where h and g are analytic in D. We call h the analytic part and g the coanalytic part of f . A necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h z | > |g z | for all z in D see 1 . Let H be the class of functions of the form 1.1 that are harmonic univalent and sense preserving in the unit disk U {z : |z| < 1} for which f 0 fz 0 − 1 0. Then fo...

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...

Let f and F be members of . The function f is said to be subordinate to F, or F is said to be superordinate to f , if there exists a function w analytic in U, with w(0)= 0 and |w(z)| < 1, and such that f (z)= F(w(z)). In such a case, we write f ≺ F or f (z)≺ F(z). If the function F is univalent in U, then f ≺ F if and only if f (0)= F(0) and f (U)⊂ F(U) (cf. [1, 2]). Let φ : C2 → C and let h be...

Abstract We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied Ahrens, Kapulkin, and Shulman, we define study bicategories. To construct examples bicategories a modular fashion, displayed , an analog 1-categories introduced Ahrens Lumsdaine. demonstrate applicability this prove that several interest are univalent. Among these catego...

A necessary and sufficient coefficient is given for functions in a class of complexvalued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.

We classify Baker domains U for entire maps with fj U univalent into three diierent types, giving several criteria which characterize them. Some new examples of such domains are presented, including a domain with disconnected boundary in C and a domain which spirals towards innnity.

The purpose of the present paper is to study a certain subclass of harmonic univalent functions associated with Dziok-Srivastava operator. We obtain coefficient conditions, distortion bounds, and extreme points for the above class of harmonic univalent functions belonging to this class and discuss a class preserving integral operator. We also show that class studied in this paper is closed unde...

In vitro killing of the human Daudi cell line by either univalent [F(ab')] or divalent (IgG) forms of rabbit anti-human Ig (RAHIg) coupled to ricin A chain can be specifically potentiated by a "piggyback" treatment with ricin B chain coupled to goat anti-rabbit Ig (GARIg). When cells are treated with univalent immunotoxin (IT) [F(ab') RAHIg-A] and then cultured, IT can be detected on the cell s...