We show that the unexpected chirality of aggregated structures based on an uncharged achiral porphyrin system originates from small temperature gradients that act as an asymmetrical physical perturbation; the consequent thermal force gives rise to the thermophoretic motion of the aggregates. We establish that the induced optical activity can be controlled, and even vanished, by minimizing the t...

We explore the influence of the phase of localized plasmon resonances on the magneto-optical activity of nanoferromagnets. We demonstrate that these systems can be described as two orthogonal damped oscillators coupled by the spin-orbit interaction. We prove that only the spin-orbit induced transverse plasmon plays an active role on the magneto-optical properties by controlling the relative amp...

Residuated lattices form the algebraic counterpart of substructural logics [4]. Rotation construction for t-norms has been introduced in [9] and has been generalized to arbitrary residuated posets in [7]. The reader is referred also to [13, 6, 5]. The rotationannihilation construction has been introduced in [10, 7]. The rotation construction has proved fundamental in the structural description ...

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 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...

A good drawing of Kn is a drawing of the complete graph with n vertices in the sphere such that: no two edges with a common end cross; no two edges cross more than once; and no three edges all cross at the same point. Gioan’s Theorem asserts that any two good drawings of Kn that have the same rotations of incident edges at every vertex are equivalent up to triangle-flips. At the time of prepara...