In the paper, we statistically analysed data on the average hourly wind speed obtained from the meteorological station Poprad (located at the Poprad-Tatry airport, the Prešov region, Northern Slovakia) for the period 2005–2021. High altitude and rough mountainous terrain influence the weather conditions considerably and are a source of occasional weather risks. Finding an appropriate wind speed distribution for modelling the wind speed data is therefore important to determine the wind profile at this particular location. In addition to the commonly used two- and three-parameter Weibull distribution, a more flexible exponentiated Weibull (EW) distribution was applied to model the wind speed. Based on the results of the goodness-of-fit criteria (the Kolmogorov–Smirnov test, the Anderson–Darling test, Akaike’s and Bayesian information criteria, the root mean square error, and the coefficient of determination), the EW distribution obtained a significantly better fit to seasonal and monthly wind speed data, especially around the peaks of the data. The EW distribution also proved to be a good model for data with high positive skewness. Therefore, we can recommend the EW distribution as a flexible distribution for modelling a dataset with extremely strong winds or outliers in the direction of the right tail. Alongside the wind speed analysis, we also provided the wind direction analysis, finding out that the most prevailing direction was west (W)—with an occurrence rate of 34.99%, and a mean wind speed of 3.91 m/s, whereas the northern (N) direction featured the lowest occurrence rate of only 4.45% and the mean wind speed of 1.99 m/s.

In this paper we study new distribution called transmuted Weibull distribution. Some properties of this distribution are described. The usefulness of the distribution for modelling data is illustrated using real data set.

According to the Green Deal, the carbon neutrality of the European Union (EU) should be reached partly by the transition from fossil fuels to alternative renewable sources. However, fossil fuels still play an essential role in energy production, and are widely used in the world with no alternative to be completely replaced with, so far. In recent years, we have observed the rapidly growing prices of commodities such as oil or gas. The analysis of past fossil fuels consumption might contribute significantly to the responsible formulation of the energy policy of each country, reflected in policies of related organisations and the industrial sector. Over the years, a number of papers have been published on modelling production and consumption of fossil and renewable energy sources on the level of national economics, industrial sectors and households, exploiting and comparing a variety of approaches. In this paper, we model the consumption of fossil fuels (gas and coal) in Slovakia based on the annual data during the years 1965–2020. To our knowledge, no such model, which analyses historical data and provides forecasts for future consumption of gas and coal, respectively, in Slovakia, is currently available in the literature. For building the model, we have used the Box–Jenkins methodology. Because of the presence of trend in the data, we have considered the autoregressive integrated moving average (ARIMA (p,d,q)) model. By fitting models with various combinations of parameters p, d, q, the best fitting model has been chosen based on the value of Akaike’s information criterion. According to this, the model for coal consumption is ARIMA(0, 2, 1) and for gas consumption it is ARIMA(2, 2, 2).

The paper develops a mathematical model of foreign currency exchange market in the form of a stochastic linear differential equation with coefficients depending on a semi-Markov process. The boundaries of the domain of its instability is determined by using moment equations.

In the present paper, the Weibull distribution is used to analyse the wind speed data of Liptovský Mikuláš-Ondrašová (49°05′52″ N, 19°35′32″ E), situated in northern Slovakia. Analysed wind speed data were collected over the 11-year period (2005-2015) and they were recorded three times a day. The results show that the seasonal values of the shape parameterkrange from 1.474 to 1.607, with yearly value of 1.546 while the seasonal values of the scale parametercrange from 2.488 to 3.010m/s, with yearly value of 2.726m/s. We find out that according to the coefficient of determination and root mean square error, the Weibull distribution performs well in fitting the wind speed data.

Valveless pumping, also known as Liebau effect, can be described as the unidirectional flow of liquid in a system without valves that is caused by the asymmetry of placing of the periodically working pump. Recently, the research in this field has been reevoked, partially due to its possible application in nanotechnologies. In this paper, a configuration of one pipe and one tank is considered from the mathematical point of view. Qualitative properties of a class of nonlinear differential equations that model the assumed system configuration are investigated. New sufficient conditions for the existence of positive T-periodic solutions are given. Correspondingly, exponential stability of periodic solution is treated. Presented results are new. They extend and complement earlier ones in the literature.