3,538 research outputs found
Derivative Formula and Applications for Degenerate Diffusion Semigroups
By using the Malliavin calculus and solving a control problem, Bismut type
derivative formulae are established for a class of degenerate diffusion
semigroups with non-linear drifts. As applications, explicit gradient estimates
and Harnack inequalities are derived.Comment: 18 page
Detection of gamma-ray emission from the Coma cluster with Fermi Large Area Telescope and tentative evidence for an extended spatial structure
Many galaxy clusters have giant halos of non-thermal radio emission,
indicating the presence of relativistic electrons in the clusters. Relativistic
protons may also be accelerated by merger and/or accretion shocks in galaxy
clusters. These cosmic-ray (CR) electrons and/or protons are expected to
produce gamma-rays through inverse-Compton scatterings or inelastic
collisions respectively. Despite of intense efforts in searching for
high-energy gamma-ray emission from galaxy clusters, conclusive evidence is
still missing so far. Here we report the discovery of MeV gamma-ray
emission from the Coma cluster direction with an unbinned likelihood analysis
of the 9 years of {\it Fermi}-LAT Pass 8 data. The gamma-ray emission shows a
spatial morphology roughly coincident with the giant radio halo, with an
apparent excess at the southwest of the cluster. Using the test statistic
analysis, we further find tentative evidence that the gamma-ray emission at the
Coma center is spatially extended. The extended component has an integral
energy flux of in the
energy range of 0.2 - 300 GeV and the spectrum is soft with a photon index of
. Interpreting the gamma-ray emission as arising from CR proton
interaction, we find that the volume-averaged value of the CR to thermal
pressure ratio in the Coma cluster is about . Our results show that
galaxy clusters are likely a new type of GeV gamma-ray sources, and they are
probably also giant reservoirs of CR protons.Comment: 10 pages, 10 figures, Accepted by Physical Review D, more spatial
models for the gamma-ray emission are used, systematic checks on the results
are adde
Hermite–Hadamard-Type Integral Inequalities for Functions Whose First Derivatives are Convex
We establish some new Hermite–Hadamard-type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities for special means.Встановлено дєякі нові нєрівності типу Ерміта - Адамара для Функцій, похідні яких мають опуклість. Ці нєрівності застосовано при побудові нерівностей для спеціальних середніх
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