Coupled systems of nonlinear wave equations and finite-dimensional lie algebras II: A nonlinear system arising from the group G 6.1 and its exact integration

In the first paper of this series a correspondence was established between coupled systems of two-dimensional nonlinear wave equations and the six-dimensional simply transitive Lie algebras. In the present paper we make use of this result to construct a Darboux integrable and exactly integrable nonlinear system associated with the six-parameter nilpotent Lie group G _6,1 and we give its exact general solution in terms of four arbitrary functions. The procedure is shown to be an exact linearization of the nonlinear problem.     

A versatile building block for pyrazole-pyrrole hybrid macrocycles

This contribution describes the synthesis of a novel pyrazole-pyrrole building block and its use in the formation of a non-aromatic, Schiff base-type macrocycle incorporating a chromophore and H-bonding donor and acceptor functionalities inside and outside of the macrocycle, which makes it predestined for molecular recognition systems.     

Chitosan derivatives as biosorbents for basic dyes

The scope of this study was to prepare and evaluate chitosan derivatives as biosorbents for basic dyes. This was achieved by grafting poly (acrylic acid) and poly (acrylamide) through persulfate induced free radical initiated polymerization processes and covalent cross-linking of the prepared materials. Remacryl Red TGL was used as the cationic dye. Equilibrium sorption experiments were carried out at different pH and initial dye concentration values. The experimental equilibrium data for each adsorbent-dye system were successfully fitted to the Langmuir, Freundlich and pH-dependent Langmuir-Freundlich sorption isotherms. Thermodynamic parameters of the adsorption process such as DeltaG degrees, DeltaH degrees, and DeltaS degrees were calculated. The negative values of free energy reflected the spontaneous nature of adsorption. The typical dependence of dye uptake on temperature and the kinetics of adsorption indicated the process to be chemisorption. The grafting modifications greatly enhanced the adsorption performance of the biosorbents, especially in the case of powdered cross-linked chitosan grafted with acrylic acid, which exhibited a maximum adsorption capacity equal to 1.068 mmol/g. Kinetic studies also revealed a significant improvement of sorption rates by the modifications. Diffusion coefficients of the dye molecule were determined to be of the order 10(-13) - 10(-12) m2/s. Furthermore, desorption experiments affirmed the regenerative capability of the loaded material.     

Stereochemical relays: communication via conformation

Stereochemistry is information, and stereoselective reactions are the means by which that information may be communicated within and between molecules. The control of remote stereogenic centres can be achieved by stereochemical relay, and the use of thermodynamic control over conformational preference is turning out to be a very powerful method for long-range transmission of stereochemical information.     

A constructive generalised Goursat normal form

We provide necessary and sufficient conditions on the derived type of a vector field distribution V in order that it be locally equivalent to a partial prolongation of the contact distribution , on the 1st order jet bundle of maps from R to Rq, q?1. This result fully generalises the Goursat normal form from the theory of exterior differential systems. Our proof is constructive: it is proven that if V is locally equivalent to a partial prolongation of then the explicit construction of contact coordinates algorithmically depends upon the integration of a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on M. Though the tools required are rather different, our main theorem may be regarded as a generalisation of the work of R.B. Gardner and W.F. Shadwick on the feedback linearisation of autonomous nonlinear control systems.