The Henderson Approximation and the Mass Action Law of Guldberg and Waage

Using contemporary accounts, we describe the scope of the Henderson approximation, and its relationship to the mass action law of Guldberg & Waage. The Henderson approximation, apparently written in logarithmic form by Hasselbalch, has the same form as the mass action law, but has a completely different meaning and a much more restricted range of applicability. The Guldberg-Waage law is the fundamental mass action relationship valid for all chemical equilibria, whereas the Henderson approximation is useful only within a limited range of a sufficiently concentrated two-component buffer mixture.     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

Alien limit cycles near a Hamiltonian 2-saddle cycle

It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

On Congruence of Complex Matrices

For each of a standard set of normal forms for (n × n) complex matrices under the relation of congruence, explicit matrices are exhibited which transform, via congruence, the normal form to its transpose.     

Ein Doppelaspirator

Ohne Zusammenfassung     

Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

We establish the existence of locally minimizing vortex solutions to the full Ginzburg-Landau energy in three dimensional simply-connected domains with or without the presence of an applied magnetic field. The approach is based upon the theory of weak Jacobians and applies to nonconvex sample geometries for which there exists a configuration of locally shortest line segments with endpoints on the boundary.Research partially supported by NSERC grant number 261955     

Reduction of Entrained Hydroxy Species in Ormosil Films for Integrated Optics

Organically modified silicates (ormosils) have been viewed as possible materials for optical signal processing devices for communications networks. One significant problem obstructing their use in this application is the absorption of infrared light by hydroxy species (present for example in silanol groups (SiOH) and water) around the communications wavelengths (1310 and 1550 nm). We have investigated several ormosil compositions, synthesised via an aqueous sol-gel method, to determine if residual hydroxy groups can be removed more effectively via reducing the connectivity of the material by increasing the number of organic groups (such as Si—CH₃). Furthermore, we have investigated the effect of different inert atmospheres on the drying process. It was found that reducing the connectivity does promote the removal of hydroxy absorption, mainly via the condensation of residual silanol groups, but also by removal of residual water, depending on the other precursors in the system. It was also found that the drying atmosphere used (nitrogen or helium) had no effect on the drying process.     

Collisional parameters of H2O lines: effects of vibration

A complex semiclassical model for the calculation of line widths and shifts of H₂O broadened by N₂, derived from the Robert and Bonamy approach, is tested by comparisons with measurements for selected transitions in various vibrational bands. The lines retained, which involve rotational states with Kc=J or J−1 have been chosen for two reasons. The first is that they show large variations of the widths with J and thus enable a severe test of the model. The second is that, as explained in this paper, they are well-suited for the study of the effects of vibration on the collisional parameters. The measured values have been extracted from an updated version of a database built years ago (JQSRT 52 (1994) 481) that contains all available measurements. Comparisons between experimental and calculated widths and shifts at room temperature illustrate the quality of the model and clearly demonstrate, for the first time, that there is a vibrational dependence of the broadening. Values of collisional parameters are first studied in fundamental bands. This shows that the theoretical approach accounts for most of the dependence of broadening and shifting on rotational quantum numbers: the variations of γ, which reach a factor of nearly 20 from low to high J values, are correctly accounted for by the model as are some specific features of the shifts δ. Analysis confirms that the bending and stretching vibrations have significantly different effects on δ, due to the vibrational dependence of the intermolecular potential. On the other hand, differences on the widths are rather small with slightly smaller broadening for lines of the bending band. Calculations show that there is a spectroscopic effect, due to the larger rotational constant A in the v₂=1 state. Calculations made for overtone bands involving numerous quanta of the stretching vibration are then presented. They predict that a significant dependence of the width should be observed for high J lines due to the effect of vibration on the interaction potential. This is confirmed by comparisons with measurements for lines involving a change of three and four quanta of stretching vibration.