Citrus volkameriana (L.) plants were grown for 43 d in nutrient solutions containing 0, 2, 14, 98, or 686 µM Mn (Mn0, Mn2, Mn14, Mn98, and Mn686, respectively). To adequately investigate the combined effects of Mn nutrition and irradiance on photosystem 2 (PS2) activity, irradiance response curves for electron transport rate (ETR), nonphotochemical quenching (qN), photochemical quenching (qP), and real photochemical efficiency of PS2 (ΦPS2) were recorded under 10 different irradiances (66, 96, 136, 226, 336, 536, 811, 1 211, 1 911, and 3 111 µmol m-2 s-1, I66 to I3111, respectively) generated with the PAM-2000 fluorometer. Leaf chlorophyll content was significantly lower under Mn excess (Mn686) compared to Mn0; its highest values were recorded in the treatments Mn2-Mn98. However, ETR and ΦPS2 values were significantly lower under Mn0 compared to the other Mn treatments, when plants were exposed to irradiances ≥96 µmol m-2 s-1. Furthermore, Mn0 plants had significantly higher values of qN and lower values of qP at irradiances ≤226 and ≥336 µmol m-2 s-1, respectively, than those grown under Mn2-Mn686. Irrespective of Mn treatment, the values of ΦPS2 and qN decreased, while those of qP increased progressively by increasing irradiance from I136 to I3111. Finally, Mn2-Mn98 plants were less sensitive to photoinhibition of photosynthesis (≥811 µmol m-2 s-1) than the Mn686 (≥536 µmol m-2 s-1) and Mn0 (≥336 µmol m-2 s-1) ones. and I. E. Papadakis ... [et al.].
\vspace{-1.6cm} The paper studies the relations between ϕ-divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam's deficiency. A new and considerably simplified approach is given to the spectral representation of ϕ-divergences already established in Österreicher and Feldman \cite{OestFeld} under restrictive conditions and in Liese and Vajda \cite{LiV06}, \cite{LiV08} in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary convex functions which are strictly convex at one point only. Bayes sufficiency is characterized with the help of a binary model that consists of the joint distribution and the product of the marginal distributions of the observation and the parameter, respectively. LeCam's deficiency is expressed in terms of ϕ-divergences where ϕ belongs to a class of convex functions whose curvature measures are finite and satisfy a normalization condition.