Subordination Agreements

1 Subordination at the Interface : the Quasi - Subordination Hypothesis

The subordination of clauses, and the recursion which results, lies at the heart of linguistic representation. Yet there are many aspects of subordination that are not fully understood. An enduring puzzle is that some clauses which appear to be structurally subordinate nevertheless pattern with main clauses in certain, but not all, respects. This paper posits that such clauses, which we term “q...

Subordination by convex functions

Fuzzy Differential Subordination

The method of differential subordination or ”admissible functions method” was introduced by P.T. Mocanu and S.S. Miller in [1], [2] and then developed in monography [3], as well as in other papers of other mathematicians. Until now, the notion of differential subordination appears in papers published in various journals specialized in complex analysis around the world. We extend this method to ...

Subordination by Convex Functions

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...

Retrieving information from subordination

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...