Estimating macrobenthic secondary production from body weight and biomass: a field test in a non-boreal intertidal habitat

Production (P) and biomass (B) data of different species from 3 stations in the intertidal zone of the Ria Formosa (southern Portugal, 37-degrees-N) were analysed. They were compared with equations from the literature to estimate P/BBAR ratios from body weight. A clear distinction must be made between (1) an intraspecific and (2) an interspecific comparison. (1) Results from 3 species supported a body weight exponent of -0.25 for the P/BBAR ratio, as is to be expected from a linear relationship between growth and respiration. (2) In an interspecific comparison, the weight exponent depends on the contribution of age or growth rate to the presence of large specimens in a sample. It is concluded that production in the specific habitat examined cannot be calculated properly from body weight and biomass by 1 simple equation which mixes interspecific and intraspecific effects, rather that both aspects should be separated into 2 different calculation steps.e Ger- man-Portuguese research project 'Die Biologie der Ria For- mosa', funded by the Bundesministerium fur Forschung und Technologie, Germany (Grant no. 03F0562Ainfo:eu-repo/semantics/publishedVersio

Higher order convergence rates for Bregman iterated variational regularization of inverse problems

We study the convergence of variationally regularized solutions to linear ill-posed operator equations in Banach spaces as the noise in the right hand side tends to $0$. The rate of this convergence is determined by abstract smoothness conditions on the solution called source conditions. For non-quadratic data fidelity or penalty terms such source conditions are often formulated in the form of variational inequalities. Such variational source conditions (VSCs) as well as other formulations of such conditions in Banach spaces have the disadvantage of yielding only low-order convergence rates. A first step towards higher order VSCs has been taken by Grasmair (2013) who obtained convergence rates up to the saturation of Tikhonov regularization. For even higher order convergence rates, iterated versions of variational regularization have to be considered. In this paper we introduce VSCs of arbitrarily high order which lead to optimal convergence rates in Hilbert spaces. For Bregman iterated variational regularization in Banach spaces with general data fidelity and penalty terms, we derive convergence rates under third order VSC. These results are further discussed for entropy regularization with elliptic pseudodifferential operators where the VSCs are interpreted in terms of Besov spaces and the optimality of the rates can be demonstrated. Our theoretical results are confirmed in numerical experiments

Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains

Integral identities for particular Bloch functions in finite periodic systems are derived. All following statements are proven for a finite domain consisting of an integer number of unit cells. It is shown that matrix elements of particular Bloch functions with respect to periodic differential operators vanish identically. The real valuedness, the time-independence and a summation property of the expectation values of periodic differential operators applied to superpositions of specific Bloch functions are derived.Comment: 10 page