Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.Comment: 18 pages. arXiv admin note: text overlap with arXiv:math/0404029 by other author

Sub-micrometer distribution of Fe oxides and organic matter in Podzol horizons

The spatial distribution of soil constituents at the micrometer scale is of great importance to understand processes controlling the formation of micro-aggregates and the stabilization of organic carbon. Here, the spatial distribution of organic and mineral constituents in Podzol horizons is studied by concerted measurements of (i) the content of various forms of Fe, Al, Si and C determined by selective extraction in the fine earth fraction of soil (f < 2 mm); (ii) the elemental composition of the clay fraction (f < 2 um) with lateral resolution using scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDS), and with surface selectivity using X-ray photoelectron spectroscopy (XPS); (iii) the specific surface area (SSA) of fine earth and clay fractions by krypton physisorption. The SSA of the fine earth in illuvial horizons is predominantly due to finely divided Fe oxides, including goethite, characterized by an equivalent particle size of about 10 mu m. Kaolinite platelets of about 2 gm size account for a large volume proportion in the clay fraction but have a minor contribution to SSA. Fe oxides and organic matter (OM) are intimately associated. Heterogeneity at the um scale is created by local variations in the relative amounts of kaolinite and Fe-OM associations. These two kinds of physical entities are in random mixture. Moreover, variation of C/Fe atomic ratios reveals sub-mu m scale heterogeneity. The latter is due to variation in the relative proportion of organic compounds and Fe oxides, indicating that aggregation of nanoparticles, and not only mere adsorption or pore filling, plays a role in these associations. In this regard, our results highlight that OM associated with Fe protects Fe oxides against physical displacement and that part of this associated OM is oxidizable by NaOCl treatment. These findings demonstrate that the concept of OM stabilization through association with Fe must be revisited when considering the sub-mu m scale level because fine Fe oxide particles can be easily dispersed during oxidation of associated carbon. Combination of physical fractionation and microanalysis (e.g. SEM-EDS, vibrational spectroscopy) offer promising perspectives to clarify the relationship between chemical composition and sub-inn scale architecture, and to better understand soil processes

Covert contraceptive use among women attending a reproductive health clinic in a municipality in Ghana.

BACKGROUND: Covert contraceptive use (CCU) in sub-Saharan Africa is an indication of women's inability to exercise autonomy in their reproductive choices. The aim of this study was to assess the prevalence and determinants of CCU among a sample of FP clients in a municipality of Ghana. METHODS: We conducted a mixed method study among women attending a public reproductive health clinic in Sunyani, a city of over 250,000 inhabitants in Ghana. An initial survey inquired into sociodemographic characteristics, use of family planning (FP) methods and partner awareness of contraceptive use. The predictors of CCU were explored using logistic regressions. We used the findings to develop a guide which we applied in-depth interviews and focus group discussions with attendants at the same facility. Qualitative data analysis was conducted using a framework approach. RESULTS: We interviewed 300 women, 48 % of whom were aged between 26-33 years. The injectable was the most widely used method (56 %). The prevalence of CCU was 34 %. In multivariate analysis, single women were more likely to practice CCU than married or co-habiting women (Adjusted OR = 12.12, 95 % C.I. 4.73-31.1). Muslim and traditionalist women were similarly more likely to practice CCU than non-Muslim, non-traditionalist (Adjusted OR = 4.56, 2.29-9.06). Women who preferred to have their first or next child in 4 or more years from the time of the interview were more likely to be in CCU than women who intended to have children within 4 years of the interview (2.57; 1.37-4.83). Single women saw in covert use a statement of their social autonomy. To succeed in CCU, women wished that clinic attendance cards would not be given to them to keep at home. Though many participants saw in CCU a source of anxiety, they expected health workers to consider it and uphold confidentiality in the provision of services. CONCLUSIONS: Covert contraceptive use was high in this municipality and being single was the strongest predictor of the practice. Providers of FP services should reflect on how to adequately address the challenges faced by women who practice CCU

Understanding Root Uptake of Nutrients, Toxic and Polluting Elements in Hydroponic Culture

peer reviewe

Non-colliding Brownian Motions and the extended tacnode process

We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.Comment: 38 pages. In the revised version a few arguments have been expanded and many typos correcte

Correlation between the optical veiling and accretion properties: A case study of the classical T Tauri star DK Tau

Classical T Tauri stars (cTTs) accrete from their circumstellar disk. The material falls onto the stellar surface, producing an accretion shock, which generates veiling in a star's spectra. In addition, the shock causes a localized accretion spot at the level of the chromosphere. Our goal is to investigate the accretion, particularly the mass accretion rates (Macc), for the cTTs DK Tau, over two periods of 17 and 29 days, using two different procedures for comparison purposes. The first method relies on the derivation of the accretion luminosity via accretion-powered emission lines. The second compares the variability of the optical veiling with accretion shock models to determine mass accretion rates. We used observations taken in 2010 and 2012 with the ESPaDOnS spectropolarimeter at the CFHT. We find peak values of the veiling (at 550 nm) ranging from 0.2 to 1.3, with a steeper trend across the wavelength range for higher peak values. When using the accretion-powered emission lines, we find mass accretion rate values ranging from log(Macc[Msol/yr]) = -8.20 to log(Macc[Msol/yr]) = -7.40. This agrees with the values found in the literature, as well as the values calculated using the accretion shock models and the veiling. In addition, we identify a power-law correlation between the values of the accretion luminosity and the optical veiling. For the 2010 observations, using the values of the filling factors (which represent the area of the star covered by an accretion spot) derived from the shock models, we infer that the accretion spot was located between +45 degrees and +75 degrees in latitude. We show that both methods of determining the mass accretion rate yield similar results. We also present a helpful means of confirming the accretion luminosity values by measuring the veiling at a single wavelength in the optical

