Computer-Assisted Prediction of Retention in Multiple-Development Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - Retention of DNP derivatives of amino acids has been described by equations based on polynomial and Snyder—Soczewiński...     

Synthesis, structure and the binding properties of the amide-based anion receptors derived from 1H-indole-7-amine

Indole-7-amine was investigated as an alternative to aniline in construction of amide-based anion receptors. Replacement of aniline with indolamine introduces additional binding site—indolyl NH, which can enhance anion binding for more than five times. The molecular modelling of indole-containing receptors revealed the correlation between their conformational preferences and their affinity towards anions.     

A Lower Estimation of the Hausdorff Dimension for Attractors with Overlaps

We give a lower estimate of the Hausdorff dimension for attractors which can be obtained by an overlapping construction.     

A Pairing Between Super Lie-Rinehart and Periodic Cyclic Homology

We consider a pairing producing various cyclic Hochschild cocycles, which led Alain Connes to cyclic cohomology. We are interested in geometrical meaning and homological properties of this pairing. We define a non-trivial pairing between the homology of a Lie-Rinehart (super-)algebra with coefficients in some partial traces and relative periodic cyclic homology. This pairing generalizes the index formula for summable Fredholm modules, the Connes-Kubo formula for the Hall conductivity and the formula computing the K⁰-group of a smooth noncommutative torus. It also produces new homological invariants of proper maps contracting each orbit contained in a closed invariant subset in a manifold acted on smoothly by a connected Lie group. Finally we compare it with the characteristic map for the Hopf-cyclic cohomology. The author was partially supported by the KBN grant 1P03A 036 26.     

Discontinuous synchrony in an array of Van der Pol oscillators

We show the phenomenon of complete synchronization in an network of coupled oscillators. We confirm that non-diagonal coupling can lead to the appearance or disappearance of synchronous windows (ragged synchronizability phenomenon) in the coupling parameter space. We also show the appearance of clusters (synchronization in one or more group) between coupled systems. Our numerical studies are confirmed by an electronic experiment.     

Dimension of measures invariant with respect to the Wa?ewska partial differential equation

We study asymptotic properties of a nonlinear first-order partial differential equation which describes the reproduction of blood cells. This equation under conditions proposed by Wa?ewska generates a semigroup of transformations with highly chaotic behaviour of trajectories. We show that this semigroup has invariant measures with arbitrary large dimension.     

Local geometry of orbits for an ordinary classical lie supergroup

In this paper we identify a real reductive dual pair of Roger Howe with an Ordinary Classical Lie supergroup. In these terms we describe the semisimple orbits of the dual pair in the symplectic space, a slice through a semisimple element of the symplectic space, an analog of a Cartan subalgebra, the corresponding Weyl group and the corresponding Weyl integration formula.