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The blazar Mrk 501 (z = 0.034) was observed at very-high-energy (VHE, E greater than or similar to 100 GeV) gamma-ray wavelengths during a bright flare on the night of 2014 June 23-24 (MJD 56832) with the H.E.S.S. phase-II array of Cherenkov telescopes. Data taken that night by H.E.S.S. at large zenith angle reveal an exceptional number of gamma-ray photons at multi-TeV energies, with rapid flux variability and an energy coverage extending significantly up to 20 TeV. This data set is used to constrain Lorentz invariance violation (LIV) using two independent channels: a temporal approach considers the possibility of an energy dependence in the arrival time of gamma-rays, whereas a spectral approach considers the possibility of modifications to the interaction of VHE gamma-rays with extragalactic background light (EBL) photons. The non-detection of energy-dependent time delays and the non-observation of deviations between the measured spectrum and that of a supposed power-law intrinsic spectrum with standard EBL attenuation are used independently to derive strong constraints on the energy scale of LIV (E-QG) in the subluminal scenario for linear and quadratic perturbations in the dispersion relation of photons. For the case of linear perturbations, the 95% confidence level limits obtained are E-QG,E-1 > 3.6 x 10(17) GeV using the temporal approach and E-QG,E-1 > 2.6 x 10(19) GeV using the spectral approach. For the case of quadratic perturbations, the limits obtained are E-QG,E-2 > 8.5 x 10(10) GeV using the temporal approach and E-QG,E-2 > 7.8 x 10(11) GeV using the spectral approach.
PKS 1830-211 is a known macrolensed quasar located at a redshift of z = 2.5. Its highenergy gamma-ray emission has been detected with the Fermi-Large Area Telescope (LAT) instrument and evidence for lensing was obtained by several authors from its high-energy data. Observations of PKS 1830-211 were taken with the High Energy Stereoscopic System (H.E.S.S.) array of Imaging Atmospheric Cherenkov Telescopes in 2014 August, following a flare alert by the Fermi-LAT Collaboration. The H.E.S.S observations were aimed at detecting a gamma-ray flare delayed by 20-27 d from the alert flare, as expected from observations at other wavelengths. More than 12 h of good-quality data were taken with an analysis threshold of similar to 67 GeV. The significance of a potential signal is computed as a function of the date and the average significance over the whole period. Data are compared to simultaneous observations by Fermi-LAT. No photon excess or significant signal is detected. An upper limit on PKS 1830-211 flux above 67 GeV is computed and compared to the extrapolation of the Fermi-LAT flare spectrum.