In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate $q$-Bernstein polynomials for a function analytic in the polydisc $D_{R_{1}}\times D_{R_{2}}=\{z\in C\colon \vert z\vert <R_{1}\} \times \{ z\in C\colon \vert z\vert <R_{1}\}$ for arbitrary fixed $q>1$. We give quantitative Voronovskaja type estimates for the bivariate $q$-Bernstein polynomials for $q>1$. In the univariate case the similar results were obtained by S. Ostrovska: $q$-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009.
We investigated the characteristics of gaseous exchanges and chlorophyll a fluorescence under different irradiances in two liana species Canavalia parviflora Benth. (Fabaceae) and Gouania virgata Reissk (Rhamnaceae), both of a semi-deciduous tropical forest of Southeast Brazil. We used cultivated plants growing under irradiances of 100, 40, 10, and 1.5 % of the photosynthetic photon flux density (PPFD). Higher net photosynthetic rates (PN) were observed during early morning under full sunlight. After this, reduced PN values were recorded due to pronounced stomatal closure. In Canavalia, the gas exchange responses diminished concomitant with reduced irradiance. Gouania exhibited a narrower range of response, with high PN values even at 10 % PPFD. Marked reduction of the effective photochemical yield (ΔF/Fm') near midday was observed, followed by increases in the non-photochemical quenching for both species under full sunlight. Despite the common occurrence of these species in open areas of the forest, both were able to maintain relatively high PN in shaded environments. We suggest that lianas present an intermediate physiological behaviour between shade and non-shade tolerant species. and M. C. Sanches, I. F. M. Válio.
The effects of foliar spray of putrescine (Put; 8 mM) on chlorophyll (Chl) metabolism and xanthophyll cycle in cucumber seedlings were investigated under saline conditions of 75 mM NaCl. Exogenous Put promoted the conversion of uroporhyrinogen III to protoporphyrin IX and alleviated decreases in Chl contents and in a size of the xanthophyll cycle pool under salt stress. Moreover, the Put treatment reduced the activities of uroporphyrinogen III synthase, chlorophyllase, and Mg-dechelatase and downregulated the transcriptional levels of glutamyl-tRNA reductase, 5-aminolevulinate dehydratase, uroporphyrinogen III synthase, uroporphyrinogen III decarboxylase, and chlorophyllide a oxygenase, but significantly increased the expression levels of non-yellow coloring 1-like, pheide a oxygenase, red chlorophyll catabolite reductase, and violaxanthin de-epoxidase. Taken together, these results suggest that Put might improve Chl metabolism and xanthophyll cycle by regulating enzyme activities and mRNA transcription levels in a way that improved the salt tolerance of cucumber plants., R. N. Yuan, S. Shu, S. R. Guo, J. Sun, J. Q. Wu., and Obsahuje bibliografii