On the Roots of a Family of Polynomials
The aim of this paper is to give a characterization of the set of roots of a special family of polynomials. This family is relevant in reliability theory since it contains the reliability polynomials of the networks created by series-parallel compositions. We prove that the set of roots is bounded,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/4/339 |
| _version_ | 1797605347781771264 |
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| author | Marilena Jianu |
| author_facet | Marilena Jianu |
| author_sort | Marilena Jianu |
| collection | DOAJ |
| description | The aim of this paper is to give a characterization of the set of roots of a special family of polynomials. This family is relevant in reliability theory since it contains the reliability polynomials of the networks created by series-parallel compositions. We prove that the set of roots is bounded, being contained in the two disks of the radius equal to the golden ratio, centered at 0 and at 1. We study the closure of the set of roots and prove that it includes two disks centered at 0 and 1 of a radius slightly greater than 1, as well as the sinusoidal spirals centered at 0 and at 1, respectively. The expression of some limit points is also provided. |
| first_indexed | 2024-03-11T04:59:50Z |
| format | Article |
| id | doaj.art-2ab223501a234bbab930913c1eb58171 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T04:59:50Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-2ab223501a234bbab930913c1eb581712023-11-17T19:19:48ZengMDPI AGFractal and Fractional2504-31102023-04-017433910.3390/fractalfract7040339On the Roots of a Family of PolynomialsMarilena Jianu0Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, RomaniaThe aim of this paper is to give a characterization of the set of roots of a special family of polynomials. This family is relevant in reliability theory since it contains the reliability polynomials of the networks created by series-parallel compositions. We prove that the set of roots is bounded, being contained in the two disks of the radius equal to the golden ratio, centered at 0 and at 1. We study the closure of the set of roots and prove that it includes two disks centered at 0 and 1 of a radius slightly greater than 1, as well as the sinusoidal spirals centered at 0 and at 1, respectively. The expression of some limit points is also provided.https://www.mdpi.com/2504-3110/7/4/339reliability polynomialcomplex rootssinusoidal spiralgolden ratio |
| spellingShingle | Marilena Jianu On the Roots of a Family of Polynomials Fractal and Fractional reliability polynomial complex roots sinusoidal spiral golden ratio |
| title | On the Roots of a Family of Polynomials |
| title_full | On the Roots of a Family of Polynomials |
| title_fullStr | On the Roots of a Family of Polynomials |
| title_full_unstemmed | On the Roots of a Family of Polynomials |
| title_short | On the Roots of a Family of Polynomials |
| title_sort | on the roots of a family of polynomials |
| topic | reliability polynomial complex roots sinusoidal spiral golden ratio |
| url | https://www.mdpi.com/2504-3110/7/4/339 |
| work_keys_str_mv | AT marilenajianu ontherootsofafamilyofpolynomials |