arXiv subjects

Shimaa Elsayed-Abdullah

Publications and source records attributed to Shimaa Elsayed-Abdullah.

2 recordsLinked to original sources

arXiv2025

On the Zeros of $q$-Hankel Transform by Using P\'{o}lya-Hurwitz Partial Fraction Method

The technique of P\'{o}lya-Hurwitz of partial fractions is implemented to investigate the zeros of finite $q$-Hankel transforms, which are defined in terms of the third $q$-Bessel function of Jackson. The new approach, which is a $q$-counterpart of P\'{o}lya-Hurwitz technique relaxes the restrictive conditions imposed on $q$ in the previously obtained results. In the present study, we use the $q$-type sampling theorems of the $q$-Hankel transforms, which lead directly to $q$-partial fractions. Various experimental examples are established.

math.NT↗

arXiv2024

On Kakeya's Geometric Proof of Enestr\"om-Kakeya's Theorem

This paper is devoted to demonstrate Kakeya's geometric proof of his theorem (1912), independently established earlier by Enestr\"om (1893). By calculating centers and radii of the interlacing circles of Kakeya's method, we prove Kakeya's geometric structure, which has not been previously established. We give an equivalent proof, which is based on the construction of internally interlacing circles, which has been geometrically considered by Tomic (1948).

math.CV↗