On the Cantor series

On the rationality of Cantor and Ahmes series

We give criteria for the rationality of Cantor series ∑ ∞ n=1 bn a1···an and series ∑ ∞ n=1 bn an where a1, a2, · · · and b1, b2, · · · are integers such that an > 0 and the series converge. We precisely say when ∑ ∞ n=1 bn a1···an is rational (i) if {an} ∞ n=1 is a monotonic sequence of integers and bn+1 − bn = o(an+1) or lim supn→∞( bn+1 an+1 − bn an ) ≤ 0, and (ii) if bn+1 an+1−1 ≤ bn an−1 f...

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...

On the Spectra of a Cantor Measure

We analyze all orthonormal bases of exponentials on the Cantor set defined by Jorgensen and Pedersen in J. Anal. Math. 75,1998, pp 185-228. A complete characterization for all maximal sets of orthogonal exponentials is obtained by establishing a one-to-one correspondence with the spectral labelings of the infinite binary tree. With the help of this characterization we obtain a sufficient condit...

On the Shape of Cantor Sets

Improvements on the Cantor-Zassenhaus Factorization Algorithm

We describe a new simplified version of the Cantor-Zassenhaus polynomial factorization algorithm, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but also enable us to derive good estimates and deterministic bounds on the number of attempts needed to factor a given polynomial. Mathematics Subject Classifi...