The paper presents an application of the asymmetry approach to spirooxindoles via Brevicolline, Cinchonidine or Cinchonine catalyzed one-pot multicomponent synthesis. Brevicolline, in comparison with Cinchonidine or Cinchonine, catalyzes the reaction of isatins, acetylacetone/ethyl 3-oxobutanoate and malononitrile, with the formation of spiro[oxindole-3,4'-4'H-pirane] derivatives in an opticall...

The perception of motion provides valuable interpolations of the visual scene. This fundamental capacity of the visual system is evident in apparent rotation: by presenting only two images of an object rotated in space, a vivid illusion of a smooth apparent motion in three dimensions can be induced. The unseen interpolated rotation views are filled in by the visual system. In the present study,...

In this paper, we discuss rotation number on the invariant curve of a one parameter family of outer billiard tables. Given a convex polygon η, we can construct an outer billiard table T by cutting out a fixed area A from the interior of η. T is piece-wise hyperbolic and the polygon η is an invariant curve of T under the billiard map φ. We will show that, if β ∈ η is a periodic point under φ wit...

We compute the generalized Lefschetz number of orientation-preserving selfhomeomorphisms of a compact punctured disk, using the fact that homotopy classes of these homeomorphisms can be identified with braids. This result is applied to study Nielsen-Thurston canonical homeomorphisms on a punctured disk. We determine, for a certain class of braids, the rotation number of the corresponding canoni...

A celebrated theorem by Herman and Yoccoz asserts that if the rotation number α of a C∞-diffeomorphism of the circle f satisfies a Diophantine condition, then f is C∞-conjugated to a rotation. In this paper, we establish explicit relationships between the Ck norms of this conjugacy and the Diophantine condition on α. To obtain these estimates, we follow a suitably modified version of Yoccoz’s p...

A simple graphical method is proposed to distinguish between two-state and gradual alterations in DNA conformation from circular dichroic spectra. The method is advantageous particularly to identify two-state conformational isomerizations which exhibit low degree of cooperativity. The usefulness of the method is illustrated on the examples of two synthetic DNA molecules which isomerize due to t...

We observe that optical activity in light scattering can be probed using types of illuminating light other than single plane (or quasi plane) waves and that this introduces new possibilities for the study of molecules and atoms. We demonstrate this explicitly for natural Rayleigh optical activity which, we suggest, could be exploited as a new form of spectroscopy for chiral molecules through th...