On geometric moment invariants

In this paper we study the geometric moments invariants. We describe an image in terms of features which are invariant to some sort of transformations i.e mentioned translation, rotation and scaling change in exposure, brightness etc. Our aim is to check the performance of components for feature vectors

Multiwavelength behaviour of the blazar 3C 279: decade-long study from γ-ray to radio

We report the results of decade-long (2008–2018) γ-ray to 1 GHz radio monitoring of the blazar 3C 279, including GASP/WEBT, Fermi and Swift data, as well as polarimetric and spectroscopic data. The X-ray and γ-ray light curves correlate well, with no delay ≳ 3 h, implying general cospatiality of the emission regions. The γ-ray–optical flux–flux relation changes with activity state, ranging from a linear to a more complex dependence. The behaviour of the Stokes parameters at optical and radio wavelengths, including 43 GHz Very Long Baseline Array images, supports either a predominantly helical magnetic field or motion of the radiating plasma along a spiral path. Apparent speeds of emission knots range from 10 to 37c, with the highest values requiring bulk Lorentz factors close to those needed to explain γ-ray variability on very short time-scales. The Mg ii emission line flux in the ‘blue’ and ‘red’ wings correlates with the optical synchrotron continuum flux density, possibly providing a variable source of seed photons for inverse Compton scattering. In the radio bands, we find progressive delays of the most prominent light-curve maxima with decreasing frequency, as expected from the frequency dependence of the τ = 1 surface of synchrotron self-absorption. The global maximum in the 86 GHz light curve becomes less prominent at lower frequencies, while a local maximum, appearing in 2014, strengthens toward decreasing frequencies, becoming pronounced at ∼5 GHz. These tendencies suggest different Doppler boosting of stratified radio-emitting zones in the jet.First author draf

Classiffication of 4-dimensional nilpotent complex Leibniz algebras

In [8] and [9] several classes of new algebras were introduced. Some of them have two generating operations and they are called dialgebras. The first motivation to introduce such algebraic structures (related with well known Lie and associative algebras) were problems in algebraic K-theory. The categories of these algebras over their operads assemble into the com- mutative diagram which re°ects the Koszul duality of those categories. The aim of the present paper is to study structural properties of one class of Lo- day's list, namely the so called Leibniz algebras. Leibniz algebras present a \non-commutative" (to be more precise, a \non- antisymmetric") analogue of Lie algebras.peerReviewe

Classification of 4-dimensional nilpotent complex Leibniz algebras

In [8] and [9] several classes of new algebras were introduced. Some of them have two generating operations and they are called dialgebras. The first motivation to introduce such algebraic structures (related with well known Lie and associative algebras) were problems in algebraic K-theory. The categories of these algebras over their operads assemble into the com- mutative diagram which re°ects the Koszul duality of those categories. The aim of the present paper is to study structural properties of one class of Lo- day's list, namely the so called Leibniz algebras. Leibniz algebras present a \non-commutative" (to be more precise, a \non- antisymmetric") analogue of Lie algebras.peerReviewe

Multiwavelength behaviour of the blazar 3C 279: Decade-long study from γ -ray to radio

© 2020 The Author(s). We report the results of decade-long (2008-2018) γ -ray to 1 GHz radio monitoring of the blazar 3C 279, including GASP/WEBT, Fermi and Swift data, as well as polarimetric and spectroscopic data. The X-ray and γ -ray light curves correlate well, with no delay ≳ 3 h, implying general cospatiality of the emission regions. The γ -ray-optical flux-flux relation changes with activity state, ranging from a linear to amore complex dependence. The behaviour of the Stokes parameters at optical and radio wavelengths, including 43 GHz Very Long Baseline Array images, supports either a predominantly helical magnetic field or motion of the radiating plasma along a spiral path. Apparent speeds of emission knots range from 10 to 37c, with the highest values requiring bulk Lorentz factors close to those needed to explain γ -ray variability on very short time-scales. The MgII emission line flux in the 'blue' and 'red' wings correlates with the optical synchrotron continuum flux density, possibly providing a variable source of seed photons for inverse Compton scattering. In the radio bands, we find progressive delays of the most prominent light-curve maxima with decreasing frequency, as expected from the frequency dependence of the τ= 1 surface of synchrotron self-absorption. The global maximum in the 86 GHz light curve becomes less prominent at lower frequencies, while a local maximum, appearing in 2014, strengthens toward decreasing frequencies, becoming pronounced at ∼5 GHz. These tendencies suggest different Doppler boosting of stratified radio-emitting zones in the jet