Denote Vn(d) the least number that every system of n cubes with total volume 1 in d-dimensional (Euclidean) space can be packed parallelly into some rectangular parallelepiped of volume Vn(d). New results V3(5)≐1.802803792, V3(7)≐2.05909680, V3(9)≐2.21897778, V3(10)≐2.27220126, V3(11)≐2.31533581, V3(12)≐2.35315527, V3(13)≐2.38661963 can be found in the paper.
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.
The paper deals with model of electricity consumption in a company providing hot and cold forming. As modelled data, there were used hourly records of electricity consumed in the manufacturing processes. The data covered working hours over a year. The probability distributions, chosen for modelling, were normal distribution, gamma distribution, logistic distribution, Weibull distribution and Rayleigh distribution. The goodness of fit of these distributions was judged based on the values of the information criteria (AIC, AICc and BIC), coefficient of determination (R2) and the root mean square error (RMSE). According to these criteria, the best fit was achieved by the two-parameter Weibull distribution.
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