Recognition of subgroups of direct products of hyperbolic groups

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic.

     

Rigidity in holomorphic and quasiregular dynamics

We consider rigidity phenomena for holomorphic functions and then more generally for uniformly quasiregular maps.

     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Structural characterization of nanopatterned surfaces

In this work, chemically and topographically nanopatterned surfaces were produced by a top-down processing approach for biosensing devices. The nanopatterning was the result of the combination of plasma polymerisation (pp) of biofunctional materials and colloidal lithography techniques. The morphological and chemical properties induced by the plasma deposition-etching treatment were characterised by optical method combining ellipsometry and Fourier Transform Infrared spectroscopy studies. This method supported by atomic force microscopy measurements, allowed the full optical characterization of each step of the top-down process. The optical characterization of the end-up nanopatterned samples demonstrated that the chosen process is able to produce well-defined nanostructured surfaces with controlled chemical and morphological properties.     

A chemoenzymatic synthesis of the linear triquinane (−)-hirsutene and identification of possible precursors to the naturally occurring (+)-enantiomer

An enantiomerically pure cis-1,2-dihydrocatechol, which is readily obtained via a toluene dioxygenase-mediated dihydroxylation of toluene in a whole-cell biotransformation process, has been converted over 17 steps into the linear triquinane (−)-hirsutene. Since the enantiomer of the starting material is also available this work constitutes a formal total synthesis of the naturally occurring (+)-form of hirsutene. Furthermore, minor modifications of the route used here offer the possibility of accessing (+)-hirsutene from the original starting material.     

Excited-state dynamics in Yb3+-Ho3+-doped fluoroindate glasses

This work has been partially supported by Gobierno Autonomo de Canarias under contact number 226–265/93.     

L-Functions for Jacobi Forms of Arbitrary Degree

A finite number ofL-functions are associated to every Jacobi cusp form of degreen. TheseL-functions are infinite series constructed with the Fourier coefficients of the form and a variables in ℂⁿ. It is proved that eachL-function has an integral representation, admits a holomorphic continuation to the whole space ℂⁿ, and the row vector formed with them satisfies a particular matrix functional equation.     

COSMIC(90): An improved molecular mechanics treatment of hydrocarbons and conjugated systems

Summary Four modifications to the COSMIC molecular mechanics force field are described, which greatly increase both its versatility and the accuracy of calculated conformational energies. The Hill non-bonded van der Waals potential function has been replaced by a two-parameter Morse curve and a new H-H potential, similar to that in MM3, incorporated. Hydrocarbon energies in particular are much improved.A simple iterative Hückel pi-electron molecular orbital calculation allows modelling of conjugated systems. Calculated bond lengths and rotational barriers for a series of conjugated hydrocarbons and nitrogen heterocycles are shown to be as accurate as those determined by the MM2 SCF method.Explicit hydrogen-bonding potentials for H-bond acceptor-donor atom pairs have been included to give better hydrogen bond energies and lengths. The van der Waals radii of protonic hydrogens are reduced to 0.5 Å and the energy well depth is increased to 1.0 kcal mol^-1.Two new general atom types, N⁺ _sp ² and O^- _sp ³ , have been introduced which allow a wide variety of charged conjugated systems to be studied. A minimum of parameterisation is required, as the new types are easily included in the Hückel scheme which automatically adjusts bond and torsional parameters according to the defined bond-order relationships.