In this work, stability analysis is performed for a cyclic dynamical model of gene regulatory networks involving time delays, under negative feedback. The model considered has nonlinearities with negative Schwarzian derivatives. Sufficient conditions implying global stability of these types of GRNs are obtained. The special case of homogenous gene regulatory networks is also studied; in this ca...

For normalized analytic functions in the unit disk, we consider subclasses of bounded turning. The geometric representation is introduced, the radii of convexity (close to convex) are calculated and some subordination relations are suggested. Moreover, the upper bound of the pre-Schwarzian norm for these functions is computed. AMS subject classifications: 30C45

Let G be a finitely generated Fuchsian group of the second kind without any parabolic element and f univalent analytic function in unit diskDcompatible withG. In this paper, westudy higher order Schwarzian derivatives: ?n+1( ) = ?? n( )?(n?1) f?? f???n( ), n ? 3, where ?3(f) stands for derivatives f, Sn(f) (f?) n?1/2 Dn( ?)? , 2. For p > 0, we show that if |?n(f)(z)|p(1?|z|2)p(n?1)?1dxdy (re...

In this note we present an application of the Schwarzian derivative. By exploiting some properties of the Schwarzian derivative, we solve the equation appearing in the gravity-dilaton-antisymmetric tensor system. We also mention that this method can also be used to solve some other equations. The Schwarzian derivative appears naturally in the transformation law of the two-dimensional stress-ene...

With his hyperbolic Dehn surgery theorem and later the orbifold theorem, Thurston demonstrated the power of using hyperbolic cone-manifolds to understand complete, non-singular hyperbolic 3-manifolds. Hodgson and Kerckhoff introduced analytic techniques to the study of cone-manifolds that they have used to prove deep results about finite volume hyperbolic 3-manifolds. In this paper we use Hodgs...

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, ...