Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

Repply to: Brito, A.C., Brotas, V., Caetano, M., Coutinho, T.P., Bordalo, A.A., Icely, J., Neto, J.M., Serôdio, J., Moita, T. (2012) "Defining phytoplankton class boundaries in Portuguese transitional waters: an evaluation of the ecological quality status according to the Water Framework Directive" [Ecological Indicators 19, 5-14]

We write to comment on the recently published paper “Defining phytoplankton class boundaries in Portuguese transitional waters: an evaluation of the ecological quality status according to the Water Framework Directive” (Brito et al., 2012). This paper presents an integrated methodology to analyse the ecological quality status of several Portuguese transitional waters, using phytoplanktonrelated metrics. One of the systems analysed, the Guadiana estuary in southern Portugal, is considered the most problematic estuary, with its upstream water bodies classified as Poor in terms of ecological status. We strongly disagree with this conclusion and we would like to raise awareness to some methodological constraints that, in our opinion, are the basis of such deceptive conclusions and should therefore not be neglected when using phytoplankton to assess the ecological status of natural waters.

Tolerance of young (Ceratonia siliqua L.) carob rootstock to NaCl

One-year-old carob (Ceratonia siliqua L.) rootstock was grown in fertilised substrate to evaluate the effects of NaCl salinity stress. The experiment consisted of seven treatments with different concentrations of NaCl in the irrigation water: 0 (control), 15, 30, 40, 80, 120 and 240 (mmol L(-1)), equivalent to electrical conductivities of 0.0, 1.5, 2.9, 3.9, 7.5, 10.9 and 20.6 dS m(-1), respectively. Several growth parameters were measured throughout the experimental period. At the end of the experiment, pH, extractable P and K, and the electrical conductivity of the substrate were assessed in each salinity level. On the same date, the mineral composition of the leaves was compared. The carob rootstock tolerated 13.4 dS m(-1) for a period of 30 days but after 60 days the limit of tolerance was only 6.8 dS m(-1). Salt tolerance indexes were 12.8 and 4.5 for 30 and 60 days, respectively. This tolerance to salinity resulted from the ability to function with concentrations of Cl(-) and Na(+) in leaves up to 24.0 and 8.5 g kg(-1), respectively. Biomass allocation to shoots and roots was similar in all treatments, but after 40 days the number of leaves was reduced, particularly at the larger concentrations (120 and 240 mmol NaCl L(-1)). Leaves of plants irrigated with 240 mmol NaCl L(-1) became chlorotic after 30 days exposure. However, concentrations of N, P. Mg and Zn in leaves were not affected significantly (P > 0.05) by salinity. Apparently, K(+) and Ca(2+) were the key nutrients affected in the response of carob rootstocks to salinity. Plants grown with 80 and 120 mmol L(-1) of NaCl contained the greatest K. concentration. Na(+)/K(+) increased with salinity, due to an elevated Na(+) content but K(+) uptake was also enhanced, which alleviated some Na. stress. Ca(2+) concentration in leaves was not reduced under salinity. Salinization of irrigation water and subsequent impacts on agricultural soils are now common problems in the Mediterranean region. Under such conditions, carob seems to be a salt as well as a drought tolerant species. (C) 2010 Elsevier B.V. All rights reserved.