If I? R is a bounded interval, we prove the boundedness of Calderón singular operator and of Hardy-Littlewood Maximal operator in the generalized weighted Grand Lebesgue spaces Lpp),?(I), 1 < p< ?.

We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is well known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux.

In this paper we establish the higher differentiability of solutions to the Dirichlet problem {div(A(x,Du))+b(x)u(x)=fin?u=0on??under a Sobolev assumption on the partial map x-> A(x, ?). The novelty here is that we take advantage from the regularizing effect of the lower order term to deal with bounded solutions.

The visual quality evaluation is one of the fundamental challenging problems in image processing. It plays a central role in the shaping, implementation, optimization, and testing of many methods. The existing image quality assessment methods centered mainly on images altered by common distortions while paying little attention to the distortion introduced by color quantization.

The feasibility of liver transplantation from old healthy donors suggests that this organ is able to preserve its functionality during aging. To explore the biological basis of this phenomenon, we characterized the epigenetic profile of liver biopsies collected from 45 healthy liver donors ranging from 13 to 90 years old using the Infinium HumanMethylation450 BeadChip. The analysis indicates that a large remodeling in DNA methylation patterns occurs, with 8823 age-associated differentially methylated CpG probes.

This paper deals with the elastic energy induced by systems of straight edge dislocations in the framework of linearized plane elasticity. The dislocations are introduced as point topological defects of the displacement-gradient fields. Following the core radius approach, we introduce a parameter ? > 0 representing the lattice spacing of the crystal, we remove a disc of radius ? around each dislocation and compute the elastic energy stored outside the union of such discs, namely outside the core region. Then, we analyze the asymptotic behaviour of the elastic energy as ?

Conformational variability and heterogeneity are crucial determinants of the function of biological macromolecules. The possibility of accessing this information experimentally suffers from severe under-determination of the problem, since there are a few experimental observables to be accounted for by a (potentially) infinite number of available conformational states. Several computational methods have been proposed over the years in order to circumvent this theoretically insurmountable obstacle.

In this paper we analyse temporal variations of the phase of a very low frequency (VLF) signal, used for the lower ionosphere monitoring, in periods around four earthquakes (EQs) with magnitude greater than 4. We provide two analyses in time and frequency domains. First, we analyse time evolution of the phase noise. And second, we examine variations of the frequency spectrum using Fast Fourier Transform (FFT) in order to detect hydrodynamic wave excitations and attenuations.

The sedimentation process in an active suspension is the result of the competition between gravity and the autonomous motion of particles. We carry out simulations of run-and-tumble squirmers that move in a fluid medium, focusing on the dependence of the non-equilibrium steady state on the swimming properties.