This note is a sequel to the paper On rings on rings by Anatole Beck [ l ] . The problem we consider (originally proposed by Paul Rosenbloom) is that of characterizing the parameter p for the annulus Q = {1< | s| <p} in terms of the ring R of bounded analytic functions nn this annulus. Beck's solution involves properties of univalent functions, and although the subset of univalent functions in ...

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to involution numbers. find initial estimates Taylor–Maclaurin coefficients |a2| |a3| for functions introduced here. also obtain a Fekete–Szegö inequality class. Several consequences our results pointed out, not yet discussed as...

The univalent hapten, nonadeca lysyl epsilon-Dnp-lysine, binds tightly to rabbit anti-2,4-dinitrophenyl antibody, and the complex has a sedimentation coefficient of 6.7, characteristic of a single antibody molecule. In this communication, we show that this complex is a good activator of the serum complement system. For activation to occur, the univalent hapten must contain the specific group wh...

Spinach chloroplasts induced the photoreduction of cytochrome c and photooxidation of epinephrine, both of which depended on oxygen and were inhibited by superoxide dismutase. This confirmed the univalent reduction of molecular oxygen in illuminated chloroplasts. In the presence of cytochrome c, hydrogen peroxide formation by chloroplasts was inhibited completely. Rates for the photoreduction o...

Let A denote the family of all analytic functions f in the unit disk D with the normalization f (0) = 0 = f ′(0)− 1. Define S = { f ∈ A : f is univalent in D}, U = { f ∈A : ∣∣ f ′(z)(z/ f (z))2−1∣∣< 1 for z ∈ D}, and P(1/2) = { f ∈A : Re( f (z)/z) > 1/2 for z ∈ D}. In this paper, we determine the radius of univalency of F(z) = z f (z)/g(z) whenever f ∈S or U , and g ∈S or P(1/2). Based on our i...

which are analytic in the open unit disk E. Also, A1 = A, the usual class of analytic functions defined in the open unit disk E = {z : |z| < 1}. Let f(z) and g(z) be analytic in E. We say that the function f is subordinate to the function g and write f(z) ≺ g(z), if and only if there exists Schwarz function w, analytic in E such that w(0) = 0, |w(z)| < 1 for z ∈ E, and f(z) = g(w(z)). In partic...

In [6] it was shown that if f ∈ is starlike of order α, α= 0.294, . . . , so is the Libera integral operator F . We also know that (see, e.g., [1]) there are functions which are univalent or spiral-like in so that their Libera integral operators are not univalent or spiral-like in . Li and Owa [5] proved that if f ∈ is univalent in , then Fn(z) is starlike in |z| < 3/8. The number 3/8 is sharp....