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Full list of authors: Jorstad, S. G.; Marscher, A. P.; Raiteri, C. M.; Villata, M.; Weaver, Z. R.; Zhang, H.; Dong, L.; Gomez, J. L.; Perel, M., V; Savchenko, S. S.; Larionov, V. M.; Carosati, D.; Chen, W. P.; Kurtanidze, O. M.; Marchini, A.; Matsumoto, K.; Mortari, F.; Aceti, P.; Acosta-Pulido, J. A.; Andreeva, T.; Apolonio, G.; Arena, C.; Arkharov, A.; Bachev, R.; Bonnoli, G.; Borman, G. A.; Bozhilov, V; Carnerero, M., I; Damljanovic, G.; Ehgamberdiev, S. A.; Elsasser, D.; Frasca, A.; Gabellini, D.; Grishina, T. S.; Gupta, A. C.; Hagen-Thorn, V. A.; Hallum, M. K.; Hart, M.; Hasuda, K.; Hemrich, F.; Hsiao, H. Y.; Ibryamov, S.; Irsmambetova, T. R.; Ivanov, D., V; Joner, M. D.; Kimeridze, G. N.; Klimanov, S. A.; Knoett, J.; Kopatskaya, E. N.; Kurtanidze, S. O.; Kurtenkov, A.; Kuutma, T.; Larionova, E. G.; Leonini, S.; Lin, H. C.; Lorey, C.; Mannheim, K.; Marino, G.; Minev, M.; Mirzaqulov, D. O.; Morozova, D. A.; Nikiforova, A. A.; Nikolashvili, M. G.; Ovcharov, E.; Papini, R.; Pursimo, T.; Rahimov, I; Reinhart, D.; Sakamoto, T.; Salvaggio, F.; Semkov, E.; Shakhovskoy, D. N.; Sigua, L. A.; Steineke, R.; Stojanovic, M.; Strigachev, A.; Troitskaya, Y., V; Troitskiy, I. S.; Tsai, A.; Valcheva, A.; Vasilyev, A. A.; Vince, O.; Waller, L.; Zaharieva, E.; Chatterjee, R., Blazars are active galactic nuclei (AGN) with relativistic jets whose non-thermal radiation is extremely variable on various timescales1,2,3. This variability seems mostly random, although some quasi-periodic oscillations (QPOs), implying systematic processes, have been reported in blazars and other AGN. QPOs with timescales of days or hours are especially rare4 in AGN and their nature is highly debated, explained by emitting plasma moving helically inside the jet5, plasma instabilities6,7 or orbital motion in an accretion disc7,8. Here we report results of intense optical and γ-ray flux monitoring of BL Lacertae (BL Lac) during a dramatic outburst in 2020 (ref. 9). BL Lac, the prototype of a subclass of blazars10, is powered by a 1.7 × 108 MSun (ref. 11) black hole in an elliptical galaxy (distance = 313 megaparsecs (ref. 12)). Our observations show QPOs of optical flux and linear polarization, and γ-ray flux, with cycles as short as approximately 13 h during the highest state of the outburst. The QPO properties match the expectations of current-driven kink instabilities6 near a recollimation shock about 5 parsecs (pc) from the black hole in the wake of an apparent superluminal feature moving down the jet. Such a kink is apparent in a microwave Very Long Baseline Array (VLBA) image. © 2022 Springer Nature Limited., The research reported here is based on work supported in part by US National Science Foundation grants AST-2108622 and AST-2107806, and NASA Fermi GI grants 80NSSC20K1567, 80NSSC21K1917 and 80NSSC21K1951; by Shota Rustaveli National Science Foundation of Georgia under contract FR-19-6174; by the Bulgarian National Science Fund of the Ministry of Education and Science under grants DN 18-10/2017, DN 18-13/2017, KP-06-H28/3 (2018), KP-06-H38/4 (2019) and KP-06-KITAJ/2 (2020), and by National RI Roadmap Project D01-383/18.12.2020 of the Ministry of Education and Science of the Republic of Bulgaria; by JSPS KAKENHI grant #19K03930 of Japan; by the Ministry of Education, Science and Technological Development of the Republic of Serbia (contract 451-03-9/2021-14/200002) and observing grant support from the Institute of Astronomy and Rozhen NAO BAS through the bilateral joint research project ‘Gaia Celestial Reference Frame (CRF) and fast variable astronomical objects’; by the Agenzia Spaziale Italiana (ASI) through contracts I/037/08/0, I/058/10/0, 2014-025-R.0, 2014-025-R.1.2015 and 2018-24-HH.0 to the Italian Istituto Nazionale di Astrofisica (INAF). H.Z. is supported by the NASA Postdoctoral Program at Goddard Space Flight Center, administered by ORAU. M.V.P. is partially supported by the Russian Foundation for Basic Research grant 20-02-00490. G.B. acknowledges support from the State Agency for Research of the Spanish MCIU through the ‘Center of Excellence Severo Ochoa’ award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) and from the Spanish ‘Ministerio de Ciencia e Innovacíon’ (MICINN) through grant PID2019-107847RB-C44. M.D.J. thanks the Brigham Young University Department of Physics and Astronomy for continued support of the extragalactic monitoring programme under way at the West Mountain Observatory. R.C. thanks ISRO for support under the AstroSat archival data utilization programme and BRNS for support through a project grant (sanction no. 57/14/10/2019-BRNS). The measurements at the Hans Haffner Observatory, Hettstadt, Germany, were supported by Baader Planetarium, Mammendorf, Germany. This study was based (in part) on observations conducted using the 1.8-m Perkins Telescope Observatory (PTO) in Arizona, USA, which is owned and operated by Boston University. These results made use of the Lowell Discovery Telescope (LDT) at Lowell Observatory. Lowell Observatory is a private, non-profit institution dedicated to astrophysical research and public appreciation of astronomy, and operates the LDT in partnership with Boston University, the University of Maryland and the University of Toledo. This paper is partly based on observations made with the IAC-80 operated on the island of Tenerife by the Instituto de Astrofisica de Canarias in the Spanish Observatorio del Teide and on observations made with the LCOGT telescopes, one of whose nodes is located at the Observatorios de Canarias del IAC on the island of Tenerife in the Observatorio del Teide. This paper is partly based on observations made with the Nordic Optical Telescope, owned in collaboration by the University of Turku and Aarhus University, and operated jointly by Aarhus University, the University of Turku and the University of Oslo, representing Denmark, Finland and Norway, the University of Iceland and Stockholm University at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofisica de Canarias. The VLBA is an instrument of the NRAO, USA. The NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Decompositions of solutions of the wave equation in terms of localized solutions from the wide class of the same equation are constructed by means of the affine Poincare continuous wavelet analysis. Two particular decompositions are considered. One of them is represented in terms of nonstationary particle-like solutions, the Gaussian wave packets. The another one is a decomposition of a monochromatic field in terms of monochromatic Gaussian beams. A comparison with known results is given.

A formal asymptotic expansion of the solutions of the stationary Maxwell equations with periodic coefficients is constructed by the method of two-scale asymptotic expansions. The solutions oscillate with the period of the medium and depend on the slow change of the variables with the period. The frequency is assumed to be close to a stationary point of the dispersion function. The asymptotic results obtained in this way are applied to the solution of a boundary value problem for the Maxwell equations in a half-space.

Two-dimensional model of a photoconducting emitter for the terahertz radiation excited by a femptosecond laser pulse is considered. Short-wave asymptotic formulas for electric fields of the emitter are presented. The contributions of both geometrical optics rays and effects of edges diffraction are taken into account.