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 |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0161-1712 1687-0425 |