We study the Schwarzian derivative from a variational viewpoint. Firstly we show that defines first integral of Euler--Lagrange equation second order Lagrangian. Secondly, itself is operator for an appropriately chosen class variations.

The CoI2(PPh3)2/Zn system effectively catalyzes the [2 + 2 + 2] ene-diyne cycloaddition of 1,6-heptadiynes with allenes in a highly regio- and chemoselective fashion to yield substituted benzene derivatives in good to excellent yields.

A new strategy for Rh(I)-catalyzed [2+2+2] cycloadditions of 1,6-diynes with potassium (Z)-(2-bromovinyl)trifluoroborate as the third two-atom unit has been realized, which provides a facile entry to polysubstituented benzene derivatives.

Hexa-substituted benzene derivatives show larger two-photon cross sections than the corresponding dipolar counterparts and the largest values of delta(max) = 2000 GM and delta(max)/MW = 2.25 GM g(-1) have been obtained with a compound having C[triple bond]C and C=C bonds in the conjugation bridge.

We have successfully developed a new synthetic approach to modulate the electrostatic potentials of metallocavitands and thus their selective recognition towards substituted benzene derivatives via integrating two metal cations of different electronegativity into a self-assembled system.

A local normal form is obtained for geodesics in the space Λ = {Γ} of analytic Jordan curves in the extended complex plane with symmetric space multiplication Γ1 · Γ2 defined by Schwarzian reflection of Γ2 in Γ1. Local geometric features of (Λ, ·) will be seen to reflect primarily the structure of the Witt algebra, while issues of global behavior of the exponential map will be viewed in the con...

In this paper we study measurable dynamics for the widest rea sonable class of smooth one dimensional maps Three principle de compositions are described in this class decomposition of the global measure theoretical attractor into primitive ones ergodic decompo sition and Hopf decomposition For maps with negative Schwarzian derivative this was done in the series of papers BL BL but the approach ...