Paweł Potorski

• PhD
• Assistant at AGH University of Krakow

Let Tf:[0,1]→[0,1] be an expanding Lorenz map, this means Tfx:=f(x)(mod 1) where f:[0,1]→[0,2] is a strictly increasing map satisfying inf⁡f′>1. Then Tf has two pieces of monotonicity. In this paper, sufficient conditions when Tf is topologically mixing are provided. For the special case f(x)=βx+α with β≥23 a full characterization of parameters (β,...

The paper proposes a methodology for incorporating uncertainties of material behaviours in the microstructure evolution model for eutectoid steels. The stochastic model of phase transformations was developed. The model accounts for a random character of the nucleation of pearlite and bainite and the differential growth equations for these structura...

The motivation for this research was the need for a reliable prediction of the distribution of microstructural parameters in steels during thermomechanical processing. The stochastic model describing the evolution of dislocation populations and grain size, which considers the random phenomena occurring during the hot forming of metallic alloys, was...

The need for a reliable prediction of the distribution of microstructural parameters in metallic materials after processing was the motivation for this work. The model describing phase transformations, which considers the stochastic character of the nucleation of the new phase, was formulated. Numerical tests of the model, including sensitivity ana...

Modern construction materials, including steels, have to combine strength with good formability. In metallic materials, these features are obtained for heterogeneous multiphase microstructures. Design of such microstructures requires advanced numerical models. It has been shown in our earlier works that models based on stochastic internal variables...

We propose a novel methodology for estimating the epidemiological parameters of a modified SIRD model (acronym of Susceptible, Infected, Recovered and Deceased individuals) and perform a short-term forecast of SARS-CoV-2 virus spread. We mainly focus on forecasting number of deceased. The procedure was tested on reported data for Poland. For some s...

In this paper a simulation comparison of the bootstrap confidence intervals for the coefficients of the autocovariance function of a periodically correlated time series is provided. Two bootstrap methods are used: the circular version of the Extension of Moving Block Bootstrap and the circular version of the Generalized Seasonal Block Bootstrap. Th...

The main objective of this paper is to establish the residual and the wild bootstrap procedures for periodically autoregressive models. We use the least squares estimators of model’s parameters and generate their bootstrap equivalents. We prove that the bootstrap procedures for causal periodic autoregressive time series with finite fourth moments a...

In the paper we provide exact lower bounds of topological entropy in the class of transitive and mixing maps preserving the Lebesgue measure which are nowhere monotone (with dense knot points).

In the chapter the performance comparison in the simulation study of the~block bootstrap methods that can be used in the problem of the overall mean estimation of a PC time series is presented. Two block bootstrap techniques are considered: the Circular Block Bootstrap and the circular version of the Generalized Seasonal Block Bootstrap. The actual...