In this paper we discuss, complement and improve some Bennett type inequalities. In particular,we prove a new refinement of a Bennett type inequality using super quadracity argument.

In this paper, we derive the maximal subspace of natural numbers { <i>n_k</i> : <i>k</i> &#8805; 0 }, such that the restricted maximal operator, defined by sup_{<i>k</i>&#8712;&#8469;} | &sigma;<i>_{n_k}F</i> | on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space <i>H</i>_1/2 to the Lebesgue space ...

Marine macroalgae form underwater "blue forests" with several important functions. Hyperspectral imaging from unmanned aerial vehicles provides a rich set of spectral and spatial data that can be used to map the distribution of such macroalgae. Results from a study using 81 annotated hyper-spectral images from the Norwegian coast are presented. A U-net convolutional network was used for classification, ...

Development of snake robots have been motivated by the ability of snakes to move efficiently in unstructured and cluttered environments. A snake robot has the potential to utilise obstacles for generating locomotion, in contrast to wheeled robots which are unable to move efficiently in rough terrain. In this paper, we propose a local path planning algorithm for snake robots based on obstacle-aided ...

In this paper, we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these new operators indeed are bounded from the martingale Hardy space H_p(G) to the Lebesgue space weak−L_p(G), for 0<p<1. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known ...

This paper provides a method for determining the economic incentives and limitations for a battery used for peak clipping, with the goal of finding an optimal mix between the battery’s power density and energy density. A ratio called the R-factor has been introduced, which helps determine the energy demand to curb the peak. The paper’s results embrace different investment scenarios showing what ...

We prove and discuss some new weak type (1, 1) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out.

We prove that by scaling nearest-neighbour ferromagnetic energies de ned on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on proving that cells with `very long' or `very short' edges of the corresponding Voronoi tessellation can be neglected. In this way we may apply Geometry Measure ...