Citizenship is a powerful concept in public discourse, often regarded as tool for promoting inclusion and racial equality. But citizenship has important limitations vehicle achieving egalitarian aspirations. As scholars have noted, an exclusionary logic, gradations of are inevitable. Contrary to the conventional wisdom, it served only weak antidote disadvantage based on race. Moreover, not alwa...

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...

We show that if (Xs, s ≥ 0) is a right-continuous process, Yt = ∫ t 0 dsXs its integral process and τ = (τl, l ≥ 0) a subordinator, then the time-changed process (Yτl , l ≥ 0) allows to retrieve the information about (Xτl , l ≥ 0) when τ is stable, but not when τ is a gamma subordinator. This question has been motivated by a striking identity in law involving the Bessel clock taken at an indepe...

If X(t) is a stochastic process taking values in some space 9C and g is a real-valued function on 9C then we may consider the process g(X(t)). Often from some knowledge about the process X(t) and the function g one can deduce properties of the process g(X(t)). For example: if X(t) is Brownian motion in R" and g is a subharmonic function on Rn that doesn't grow too fast then g(X(t)) is a semimar...

We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of Lp-norm of a subordinated one via the same norm of a dominating one. In this setting this was done by Burkholder in [Bu1]–[Bu8]. If one of the martingales is orthogonal, the constant should drop. This was demonstrated in [BaJ1], when the orthogona...

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.

In this paper, we obtain some subordination results for certian subclasses of univalent functions defined by convolution.