Min-max theory,Willmore conjecture and the energy of links

In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors [19] and on joint work of I. Agol and the authors [1].     

Thermal decomposition of the [Pt(NH3)4]2+ complex in NaX zeolite

The effect of the calcination procedure on the decomposition of the [Pt(NH₃)₄]²⁺ complex in a cesium-containing NaX zeolite was studied by thermal decomposition accompanied by mass spectrometry and diffuse reflectance spectroscopy, as well as electron paramagnetic resonance and infrared spectroscopy. The decomposition of the complex took place in two steps. Under oxygen, the [Pt(NH₃)₄]²⁺ complex was first converted into the [Pt(NH₃)₂]²⁺ complex in the first step, with predominant nitrogen release. In the second step, corresponding to the decomposition of the remaining two amine ligands, NO was also formed and adsorbed. Oxygen paramagnetic species were also observed. Under He, the decomposition also occurred in two steps with H₂ release.     

Suzuki cross‐coupling reaction of aryl and heterocyclic bromides and aromatic polybromides on a Pd(II)‐hydrotalcite catalyst

The Suzuki cross‐coupling reaction of various bromine‐containing substrates and phenylboronic acid in toluene at 90 °C on a Pd(AcO)₂Py₂ catalyst supported on an Mg? Al hydrotalcite, using K₂CO₃ as the base, was studied. The conversion and selectivity results obtained for many of the substrates were excellent and similar to those provided by more active or even homogeneous catalysts. The reactions of aryl polybromides and phenylboronic acid gave the corresponding polyaromatic compounds in variable yields depending on the particular substrate. Arylation occurred in a consecutive manner by substitution of the different Br atoms. ICP‐MS measurements of the palladium content of the catalyst performed prior to and after the reaction revealed that part of the metal is incorporated into the bulk solution; therefore, the catalytic process is not purely heterogeneous. Copyright © 2008 John Wiley & Sons, Ltd.     

The time-evolution operator for singular Lagrangians

We give an intrinsic characterization of an operator K recently introduced for relating the Lagrangian and Hamiltonian constraints and describing the time evolution of functions in T ^*Q in terms of those of TQ. Its most remarkable properties are also studied.