Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...

We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category $\mathbb{EFF}$. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category $\mathbb{EFF}$ one can i...

The purpose of this work is to present a class harmonic univalent functions de?ned by the Dziok-Srivastava operator. Some geometric properties like coefficients conditions, distortion theorem, convolution (Hadamard product), convex combination and extreme points are investigated.
 2000 Mathematics Subject Classi?cation: 30C45, 30C50

FMN and flavodoxin, when reduced by the action of ferredoxin-TPN+ oxidoreductase, have been shown to cause both univalent and divalent reductions of oxygen. Superoxide radicals, so generated, were detected by their abilities to oxidize epinephrine to adrenochrome and to reduce cytochrome c. Superoxide dismutase inhibited these actions of the superoxide radical. The ratio of the univalent reduct...

We investigate the relationship between the univalence of f and of h in the decomposition f = h+g of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + g with |g| < c|h| is univalent. The notion of a linearly connected domain appea...

The goal of this paper is to give a preliminary formalization of the p-adic numbers, in the context of the Univalent Foundations. We also provide the corresponding code verifying the construction in the proof assistant Coq. Because work in the univalent setting is ongoing, the structure and organization of the construction of the p-adic numbers we give in this paper is expected to change as Coq...