f " ' f " 2 where Sf := (p-) 1⁄2 (iv) denotes the Schwarzian derivative, and that this result is sharp, as the function f(z) = 1⁄2 log 11 z + z shows. Tile method of the proof does not give all sharp functions. We shall show that the sharp function is essentially unique using another approach implying Nehari's result. This shows furthermore that all convex domains except of parallel strip domai...

In this paper we study the topological class of universal covering maps from the plane to the sphere with two removed points; we call the elements topological transcendental maps with two asymptotic values and we denote the space byAV2. We prove that an element f ∈ AV2 with finite post-singular set is combinatorially equivalent to a meromorphic transcendental map g with constant Schwarzian deri...

In this paper we investigate rational minimal surfaces { a special class of umbilic-free minimal surfaces with nite total curvature and Enneper type ends. We deene an iteration for Gauss maps and show that it can be used to produce innnitely many families of rational functions that yield rational minimal surfaces{the Schwarzian derivative plays an important role in the proof. We also investigat...

The paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster’s Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter. The bifurcation of its Nash equilibrium is analyzed with ...

Two complementary analyses of a cyclic negative feedback system with delay are considered in this paper. The first analysis applies the work by Sontag, Angeli, Enciso and others regarding monotone control systems under negative feedback, and it implies the global attractiveness towards an equilibrium for arbitrary delays. The second one concerns the existence of a Hopf bifurcation with respect ...

We prove that non-hyperbolic non-renormalizable quadratic polynomials are expansion inducing. For renormalizable polynomials a counterpart of this statement is that in the case of unbounded combinatorics renormalized mappings become almost quadratic. Technically, this follows from the decay of the box geometry. Specific estimates of the rate of this decay are shown which are sharp in a class of...