The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential -- a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the...

Road safety modelling on regional level of NUTS 2 in the EU is the complex issue and authors of this article indicate this in previous publications. NUTS 2 are basic regions for the application of regional policies (0.8-3 m inhabitants). During multivariate models development they discovered that it is difficult to make regression model well described all regions, even if they are from one country. In the first step Poisson model...

W pracy przedstawiono dowód twierdzenia o reprezentacji jąder Poissona dla wielomianów Jacobiego wypukłą kombinacją nieujemnych jąder typu Durrmeyera. Podobne rezultaty uzyskano dla jąder Poissona dla dyskretnych wielomianów Hahna.

We study a variational formulation for reconstructing nonlinearly distorted signals corrupted with a Poisson-Gaussian noise. In this situation, the data fidelity term consists of a sum of a weighted least squares term and a logarithmic one. Both of them are precomposed by a nonlinearity, modelling a clipping effect, which is assumed to be rational. A regularization term, being a piecewise rational approximation of the ℓ0 function...

In this paper multilevel approach to the issue of road safety level on the road network of European regions, classified as NUTS 2 in statistical databases of the European Union, has been presented. Following the pattern of many publications on road safety it has been assumed that the risk calculated as the number of death casualties in road accidents per 100,000 inhabitants of a given region has Poisson distribution. Therefore,...