Higher-order degenerated versions of Fay’s trisecant identity are presented. It is shown that these lead to solutions for Schwarzian Kadomtsev–Petviashvili equations.

For normalized analytic functions f in the unit disk D = {z ∈ C : |z| < 1}, we consider

Combining the definition of Schwarzian derivative for conformal mappings between Riemannian manifolds given by Osgood and Stowe with that for parametrized curves in Euclidean space given by Ahlfors, we establish injectivity criteria for holomorphic curves φ : D → C. The result can be considered a generalization of a classical condition for univalence of Nehari.

Period adding with the coexistence of successive at tract ing periodic orbit s is observed in the model of a chemical system when the bifurcation parameter is changed. This phenomenon is characterized by a family of one-dimensional return maps having a cusp shape with positive Schwarzian derivative that exhibits a saddle-node bifurcation.

The first group of differentiable cohomology of Diff(S 1), vanishing on the Möbius subgroup P SL(2, R) ⊂ Diff(S 1), with coefficients in modules of linear differential operators on S 1 is calculated. We introduce three non-trivial P SL(2, R)-invariant 1-cocycles on Diff(S 1) generalizing the Schwarzian derivative.

Transient precursor states are often experimentally observed for molecules adsorbing on surfaces. However, such precursor states are typically rather short-lived, quickly yielding to more stable adsorption configurations. Here we employ first-principles calculations to systematically explore the interaction mechanism for benzene derivatives on metal surfaces, enabling us to selectively tune the...

An< accurate, stable and very fast corner finder (for feature based vision) has been developed', based on a novel definition of corners, using:no image derivatives. This note describes the algorithm and the results obtained from its use.