About H-models Of Noninertial System

In this paper we consider the problem of modeling noninertial processes with stochastic dependence between the input variables. Such processes are called H-processes ("tubular" structure processes). A new class of parametric identification algorithms with the indicator function of multidimensional static objects is suggested to use. The results of some computational experiments are presented

Analysis of the intra-night variability of BL Lacertae during its August 2020 flare

We present an analysis of the $BVRI$ photometry of the blazar BL Lacertae on diverse timescales from mid-July to mid-September 2020. We have used 11 different optical telescopes around the world and have collected data over 84 observational nights. The observations cover the onset of a new activity phase of BL Lacertae started in August 2020 (termed as the August 2020 flare by us), and the analysis is focused on the intra-night variability. On short-term timescales, (i) flux varied with ~2.2\,mag in $R$ band, (ii) the spectral index was found to be weakly dependent on the flux (i.e., the variations could be considered mildly chromatic) and (iii) no periodicity was detected. On intra-night timescales, BL Lacertae was found to show bluer-when-brighter chromatism predominantly. We also found two cases of significant inter-band time lags of the order of a few minutes. The duty cycle of the blazar during the August 2020 flare was estimated to be quite high (~90\% or higher). We decomposed the intra-night light curves into individual flares and determined their characteristics. On the basis of our analysis and assuming the turbulent jet model, we determined some characteristics of the emitting regions: Doppler factor, magnetic field strength, electron Lorentz factor, and radius. The radii determined were discussed in the framework of the Kolmogorov theory of turbulence. We also estimated the weighted mean structure function slope on intra-night timescales, related it to the slope of the power spectral density, and discussed it with regard to the origin of intra-night variability.Comment: 46 pages, 19 figures, 8 tables, accepted for publication in The Astrophysical Journal Supplement Series (manuscript version after proof correction

Duality for the Jordanian Matrix Quantum Group GLg,h(2)GL_{g,h}(2)

We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group $GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters and is split in two subalgebras: $U'_{g,h}$ (with three generators) and $U(Z)$ (with one generator). The subalgebra $U(Z)$ is a central Hopf subalgebra of $U_{g,h}$. The subalgebra $U'_{g,h}$ is not a Hopf subalgebra and its coalgebra structure depends on both parameters. We discuss also two one-parameter special cases: $g =h$ and $g=-h$. The subalgebra $U'_{h,h}$ is a Hopf algebra and coincides with the algebra introduced by Ohn as the dual of $SL_h(2)$. The subalgebra $U'_{-h,h}$ is isomorphic to $U(sl(2))$ as an algebra but has a nontrivial coalgebra structure and again is not a Hopf subalgebra of $U_{-h,h}$.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC nonlinear ma

Duality for Exotic Bialgebras

In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq

Dissecting the long-term emission behaviour of the BL Lac object Mrk 421

We report on long-term multiwavelengthmonitoring of blazar Mrk 421 by the GLAST-AGILE Support Program of the Whole Earth Blazar Telescope (GASP-WEBT) collaboration and Steward Observatory, and by the Swift and Fermi satellites. We study the source behaviour in the period 2007–2015, characterized by several extreme flares. The ratio between the optical, X-ray and γ -ray fluxes is very variable. The γ -ray flux variations show a fair correlation with the optical ones starting from 2012.We analyse spectropolarimetric data and find wavelengthdependence of the polarization degree (P), which is compatible with the presence of the host galaxy, and no wavelength dependence of the electric vector polarization angle (EVPA). Optical polarimetry shows a lack of simple correlation between P and flux and wide rotations of the EVPA.We build broad-band spectral energy distributions with simultaneous near-infrared and optical data from the GASP-WEBT and ultraviolet and X-ray data from the Swift satellite. They show strong variability in both flux and X-ray spectral shape and suggest a shift of the synchrotron peak up to a factor of ∼50 in frequency. The interpretation of the flux and spectral variability is compatible with jet models including at least two emitting regions that can change their orientation with respect to the line of sight.http://10.0.4.69/mnras/stx2185Accepted manuscrip

A new activity phase of the blazar 3C 454.3. Multifrequency observations by the WEBT and XMM-Newton in 2007-2008

We present and analyse the WEBT multifrequency observations of 3C 454.3 in the 2007-2008 observing season, including XMM-Newton observations and near-IR spectroscopic monitoring, and compare the recent emission behaviour with the past one. In the optical band we observed a multi-peak outburst in July-August 2007, and other faster events in November 2007 - February 2008. During these outburst phases, several episodes of intranight variability were detected. A mm outburst was observed starting from mid 2007, whose rising phase was contemporaneous to the optical brightening. A slower flux increase also affected the higher radio frequencies, the flux enhancement disappearing below 8 GHz. The analysis of the optical-radio correlation and time delays, as well as the behaviour of the mm light curve, confirm our previous predictions, suggesting that changes in the jet orientation likely occurred in the last few years. The historical multiwavelength behaviour indicates that a significant variation in the viewing angle may have happened around year 2000. Colour analysis reveals a complex spectral behaviour, which is due to the interplay of different emission components. All the near-IR spectra show a prominent Halpha emission line, whose flux appears nearly constant. The analysis of the XMM-Newton data indicates a correlation between the UV excess and the soft-X-ray excess, which may represent the head and the tail of the big blue bump, respectively. The X-ray flux correlates with the optical flux, suggesting that in the inverse-Compton process either the seed photons are synchrotron photons at IR-optical frequencies or the relativistic electrons are those that produce the optical synchrotron emission. The X-ray radiation would thus be produced in the jet region from where the IR-optical emission comes.Comment: 10 pages, 12 figures (7 included in the text, 5 in GIF format), accepted for publication in A&

WEBT multiwavelength monitoring and XMM-Newton observations of BL Lacertae in 2007-2008. Unveiling different emission components

In 2007-2008 we carried out a new multiwavelength campaign of the Whole Earth Blazar Telescope (WEBT) on BL Lacertae, involving three pointings by the XMM-Newton satellite, to study its emission properties. The source was monitored in the optical-to-radio bands by 37 telescopes. The brightness level was relatively low. Some episodes of very fast variability were detected in the optical bands. The X-ray spectra are well fitted by a power law with photon index of about 2 and photoelectric absorption exceeding the Galactic value. However, when taking into account the presence of a molecular cloud on the line of sight, the data are best fitted by a double power law, implying a concave X-ray spectrum. The spectral energy distributions (SEDs) built with simultaneous radio-to-X-ray data at the epochs of the XMM-Newton observations suggest that the peak of the synchrotron emission lies in the near-IR band, and show a prominent UV excess, besides a slight soft-X-ray excess. A comparison with the SEDs corresponding to previous observations with X-ray satellites shows that the X-ray spectrum is extremely variable. We ascribe the UV excess to thermal emission from the accretion disc, and the other broad-band spectral features to the presence of two synchrotron components, with their related SSC emission. We fit the thermal emission with a black body law and the non-thermal components by means of a helical jet model. The fit indicates a disc temperature greater than 20000 K and a luminosity greater than 6 x 10^44 erg/s.Comment: 11 pages, 7 figures, accepted for publication in A&