We consider some discrete approximation polynomials, namely discrete de la Vallée Poussin means, which have been recently deduced from certain delayed arithmetic means of the Fourier-Jacobi partial sums, in order to get a near-best approximation in suitable spaces of continuous functions equipped with the weighted uniform norm. By the present paper we aim to analyze the behavior of such discrete de la Vallée means in weighted L1 spaces, where we provide error bounds for several classes of functions, included functions of bounded variation.

MIPAS on ENVISAT performed almost continuous and global measurements of atmospheric temperature and composition from June 2002 to April 2012.

Infection by Leishmania protozoan parasites can cause a variety of disease outcomes in humans and other mammals, from single self-healing cutaneous lesions to a visceral dissemination of the parasite. The correlation between chronic lesions and ecto-nucleotidase enzymes activity on the surface of the parasite is addressed here using damage caused in epithelial cells by nitric oxide.

We prove estimates for weak solutions to a class of Dirichlet problems associated to anisotropic elliptic equations with a zero order term.

The problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal results are obtained in the framework of Orlicz spaces, and in the more general setting of all rearrangement-invariant spaces. Applications to special instances are exhibited, which provide new gradient bounds, or improve certain results available in the literature.

The problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal results are obtained in the framework of Orlicz spaces, and in the more general setting of all rearrangement-invariant spaces. Applications to special instances are exhibited, which provide new gradient bounds, or improve certain results available in the literature.

Cloud computing offers unprecedented ways to split and offload the workload of parallel algorithms to remote computing nodes. However, such remote parties can potentially misbehave, for instance by providing fake computation results in order to save resources. In turn, these erroneous partial results can affect the timeliness and correctness of the overall outcome of the algorithm. The widely successful cloud approach increases the economic feasibility of leveraging computational redundancy to enforce some degree of assurance about the results.

A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited.

A Leaky Integrate-and-Fire (LIF) model with stochastic current-based linkages is considered to describe the firing activity of neurons interacting in a (2. ×. 2)-size feed-forward network. In the subthreshold regime and under the assumption that no more than one spike is exchanged between coupled neurons, the stochastic evolution of the neuronal membrane voltage is subject to random jumps due to interactions in the network. Linked Gauss-Diffusion processes are proposed to describe this dynamics and to provide estimates of the firing probability density of each neuron.