Convergence

Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative

In this paper, we investigate the numerical approximation of Hamilton-Jacobi equations with the Caputo time-fractional derivative. We introduce an explicit in time discretization of the Caputo derivative and a finite difference scheme for the approximation of the Hamiltonian. We show that the approximation scheme so obtained is stable under an appropriate condition on the discretization parameters and converges to the unique viscosity solution of the Hamilton-Jacobi equation.

Developmental industrial policies for convergence within the European Monetary Union

The Eurozone faces two great challenges: a structural core-periphery divide, which resulted in the deepest economic crisis since the war, and several significant societal problems. To restore sustainable growth, EU policies must address both: tackle the fragility of the
periphery’s industrial base, reducing the divergences in industrial capabilities, and create a new agenda for innovation and growth. The
following sections argue that this calls for a policy combining support for demand with industrial policies tailored to the specific needs of

Environmental variation is a major predictor of global trait turnover in mammals

Aim: To evaluate how environment and evolutionary history interact to influence global patterns of mammal trait diversity (a combination of 14 morphological and life-history traits). Location: The global terrestrial environment. Taxon: Terrestrial mammals. Methods: We calculated patterns of spatial turnover for mammalian traits and phylogenetic lineages using the mean nearest taxon distance. We then used a variance partitioning approach to establish the relative contribution of trait conservatism, ecological adaptation and clade specific ecological preferences on global trait turnover.

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