Overcomplete representations such as wavelets and windowed Fourier expansions have become mainstays of modern statistical data analysis. In the present work, in the context of general finite frames, we derive an oracle expression for the mean quadratic risk of a linear diagonal de-noising procedure which immediately yields the optimal linear diagonal estimator. Moreover, we obtain an expression for an unbiased estimator of the risk of any smooth shrinkage rule.

The melting of glaciers coming with climate change threatens the heritage of the last glaciation of Europe likely contained in subglacial lakes in Greenland and Svalbard, which look fated to disappear. This aspect urges specialists to focus their studies (theoretical, numerical and on-field) on such fascinating objects.

Atmospheric emissions of carbon tetrachloride (CCl4) are regulated by the Montreal Protocol due to its role as a strong ozone-depleting substance. The molecule has been the subject of recent increased interest as a consequence of the so-called "mystery of CCl4", the discrepancy between atmospheric observations and reported production and consumption. Surface measurements of CCl4 atmospheric concentrations have declined at a rate almost 3 times lower than its lifetime-limited rate, suggesting persistent atmospheric emissions despite the ban.

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.

In this paper we propose a method to couple two or more explicit numerical schemes approximating the same time-dependent PDE, aiming at creating a new scheme which inherits advantages of the original ones. We consider both advection equations and nonlinear conservation laws. By coupling a macroscopic (Eulerian) scheme with a microscopic (Lagrangian) scheme, we get a new kind of multiscale numerical method.

3D printers based on the additive manufacturing technology create objects layer-by-layer dropping fused material. As a consequence, strong overhangs cannot be printed because the new-come material does not find a suitable support over the last deposed layer. In these cases, one can add support structures (scaffolds) which make the object printable, to be removed at the end. In this paper, we propose a level set based method to create object-dependent support structures, specifically conceived to reduce both the amount of additional material and the printing time.

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.