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Abstract

The known standard recursion methods of computing the full normalized associated Legendre functions do not give the necessary precision due to application of IEEE754-2008 standard, that creates a problems of underflow and overflow. The analysis of the problems of the calculation of the Legendre functions shows that the problem underflow is not dangerous by itself. The main problem that generates the gross errors in its calculations is the problem named the effect of “absolute zero”. Once appeared in a forward column recursion, “absolute zero” converts to zero all values which are multiplied by it, regardless of whether a zero result of multiplication is real or not. Three methods of calculating of the Legendre functions, that removed the effect of “absolute zero” from the calculations are discussed here. These methods are also of interest because they almost have no limit for the maximum degree of Legendre functions. It is shown that the numerical accuracy of these three methods is the same. But, the CPU calculation time of the Legendre functions with Fukushima method is minimal. Therefore, the Fukushima method is the best. Its main advantage is computational speed which is an important factor in calculation of such large amount of the Legendre functions as 2 401 336 for EGM2008
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Authors and Affiliations

Elena Novikova
Alexander Dmitrenko
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Abstract

The aim study is the development of the classification of agricultural enterprises, based on the properties of the distribution of enterprises depending on the size of the land bank. To achieve this aim, open databases of agricultural enterprises were used, from which data for the Dnipropetrovsk district were selected. The data is not official. They are collected according to the data provided by the agricultural enterprises themselves. Since the official statistics group of small enterprises with up to 200 ha of land includes a fairly large number of enterprises that exist only formally, and since actively functioning enterprises are voluntarily registered in the databases used for the study, the developed classification reflects the real situation with agricultural enterprises in the Dnipropetrovsk district. The proposed scheme of a grouping of agricultural enterprises is regular, logarithmically uniform and based on the exponential increase of the land bank of agricultural enterprises. Its parameters are chosen in such a way as to take into account the classification of farms used in the Tax Code of Ukraine. The developed grouping of agricultural enterprises was used to analyze such characteristics of enterprises as types of production and organizational and legal forms of management. The analysis of the distribution showed that with the decrease of the land bank the number of farms increases and the number of enterprises, whose forms of management are joint-stock companies of different types, decreases.
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Authors and Affiliations

Elena Novikova
1
ORCID: ORCID
Alena Palamar
1
ORCID: ORCID
Daria Bondarenko
1
ORCID: ORCID
Maksym Hanchuk
2
ORCID: ORCID
Vladyslav Riabchii
3
ORCID: ORCID

  1. Kryvyi Rih National University, Kryvyi Rih, Ukraine
  2. Dmytro Motornyi Tavria State Agrotechnological University, Melitopol, Ukraine
  3. Dnipro University of Technology, Dnipro, Ukraine

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