Sturm-Liouville operators on time scales

We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have been obtained by various authors in the past.Comment: 12 page

Multi-Wavelength Monitoring of the Changing-Look AGN NGC 2617 during State Changes

Optical and near-infrared photometry, optical spectroscopy, and soft X-ray and UV monitoring of the changing-look active galactic nucleus NGC 2617 show that it continues to have the appearance of a type-1 Seyfert galaxy. An optical light curve for 2010-2017 indicates that the change of type probably occurred between 2010 October and 2012 February and was not related to the brightening in 2013. In 2016 and 2017 NGC 2617 brightened again to a level of activity close to that in 2013 April. However, in 2017 from the end of the March to end of July 2017 it was in very low level and starting to change back to a Seyfert 1.8. We find variations in all passbands and in both the intensities and profiles of the broad Balmer lines. A new displaced emission peak has appeared in Hβ. X-ray variations are well correlated with UV-optical variability and possibly lead by ̃2-3 d. The K band lags the J band by about 21.5 ± 2.5 d and lags the combined B + J bands by ̃25 d. J lags B by about 3 d. This could be because J-band variability arises predominantly from the outer part of the accretion disc, while K-band variability is dominated by thermal re-emission by dust. We propose that spectral-type changes are a result of increasing central luminosity causing sublimation of the innermost dust in the hollow bi-conical outflow. We briefly discuss various other possible reasons that might explain the dramatic changes in NGC 2617.Fil: Oknyansky, V. L.. Sternberg Astronomical Institute; RusiaFil: Gaskell, C. M.. Department of Astronomy and Astrophysics. University of California. Santa Cruz; Estados UnidosFil: Mikailov, K. M.. Shamakhy Astrophysical Observatory, National Academy of Sciences. Pirkuli; AzerbaiyánFil: Lipunov, V. M.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University ; RusiaFil: Shatsky, N. I.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University; RusiaFil: Tsygankov, S. S.. Tuorla Observatory, Department of Physics and Astronomy. University of Turku.; FinlandiaFil: Gorbovskoy, E. S.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University; RusiaFil: Tatarnikov, A. M.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University; RusiaFil: Metlov, V. G.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University; RusiaFil: Malanchev, K. L.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University; RusiaFil: Brotherton, M.B.. University of Wyoming; Estados UnidosFil: Kasper, D.. University of Wyoming; Estados UnidosFil: Du, P.. Institute of High Energy Physics. Chinese Academy of Sciences; ChinaFil: Chen, X.. School of Space Science and Physics. Shandong University; ChinaFil: Burlak, M. A.. Sternberg Astronomical Institute. M.V.Lomonosov Moscow State University; RusiaFil: Buckley, D. A. H.. The South African Astronomical Observatory; SudáfricaFil: Rebolo, R.. Instituto de Astrofisica de Canarias; EspañaFil: Serra-Ricart, M.. Instituto de Astrofisica de Canarias; EspañaFil: Podestá, R.. Universidad Nacional de San Juan; ArgentinaFil: Levato, O. H.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Ciencias Astronómicas, de la Tierra y del Espacio. Universidad Nacional de San Juan. Instituto de Ciencias Astronómicas, de la Tierra y del Espacio; Argentin

Identifying damage in a bridge by analysing rotation response to a moving load

This is the author accepted manuscript. The final version is available from Routledge via the DOI in this recordThis article proposes a bridge damage detection method using direct rotation measurements. Initially, numerical analyses are carried out on a one-dimensional (1D) simply supported beam model loaded with a single moving point load to investigate the sensitivity of rotation as a main parameter for damage identification. As a result of this study, the difference in rotation measurements due to a single moving point load obtained for healthy and damaged states is proposed as a damage indicator. A relatively simple laboratory experiment is conducted on a 3-m long simply supported beam structure to validate the results obtained from the numerical analysis. The case of multi-axle vehicles is investigated through numerical analyses of a 1D bridge model and a theoretical basis for damage detection is presented. Finally, a sophisticated 3D dynamic finite element model of a 20-m long simply supported bridge structure is developed by an independent team of researchers and used to test the robustness of the proposed damage detection methodology in a series of blind tests. Rotations from an extensive range of damage scenarios were provided to the main team who applied their methods without prior knowledge of the extent or location of the damage. Results from the blind test simulations demonstrate that the proposed methodology provides a reasonable indication of the bridge condition for all test scenarios.European Union Horizon 202