This paper is devoted to investigating the sequence of some linear functionals in the space BV of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In particular, the obtained results can be used to study convergence of some general Fourier series. Moreover, the obtained conditions seem to be new and useful also for ...

The paper deals with periodic homogenization problem for a para\-bo\-lic equation whose elliptic part is a convolution type operator with rapidly oscillating coefficients. It is assumed that the coefficients are rapidly oscillating periodic functions both in spatial and temporal variables and that the scaling is diffusive that is the scaling factor of the temporal variable is equal to the square of ...

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 ...

This master’s thesis examines the viability of using a low-performance, low- power-consumption remote robot agent to collect sensor data for use in a vSLAM system. Selections for the components of the robot agent were made based on results from a small initial study, the robot was assembled, and software to run it was created. A remote server application was created to communicate with the robot ...

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, ...

Over the decades medical analyses have grown in importance and practice possibilities. Digital operations like split-image procedures have become an integral part of modern medical practices and are still gaining momentum. Through the application of this technique medical computed tomography (CT) and magnetic resonance imaging scans (MRI) can be converted to three-dimensional bodies. This paper ...

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 ...