Sur les solutions extrêmales d'un système incompatible d'équations

Sans résumé     

Hamiltonian circuits in Cayley graphs

The following result is proved: If either G is a finite abelian group or a semidirect product of a cyclic group of prime order by a finite abelian group of odd order, then every connected Cayley graph of G is hamiltonian.     

Hole interactions with molecular vibrations on DNA

We report on a study of the interactions between holes and molecular vibrations on dry DNA using photoinduced infrared absorption spectroscopy. Laser photoexcited holes are found to have a room-temperature lifetime in excess of tau > 1 ms, clearly indicating the presence of localization. However, from a quantitative model analysis of the frequency shifts of vibrational modes caused by the holes, we find the hole-vibrational coupling constant to be relatively small, lambda approximately 0.2. This interaction leads to a change in the conformational energy of DeltaE0 approximately 0.015 eV, which is too small to cause self-trapping at room temperature. We conclude that, at least in the dry (A) form, DNA is best understood in terms of a double chain of coupled quantum dots arising from the pseudorandom chain sequence of base pairs, in which Anderson localization prevents the formation of a metallic state.     

Phosphorus as sintering activator in powder metallurgical steels: characterization of the distribution and its technological impact

Powder metallurgy is a highly developed method of manufacturing reliable ferrous parts. The main processing steps in a powder metallurgical line are pressing and sintering. Sintering can be strongly enhanced by the formation of a liquid phase during the sintering process when using phosphorus as sintering activator. In this work the distribution (effect) of phosphorus was investigated by means of secondary ion mass spectrometry (SIMS) supported by Auger electron spectroscopy (AES) and electron probe micro analysis (EPMA). To verify the influence of the process conditions (phosphorus content, sintering atmosphere, time) on the mechanical properties, additional measurements of the microstructure (pore shape) and of impact energy were performed. Analysis of fracture surfaces was performed by means of scanning electron microscopy (SEM). The concentration of phosphorus differs in the samples from 0 to 1% (w/w). Samples with higher phosphorus concentrations (1% (w/w) and above) are also measurable by EPMA, whereas the distributions of P at technically relevant concentrations and the distribution of possible impurities are only detectable (visible) by means of SIMS. The influence of the sintering time on the phosphorus distribution will be demonstrated. In addition the grain boundary segregation of P was measured by AES at the surface of in-situ broken samples. It will be shown that the distribution of phosphorus depends also on the concentration of carbon in the samples.     

An unusual decomposition of a complete 7-partite graph of order 28

A decomposition of the complete 7-partite graph on 28 vertices where each set in the partition has four vertices is given. Several unusual properties of this decomposition are discussed, giving rise to several natural questions.     

Terahertz imaging through self-mixing in a quantum cascade laser

We demonstrate terahertz (THz) frequency imaging using a single quantum cascade laser (QCL) device for both generation and sensing of THz radiation. Detection is achieved by utilizing the effect of self-mixing in the THz QCL, and, specifically, by monitoring perturbations to the voltage across the QCL, induced by light reflected from an external object back into the laser cavity. Self-mixing imaging offers high sensitivity, a potentially fast response, and a simple, compact optical design, and we show that it can be used to obtain high-resolution reflection images of exemplar structures.     

Corrigendum to “On norms of composition operators acting on Bergman spaces” [J. Math. Anal. Appl. 291 (2004) 189-202]

A theorem and a corollary in the paper cited in the title were stated incorrectly, as was pointed out by Christopher Hammond. We now state correctly and prove both of them. These results still generalize and explain the geometric meaning of the Cowen-Hurst norm formula. We also include additional references and provide an example relevant for further study.