Let D ⊂ C and 0 ∈ D. A set D is circularly symmetric if for each % ∈ R a set D ∩ {ζ ∈ C : |ζ| = %} is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing %. A function f ∈ A is circularly symmetric if f(∆) is a circularly symmetric set. The class of all such functions we denote by X. The above definitions were given by Jenkins in [2]. In ...

The main objective of this paper is to study certain geometric properties (like univalence, starlikeness, convexity, close-to-convexity) for the normalized Miller-Ross function. various results, which we have established in present investigation, are believed be new, and their importance illustrated by several interesting consequences examples. Furthermore, some results improve corresponding av...

We show that for α ∈ (0, 2], if f ∈ A with f ′(z) 6= 0, z ∈ E, satisfies the condition (1− α)f ′(z) + α ( 1 + zf ′′(z) f ′(z) ) ≺ F (z), then f is univalent in E, where F is the conformal mapping of the unit disk E with F (0) = 1 and F (E) = C \ { w ∈ C : < w = α, |= w| ≥ √ α(2− α) } . Our result extends the region of variability of the differential operator (1− α)f ′(z) + α ( 1 + zf ′′(z) f ′(...

Between 1989 and 1992 meiotic chromosome studies and synaptonemal complex analyses were evaluated using light and, in part, electron microscopy in 46 infertile males with highly abnormal spermiograms. This examination focused on whether the breakdown of spermatogenesis could be attributed to pairing anomalies of bivalents. The study of meiotic chromosomes and synaptonemal complexes indicated no...

A multiset consists of elements, but the notion of a multiset is distinguished from that of a set by carrying information of how many times each element occurs in a given multiset. In this work we will investigate the notion of iterative multisets, where multisets are iteratively built up from other multisets, in the context Martin-Löf Type Theory, in the presence of Voevodsky’s Univalence Axio...