Papers by Tariq Al-Fadhel
Abstract: This paper studies the rate of convergence of purely periodic continued fractions, and ... more Abstract: This paper studies the rate of convergence of purely periodic continued fractions, and gives an explicit formula for calculating it. It also generalizes the concept to calculate the rate of convergence of any continued fraction. It relates the rate of convergence of any continued fraction,...],;0 [ 21 aa=γ to its Lyapunov exponent γλ, and to its)(γnB, where 110,1 aBB = = , and 21 − − + = nnnn BBaB. It is proved in this paper that the rate of convergence of any infinite continued fraction is always less than or equal to 38196601.0 2
Far East Journal of Applied Mathematics
This paper shows that any Möbius transformation with at least one 2-cycle has the form f(z)=αz+β ... more This paper shows that any Möbius transformation with at least one 2-cycle has the form f(z)=αz+β z-α, where α,β∈ℂ and α 2 +β≠0. Also, it is shown that f(z) maps any circle passing through its fixed points into itself.
Arab Journal of Mathematical Sciences, 2013
Let M be the group of Mo¨bius transformations on C 1 ¼ C [ f1g and hf i M ¼ ff n ; n 2 Zg the cyc... more Let M be the group of Mo¨bius transformations on C 1 ¼ C [ f1g and hf i M ¼ ff n ; n 2 Zg the cyclic subgroup of M generated by f , for f 2 M. If hf i M is finite of order n, f is called an n-cycle. We prove in the first part that if f is an n-cycle, then for any a 2 C 1 , the set ff n ðaÞ; n 2 Zg ¼ Of ðaÞ lies on a circle. Furthermore we characterize with geometric arguments the circles which are invariant under this kind of transformations.
Applied Mathematics and Computation, Jan 1, 2007
ABSTRACT This paper shows that blocks of different entries and different lengths can have the sam... more ABSTRACT This paper shows that blocks of different entries and different lengths can have the same probability of occurrence in the representation of any continued fraction which its orbit distributed according to Gauss measure.More precisely there are blocks of even lengths and 3-blocks which their probability of occurrence equals to the probability of occurrence of a unit block, and this property is not satisfied by the Bernoulli shift.
WSEAS Transactions on Systems, Jan 1, 2006
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Papers by Tariq Al-Fadhel