Canonical connection on a class of Riemannian almost product manifolds

The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012

Kaehler Manifolds of Quasi-Constant Holomorphic Sectional Curvatures

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kaehler metrics into Kaehler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kaehler metrics is shown to be exactly the class of Kaehler metrics whose potential function is only a function of the distance from the origin in complex Euclidean space. Finally we show that any rotational even dimensional hypersurface carries locally a natural Kaehler structure, which is of quasi-constant holomorphic sectional curvatures.Comment: 36 page

INVESTIGATION OF THE VIRUS STATUS OF THE POTATOES IN SOME REGIONS PRODUCING HIGH QUALITY SEED POTATOES IN BULGARIA

ABSTRAC

Natural Connection with Totally Skew-Symmetric Torsion on Riemannian Almost Product Manifolds

On a Riemannian almost product manifold $(M,P,g)$ we consider a linear connection preserving the almost product structure $P$ and the Riemannian metric $g$ and having a totally skew-symmetric torsion. We determine the class of the manifolds $(M,P,g)$ admitting such a connection and prove that this connection is unique in terms of the covariant derivative of $P$ with respect to the Levi-Civita connection. We find a necessary and sufficient condition the curvature tensor of the considered connection to have similar properties like the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the case when the torsion of the connection is parallel. We consider this connection on a Riemannian almost product manifold $(G,P,g)$ constructed by a Lie group $G$.Comment: 14 pages, a revised edition, an example is adde

The Hubble Constant from the Gravitational Lens B1608+656

We present a refined gravitational lens model of the four-image lens system B1608+656 based on new and improved observational constraints: (i) the three independent time-delays and flux-ratios from VLA observations, (ii) the radio-image positions from VLBA observations, (iii) the shape of the deconvolved Einstein Ring from optical and infrared HST images, (iv) the extinction-corrected lens-galaxy centroids and structural parameters, and (v) a stellar velocity dispersion, sigma_ap=247+-35 km/s, of the primary lens galaxy (G1), obtained from an echelle spectrum taken with the Keck--II telescope. The lens mass model consists of two elliptical mass distributions with power-law density profiles and an external shear, totaling 22 free parameters, including the density slopes which are the key parameters to determine the value of H_0 from lens time delays. This has required the development of a new lens code that is highly optimized for speed. The minimum-chi^2 model reproduces all observations very well, including the stellar velocity dispersion and the shape of the Einstein Ring. A combined gravitational-lens and stellar dynamical analysis leads to a value of the Hubble Constant of H_0=75(+7/-6) km/s/Mpc (68 percent CL; Omega_m=0.3, Omega_Lambda=0.7. The non-linear error analysis includes correlations between all free parameters, in particular the density slopes of G1 and G2, yielding an accurate determination of the random error on H_0. The lens galaxy G1 is ~5 times more massive than the secondary lens galaxy (G2), and has a mass density slope of gamma_G1=2.03(+0.14/-0.14) +- 0.03 (68 percent CL) for rho~r^-gamma', very close to isothermal (gamma'=2). (Abridged)Comment: 17 pages, 6 figures, 5 tables; revised version with correct fig.6 and clarified text based on referee report; conclusions unchange

Nature of Intra-night Optical Variability of BL Lacertae

We present the results of extensive multi-band intra-night optical monitoring of BL Lacertae during 2010--2012. BL Lacertae was very active in this period and showed intense variability in almost all wavelengths. We extensively observed it for a total for 38 nights; on 26 of them observations were done quasi-simultaneously in B, V, R and I bands (totaling 113 light curves), with an average sampling interval of around 8 minutes. BL Lacertae showed significant variations on hour-like timescales in a total of 19 nights in different optical bands. We did not find any evidence for periodicities or characteristic variability time-scales in the light curves. The intranight variability amplitude is generally greater at higher frequencies and decreases as the source flux increases. We found spectral variations in BL Lacertae in the sense that the optical spectrum becomes flatter as the flux increases but in several flaring states deviates from the linear trend suggesting different jet components contributing to the emission at different times.Comment: 12 Pages, 5 figures, 3 Tables, Accepted for Publication in MNRA

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

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

Parental Smoking in the Vicinity of Children and Tobacco Control Policies in the European Region

Objective: To ascertain patterns of parental smoking in the vicinity of children in Eastern and Western Europe and their relation to Tobacco Control Scale (TCS) scores. Methods: Data on parental smoking patterns were obtained from the School Child Mental Health Europe (SCMHE), a 2010 cross-sectional survey of 5141 school children aged 6 to 11 years and their parents in six countries: Germany, Netherlands, Lithuania, Romania, Bulgaria and Turkey ranked by TCS into three level categories toward tobacco control policies. Results: A slightly higher proportion of Eastern compared to Western European mothers (42.4 vs. 35.1%) were currently smoking in but the difference was not statistically significant after adjusting for maternal age and maternal educational attainment. About a fifth (19.3%) and a tenth (10.0%) of Eastern and Western European mothers, respectively, smoked in the vicinity of their children, and the difference was significant even after adjustment for potential confounders (p less than 0.001). Parents with the highest educational attainment were significantly less likely to smoke in the vicinity of their children than those with the lowest attainment. After control of these covariates lax tobacco control policies, compared to intermediate policies, were associated with a 50% increase in the likelihood of maternal smoking in the vicinity of children adjusted odds ratio (AOR) = 1.52 and 1.64. Among fathers, however, the relationship with paternal smoking and TCS seems more complex since strict policy increases the risk as well AOR = 1,40. Only one country, however belongs to the strict group. Significance: Tobacco control policies seem to have influenced maternal smoking behaviors overall to a limited degree and smoking in the vicinity of children to a much greater degree. Children living in European countries with lax tobacco control policies are more likely to be exposed to second hand smoking from maternal and paternal smoking