Exotic Bialgebra S03: Representations, Baxterisation and Applications

The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of the dual algebra is given in two different parametrisations. The finite-dimensional representations of $s03_F$ are considered. Diagonalisations of the braid matrices are used to yield remarkable insights concerning representations of the L-algebra and to formulate the fusion of finite-dimensional representations. Possible applications are considered, in particular, an exotic eight-vertex model and an integrable spin-chain model.Comment: 24 pages, Latex; V2: revised subsection 4.1, added 9 references, to appear in Annales Henri Poincare in the volume dedicated to D. Arnaudo

Duality and Representations for New Exotic Bialgebras

We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic bialgebras S03 and S14 which are not deformations of the of the classical algebras of functions on GL(2) or GL(1|1). With this we finalize the classification of the matrix bialgebras which unital associative algebras generated by four elements. We also find the corresponding dual bialgebras of these new exotic bialgebras and study their representation theory in detail. We also discuss in detail a special case of R_{S1,4} in which the corresponding algebra turns out to be a special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn; reference updated; v3: corrections in subsection 3.

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

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

UBVRI observations of the flickering of RS Ophiuchi at Quiescence

We report observations of the flickering variability of the recurrent nova RS Oph at quiescence on the basis of simultaneous observations in 5 bands (UBVRI). RS Oph has flickering source with (U-B)_0=-0.62 \pm 0.07, (B-V)_0=0.15 \pm 0.10, (V-R)_0=0.25 \pm 0.05. We find for the flickering source a temperature T_fl = 9500 \pm 500 K, and luminosity L_fl = 50 - 150 L_sun (using a distance of d=1.6kpc). We also find that on a (U-B) vs (B-V) diagram the flickering of the symbiotic stars differs from that of the cataclysmic variables. The possible source of the flickering is discussed. The data are available upon request from the authors and on the web www.astro.bas.bg/~rz/RSOph.UBVRI.2010.MNRAS.tar.gz.Comment: 7 pages, MNRAS (accepted

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

Eficienta economică şi tehnologică a utilizării giberelinei la soiurile pentru struguri de masă

iticulture for the agriculture of Moldova is an important and effective branch, but the table grapes sector is an efficient and more important for small, medium and family business. Increasing the quality of table grapes is a necessity for society and consumers. The purpose of the research from this article is to study the influence of Gobbi Gib 2LG on the quantity, quality and economic efficiency of grapes of Beauty Seedless and Prezentabil varieties. The research was conducted in the vineyards of the „Terra Vitis” LTd, from Southern wine region in Moldova. Research results have shown that the dose of 2.4 l/ha is most useful for conditions by the south part of Moldova, for Beauty seedless variety and the dose of 0,98 l/ha for Prezentabil varieti

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