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...

In addition to the separable solutions of the rotation equation, relating the perturbations of the metric tensor to the angular velocity of the matter on the brane, we show that the rotation equation admits solutions for a special class of non-separable angular velocity of the matter distribution on the brane. The general solution of the rotation equation is expressed in terms of an arbitrary, ...

We investigate the effect of weak rotation on the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection, using the theory for cessations in a low-dimensional stochastic model of the flow previously studied. We determine the cessation frequency of the LSC as a function of rotation, and calculate the statistics of the amplitude and azimuthal velocity fluctuations of the LSC as a f...

Rotation curves of spiral galaxies are known with reasonable precision for a large number of galaxies with similar morphologies. The data implies that non-Keplerian fall–off is seen. This implies that (i) large amounts of dark matter must exist at galactic scales or (ii) that Newtonian gravity must somehow be corrected. We present a method for inverting the integral relation between an elementa...

Data were obtained from 1980 to 1987 on animals belonging to one of three breeding systems: Hereford, small rotation, and large rotation. Differences among Angus-, Gelbvieh-, Pinzgauer-, and Tarentaise-sired calves within the small rotation system were generally not detected as significant for the preweaning traits of gestation length, calving ease, birth weight, gain to weaning, or creep feed ...

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...