Chern numbers for two families of noncommutative Hopf fibrations

We consider noncommutative line bundles associated with the Hopf fibrations of SU_q(2) over all Podle? spheres and with a locally trivial Hopf fibration of S³_pq. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SU_q(2) and S³_pq. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them. To cite this article: P.M. Hajac et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

Synthesis,Antibacterial, and Antioxidant Evaluation of Novel Series of Condensed Thiazoloquinazoline with Pyrido,Pyrano, and Benzol Moieties as Five- and Six-Membered Heterocycle Derivatives

A novel synthesis of thiazolo[2,3-b]quinazolines 4(a–e), pyrido[2′,3′:4,5]thiazolo[2,3-b]quinazolines {5(a–e), 6(a–e), and 7(a–e)}, pyrano[2′,3′:4,5]thiazolo[2,3-b]quinazolines 8(a–e), and benzo[4,5]thiazolo[2,3-b]quinazoloine9(a–e) derivatives starting from 2-(Bis-methylsulfanyl-methylene)-5,5-dimethyl-cyclohexane-1,3-dione 2 as efficient α,α dioxoketen dithioacetal is reported and the synthetic approaches of these types of compounds will provide an innovative molecular framework to the designing of new active heterocyclic compounds. In our study, we also present optimization of the synthetic method along with a biological evaluation of these newly synthesized compounds as antioxidants and antibacterial agents against the bacterial strains, like S. aureus, E. coli, and P. aeruginosa. Among all the evaluated compounds, it was found that some showed significant antioxidant activity at 10 μg/mL while the others exhibited better antibacterial activity at 100 μg/mL. The results of this study showed that compound 6(c) possessed remarkable antibacterial activity, whereas compound 9(c) exhibited the highest efficacy as an antioxidant. The structures of the new synthetic compounds were elucidated by elemental analysis, IR, ¹H-NMR, and ¹³C-NMR.     

Abtrennung von Palladiumspuren aus Reinstplatin nach Neutronenaktivierung unter Berücksichtigung weiterer Spurenverunreinigungen

As first step the separation of¹⁰⁹Pd (T1/2=13.5 h) after neutron activation from the highly radioactive platinum is performed after addition of Pd carrier as chloro-complex on strong basic anion-exchangers. The simultaneous separation of some further short living radionuclides of trace element stakes place. After a purification step with dimethylglyoxime decontamination factors up to 10⁶ are attainable. Using an Ge(Li)-detector and evaluating theγ-irradiation of the¹⁰⁹Pd daughter^109mAg 0.4 μg of Pd could be determined with a standard deviation of 6.5%.     

Bridging the gap between homogeneous and heterogeneous catalysis: ortho/para H(2) conversion, hydrogen isotope scrambling, and hydrogenation of olefins by Ir(CO)Cl(PPh(3))(2)

Some transition metal complexes are known to catalyze ortho/para hydrogen conversion, hydrogen isotope scrambling, and hydrogenation reactions in liquid solution. Using the example of Vaska's complex, we present here evidence by NMR that the solvent is not necessary for these reactions to occur. Thus, solid frozen solutions or polycrystalline powdered samples of homogeneous catalysts may become heterogeneous catalysts. Comparative liquid- and solid-state studies provide novel insight into the reaction mechanisms.     

Novel microscopic mechanism of intermixing during growth on soft metallic substrates

Generic computer simulations using empiric interatomic potentials suggest a new, collective mechanism that could be responsible for mixing at heteroepitaxial interfaces. Even if single adsorbate atoms diffuse by hopping on the substrate surface and do not mix at the terraces, two-dimensional islands formed by nucleation may become unstable above a certain critical size and explode upwards forming clusters of several atomic layers. This process is accompanied by strong distortions of the underlying atomic layers, and on soft materials it can result in surface etching and incorporation of substrate atoms into the islands.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.