Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1
We deal with the family B(n,k,r) of trinomial arcs defined as the set of roots of the trinomial equation zn=αzk+(1−α), where z=ρeiθ is a complex number, n and k are two integers such that 0<k<n, and α is a real number between 0 and 1. These arcs B(n,k,r) are continuous arcs inside the unit dis...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/91535 |
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| _version_ | 1832554415220850688 |
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| author | Kaoutar Lamrini Uahabi Mohammed Zaoui |
| author_facet | Kaoutar Lamrini Uahabi Mohammed Zaoui |
| author_sort | Kaoutar Lamrini Uahabi |
| collection | DOAJ |
| description | We deal with the family B(n,k,r) of trinomial arcs defined as the set of roots of the trinomial equation
zn=αzk+(1−α), where z=ρeiθ is a complex number, n and k are two integers such that 0<k<n, and
α is a real number between 0 and 1. These arcs
B(n,k,r) are continuous arcs inside the unit disk, expressed in
polar coordinates (ρ,θ). The question is to prove that
ρ(θ) is a decreasing function, for each
trinomial arc B(n,k,r). |
| format | Article |
| id | doaj-art-46d6a42acbd94b6d9e287ccca358ecf7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-46d6a42acbd94b6d9e287ccca358ecf72025-02-03T05:51:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/9153591535Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1Kaoutar Lamrini Uahabi0Mohammed Zaoui1Forces Armées Royales Boulevard 49, Apartment no. 9, Nador 62000, MoroccoDepartment of Mathematics, Faculty of Sciences, Mohamed first University, P.O. Box 524, Oujda 60000, MoroccoWe deal with the family B(n,k,r) of trinomial arcs defined as the set of roots of the trinomial equation zn=αzk+(1−α), where z=ρeiθ is a complex number, n and k are two integers such that 0<k<n, and α is a real number between 0 and 1. These arcs B(n,k,r) are continuous arcs inside the unit disk, expressed in polar coordinates (ρ,θ). The question is to prove that ρ(θ) is a decreasing function, for each trinomial arc B(n,k,r).http://dx.doi.org/10.1155/2007/91535 |
| spellingShingle | Kaoutar Lamrini Uahabi Mohammed Zaoui Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 International Journal of Mathematics and Mathematical Sciences |
| title | Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 |
| title_full | Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 |
| title_fullStr | Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 |
| title_full_unstemmed | Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 |
| title_short | Behavior of the Trinomial Arcs B(n,k,r) when 0<α<1 |
| title_sort | behavior of the trinomial arcs b n k r when 0 α 1 |
| url | http://dx.doi.org/10.1155/2007/91535 |
| work_keys_str_mv | AT kaoutarlamriniuahabi behaviorofthetrinomialarcsbnkrwhen0a1 AT mohammedzaoui behaviorofthetrinomialarcsbnkrwhen0a1 |