A ~e on some empirical properties of the Mandelbrot Set

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Topological, Geometric and Complex Analytic Properties of Julia Sets

In this paper, we discuss several aspects of Julia sets, as well as those of the Mandelbrot set. We are interested in topological properties such as connectivity and local connectivity, geometric properties such as Hausdorff dimension and Lebesgue measure, and complex analytic properties such as holomorphic removability. As one can easily see from the pictures of numerical experiments, there is...

On some forms of e*-irresoluteness

‎The main goal of this paper is to introduce and study two new class of functions‎, ‎called weakly $e^*$-irresolute functions and strongly $e^*$-irresolute functions‎, ‎via the notion of $e^*$-open set defined by Ekici [7]. ‎We obtain several fundamental properties and characterizations of these functions‎. ‎Moreover‎, ‎we investigate not only some of their basic properties but also their relat...

Hypercomputing the Mandelbrot Set?

The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which are treated much more thoroughly and technically in [1], [2], [3] and [4] amon...

On Some Properties and Estimation of a Skew Symmetric Density Function

 In this paper we consider a general setting of skew-symmetric distribution which was constructed by Azzalini (1985), and its properties are presented. A suitable empirical estimator for a skew-symmetric distribution is proposed. In data analysis, by comparing this empirical model with the estimated skew-normal distribution, we show that the proposed empirical model has a better fit in den...