On the covariance of the level sizes in random recursive trees

In this paper we study the covariance structure of the number of nodes k and l steps away from the root in random recursive trees. We give an analytic expression valid for all k, l and tree sizes N. The fraction of nodes k steps away from the root is a random probability distribution in k. The expression for the covariances allows us to show that the total variation distance between this (random) probability distribution and its mean converges in probability to zero. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 20: 519–539, 2002     

Metric foliations and curvature

We prove a rigidity theorem for Riemannian fibrations of flat spaces over compact bases and give a metric classification of compact four-dimensional manifolds of nonnegative curvature that admit totally geodesic Riemannian foliations.     

Harze und Harzs?uren

Ohne Zusammenfassung     

Transition-metal-templated synthesis of rotaxanes and catenanes: From small molecules to polymers

This article provides an overview of the fundamental principles of the synthesis of metallocatenanes and metallorotaxanes. It also describes the synthesis and properties of electronic conducting polymers—polypyrrole and polythiophene—built around metallocatenanes and metallorotaxanes. The particular properties of this new class of polymers, including the possibility of transmetallation reactions being performed with them and the observation of electronic coupling between the metal centers and the conducting matrix, are discussed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3470–3477, 2003     

Magnetic silica colloids for catalysis

Monodisperse magnetizable colloidal silica particles in a stable dispersion have been functionalized with a homogeneous catalyst: a PCP–pincer Pd-complex. In a proof-of-principle experiment we demonstrate the catalytic activity of the colloids in a C–C bond formation reaction. Advantages of the magnetic silica carriers are the large surface-to-volume ratio and the easy recovery by magnetic separation. After magnetic separation, the catalyst-loaded particles are readily redispersed for further use.     

Thermoanalytical investigation of layered titanium salts

The investigated materials have similar routes of thermal decomposition; i.e. they lose their crystal water first, then at a higher temperature their structural one. At least the result TiP₂O₇ goes through a phase change at about 1000 K. The amorphous titanium phosphate lost its crystal and structural water at higher temperature than those of crystalline forms. Both α- and γ-titanium phosphates and also their transition metal containing forms have layered structure. In case of α- and γ-forms after the loss of crystal water a phase change occurs which is followed by the decomposition of the molecule. Various transition metals containing γ-titanium phosphates lose their crystal water at the same temperature, with the exception of Ni containing ones. The process is finished in this case at temperature 90 K higher than that of the others. This revised version was published online in July 2006 with corrections to the Cover Date.     

Glutathione Synthesis Is Not Involved in Protection by N-Acetyl cysteine Against UVB-lnduced Systemic Immunosuppression in Mice

The photophysics of 5,10,15,20-tetraarylethynylporphyrinatozinc(II) complexes, 1 and 2, are reported. Compared to 5,10,15,20-tetraphenylporphyrinatozinc(II) (ZnTPP), the UV/visible spectra of 1 and 2 have red-shifted B and Q bands, with the Q bands of increased intensity relative to the B band. FIuorescence quantum yields and lifetimes and triplet quantum yields and lifetimes are similar to ZnTPP. However, quantum yields for in vitro singlet-oxygen generation are much larger than for ZnTPP and for 2 the quantum yield is near unity. These findings suggest that the title compounds could be potential lead compounds as sensitizers for photodynamic therapy.     

SELECTIVE DEGRADATION OF AMINO ACIDS PHOTOSENSITIZED BY TRYPTOPHAN IN POLYPEPTIDE STRUCTURES

Polypeptides containing a basic amino acid close to their single tryptophan residue were irradiated with monochromatic 302 nm radiation. Tryptophan photolysis was monitored by absorption and fluorescence spectroscopy. Amino acid loss was evaluated by amino acid analysis. Only the protonated residues adjacent to tryptophan in the sequence were destroyed upon tryptophan excitation. This reaction is probably due essentially to direct interaction between the excited tryptophan and the neighbouring residue without electron solvation.