The recursive algorithm to construct Dirichlet function
The problem of determining the total number of rational fractions with values are equal to x is considered. The importance of this problem is demonstrated for the procedures processing statistical data, representing the ratio of two discrete variables with a variable denominator. It is found out, th...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
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Educational institution «Belarusian State University of Informatics and Radioelectronics»
2019-06-01
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| Series: | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
| Subjects: | |
| Online Access: | https://doklady.bsuir.by/jour/article/view/75 |
| _version_ | 1797881218824404992 |
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| author | A. N. Lysiuk S. S. Derechennik |
| author_facet | A. N. Lysiuk S. S. Derechennik |
| author_sort | A. N. Lysiuk |
| collection | DOAJ |
| description | The problem of determining the total number of rational fractions with values are equal to x is considered. The importance of this problem is demonstrated for the procedures processing statistical data, representing the ratio of two discrete variables with a variable denominator. It is found out, that that required number of fractions is equal to the Dirichlet function value at the x point, and the original rule is proposed to construct it, which has a simple geometric interpretation. A proposed implementation of this algorithm shows its computational efficiency, and its importance is noted for problems requiring generation of relatively prime numbers. |
| first_indexed | 2024-04-10T03:16:30Z |
| format | Article |
| id | doaj.art-5e555d69859e45239bf58edc42037bc8 |
| institution | Directory Open Access Journal |
| issn | 1729-7648 |
| language | Russian |
| last_indexed | 2024-04-10T03:16:30Z |
| publishDate | 2019-06-01 |
| publisher | Educational institution «Belarusian State University of Informatics and Radioelectronics» |
| record_format | Article |
| series | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
| spelling | doaj.art-5e555d69859e45239bf58edc42037bc82023-03-13T07:33:10ZrusEducational institution «Belarusian State University of Informatics and Radioelectronics»Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki1729-76482019-06-010511612174The recursive algorithm to construct Dirichlet functionA. N. Lysiuk0S. S. Derechennik1Брестский государственный технический университетБрестский государственный технический университетThe problem of determining the total number of rational fractions with values are equal to x is considered. The importance of this problem is demonstrated for the procedures processing statistical data, representing the ratio of two discrete variables with a variable denominator. It is found out, that that required number of fractions is equal to the Dirichlet function value at the x point, and the original rule is proposed to construct it, which has a simple geometric interpretation. A proposed implementation of this algorithm shows its computational efficiency, and its importance is noted for problems requiring generation of relatively prime numbers.https://doklady.bsuir.by/jour/article/view/75функция дирихлефракталрекурсивный алгоритмвзаимно простые числастатистическая обработка данных |
| spellingShingle | A. N. Lysiuk S. S. Derechennik The recursive algorithm to construct Dirichlet function Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki функция дирихле фрактал рекурсивный алгоритм взаимно простые числа статистическая обработка данных |
| title | The recursive algorithm to construct Dirichlet function |
| title_full | The recursive algorithm to construct Dirichlet function |
| title_fullStr | The recursive algorithm to construct Dirichlet function |
| title_full_unstemmed | The recursive algorithm to construct Dirichlet function |
| title_short | The recursive algorithm to construct Dirichlet function |
| title_sort | recursive algorithm to construct dirichlet function |
| topic | функция дирихле фрактал рекурсивный алгоритм взаимно простые числа статистическая обработка данных |
| url | https://doklady.bsuir.by/jour/article/view/75 |
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