states become allowed. Field induced spontaneous decay rates are calculated for a wide range of states. For an ion stored in a high-field (B ~ 10 T) Penning trap, it is shown that the lifetimes of excited rovibrational states can be shortened by typically 1-3 orders of magnitude by placing the ion in a large cyclotron orbit. This can greatly facilitate recently proposed [E. G. Myers, Phys. Rev. A 98, 010101 (2018)] high-precision spectroscopic measurements on H2+ and its antimatter counterpart for tests of CPT symmetry

Analysis of Scarp Profiles: Evaluation of Errors in Morphologic Dating

Morphologic analysis of scarp degradation can be used quantitatively to determine relative ages of different scarps formed in cohesionless materials, under the same climatic conditions. Scarps of tectonic origin as well as wavecut or rivercut terraces can be treated as topographic impulses that are attenuated by surface erosional processes. This morphological evolution can be modelled as the convolution of the initial shape with erosion (or degradation) function whose width increases with time. Such modeling applies well to scarps less than 10m high, formed in unconsolidated fanglomerates. To a good approximation, the degradation function is Gaussian with a variance measuring the degree of rounding of the initial shape. This geometric parameter can be called the degradation coefficient. A synthetic experiment shows that the degradation coefficient can be obtained by least squares fitting of profiles levelled perpendicular to the scarp. Gravitational collapse of the free face is accounted for by assuming initial scarp slopes at the angle of repose of the cohesionless materials (30°–35°). Uncertainties in the measured profiles result in an uncertainty in degradation coefficient that can be evaluated graphically. Because the degradation coefficient is sensitive to the regional slope and to three-dimensional processes (gullying, loess accumulation, stream incision, etc.), a reliable and accurate determination of degradation coefficient requires several long profiles across the same scarp. The linear diffusion model of scarp degradation is a Gaussian model in which the degradation coefficient is proportional to numerical age. In that case, absolute dating requires only determination of the propotionality constant, called the mass diffusivity constant. For Holocene scarps a few meters high, in loose alluvium under arid climatic conditions, mass diffusivity constants generally range between 1 and 6 m^2/kyr. Morphologic analysis is a reliable method to compare ages of different scarps in a given area, and it can provide approximate absolute ages of Holocene scarplike landforms

Variation of the constants in the late and early universe

Recent key observational results on the variation of fine structure constant, the proton to electron mass ratio and the gravitational constant are reviewed. The necessity to substantiate the dark sector of cosmology and to test gravity on astrophysical scales is also emphasized.Comment: 19 pages, 6 figures, Invited talk at the conference "The Quest for Cosmological Scalar Fields", Porto, 8-10 July 200

Extensions and applications of ACF mappings

Using a definition of ASF sequences derived from the definition of asymptotic contractions of the final type of ACF, we give some new fixed points theorem for cyclic mappings and alternating mapping which extend results from T.Suzuki and X.Zhang

Multiwavelength modeling of TeV AGN observed by HESS

The High Energy Stereoscopic System (H.E.S.S.) experiment, a ground-based gamma-ray Cherenkov telescope array located in Namibia, has now detected many extragalactic objects, which redshifts range from z=0.00183 up to z=0.2, possibly more. With the increasing performances of Cherenkov telescopes, it now becomes possible to probe these objects at small timescales in gamma-ray, allowing the study of regions thought to be very close to the central supermassive black holes. Furthermore, H.E.S.S. has confirmed a gamma-ray emission from M87, which is thus the first extragalactic source seen at the TeV range that is not a blazar. Among blazars, TeV BL Lacs are the most challenging objects to test the jet emission models and to shed light on particle acceleration mechanisms. The study of blazars with H.E.S.S. also revealed various temporal behaviors among them. Some objects presents a highly variable X-ray flux with small variation of the gamma-ray, while others show the inverse behavior. The interpretation of such differences is puzzling. Observations at very high energies also bring indirect measurements of the infrared extragalactic background light (EBL). The interpretation of gamma-ray emission of radiogalaxies such as M87 in terms of misaligned blazars and the understanding of the properties of the EBL represent new challenges brought by H.E.S.S. observations of extragalactic sources.Comment: 3 pages, 5 figures; to appear in "The Nuclear Region, Host Galaxy and Environment of Active Galaxies", eds. E. Benitez, I. Cruz-Gonzalez and Y. Krongold, RevMexAA (Serie de Conferencias); added reference