Tracing the origin of dissolved silicon transferred from various soil-plant systems towards rivers: a review

Silicon (Si) released as H4SiO4 by weathering of Si-containing solid phases is partly recycled through vegetation before its land-to-rivers transfer. By accumulating in terrestrial plants to a similar extent as some major macronutrients (0.1–10% Si dry weight), Si becomes largely mobile in the soil-plant system. Litter-fall leads to a substantial reactive biogenic silica pool in soil, which contributes to the release of dissolved Si (DSi) in soil solution. Understanding the biogeochemical cycle of silicon in surface environments and the DSi export from soils into rivers is crucial given that the marine primary bio-productivity depends on the availability of H4SiO4 for phytoplankton that requires Si. Continental fluxes of DSi seem to be deeply influenced by climate (temperature and runoff) as well as soil-vegetation systems. Therefore, continental areas can be characterized by various abilities to transfer DSi from soil-plant systems towards rivers. Here we pay special attention to those processes taking place in soil-plant systems and controlling the Si transfer towards rivers. We aim at identifying relevant geochemical tracers of Si pathways within the soil-plant system to obtain a better understanding of the origin of DSi exported towards rivers. In this review, we compare different soil-plant systems (weathering-unlimited and weathering-limited environments) and the variations of the geochemical tracers (Ge/Si ratios and d30Si) in DSi outputs. We recommend the use of biogeochemical tracers in combination with Si mass-balances and detailed physico-chemical characterization of soil-plant systems to allow better insight in the sources and fate of Si in these biogeochemical systems

Super-solar metallicity at the position of the ultra-long GRB130925A

Over the last decade there has been immense progress in the follow-up of short and long GRBs, resulting in a significant rise in the detection rate of X-ray and optical afterglows, in the determination of GRB redshifts, and of the identification of the underlying host galaxies. Nevertheless, our theoretical understanding on the progenitors and central engines powering these vast explosions is lagging behind, and a newly identified class of `ultra-long' GRBs has fuelled speculation on the existence of a new channel of GRB formation. In this paper we present high signal-to-noise X-shooter observations of the host galaxy of GRB130925A, which is the fourth unambiguously identified ultra-long GRB, with prompt gamma-ray emission detected for ~20ks. The GRB line of sight was close to the host galaxy nucleus, and our spectroscopic observations cover both this region along the bulge/disk of the galaxy, in addition to a bright star-forming region within the outskirts of the galaxy. From our broad wavelength coverage we obtain accurate metallicity and dust-extinction measurements at both the galaxy nucleus, and an outer star-forming region, and measure a super-solar metallicity at both locations, placing this galaxy within the 10-20% most metal-rich GRB host galaxies. Such a high metal enrichment has implications on the progenitor models of both long and ultra-long GRBs, although the edge-on orientation of the host galaxy does not allow us to rule out a large metallicity variation along our line of sight. The spatially resolved spectroscopic data presented in this paper offer important insight into variations in the metal and dust abundance within GRB host galaxies. They also illustrate the need for IFU observations on a larger sample of GRB host galaxies at varies metallicities to provide a more quantitative view on the relation between the GRB circumburst and the galaxy-whole properties.Comment: 9 pages, 3 figures, A&A in press, matches published versio

Non-intersecting squared Bessel paths at a hard-edge tacnode

The squared Bessel process is a 1-dimensional diffusion process related to the squared norm of a higher dimensional Brownian motion. We study a model of $n$ non-intersecting squared Bessel paths, with all paths starting at the same point $a>0$ at time $t=0$ and ending at the same point $b>0$ at time $t=1$. Our interest lies in the critical regime $ab=1/4$, for which the paths are tangent to the hard edge at the origin at a critical time $t^*\in (0,1)$. The critical behavior of the paths for $n\to\infty$ is studied in a scaling limit with time $t=t^*+O(n^{-1/3})$ and temperature $T=1+O(n^{-2/3})$. This leads to a critical correlation kernel that is defined via a new Riemann-Hilbert problem of size $4\times 4$. The Riemann-Hilbert problem gives rise to a new Lax pair representation for the Hastings-McLeod solution to the inhomogeneous Painlev\'e II equation $q"(x) = xq(x)+2q^3(x)-\nu,$ where $\nu=\alpha+1/2$ with $\alpha>-1$ the parameter of the squared Bessel process. These results extend our recent work with Kuijlaars and Zhang \cite{DKZ} for the homogeneous case $\nu = 0$.Comment: 54 pages, 13 figures. Corrected error in Theorem 2.