Potenzbeschränktheit und Wertebereich einer Matrix

Ohne ZusammenfassungDie nachstehende Arbeit wurde im Rahmen des Vertrages zwischen dem Institut für Plasmaphysik GmbH und der Europäischen Atomgemeinschaft über die Zusammenarbeit auf dem Gebiete der Plasmaphysik durchgeführt.     

Constructive solution of a bilinear control problem

We present an optimization method of a quantum control problem giving rise to a sequence of controls increasing monotonically the values of a cost functional. We first claim some results about the regularity of this cost functional. Those enable to extend an inequality due to ?ojasiewicz to the infinite dimensional case. Lastly, a sequence of inequalities proving the Cauchy character of the monotonic sequence is obtained, and we can also estimate the rate of convergence. The detailed proof will be given in [L. Baudouin, J. Salomon, Constructive solution of a bilinear quantum control problem, 2005, in preparation. [3]]. To cite this article: L. Baudouin, J. Salomon, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Experimental realization of linear-optical partial swap gates

We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling sqrt[SWAP], can be obtained by changing a classical control parameter, namely, the path difference in the interferometer. Reconstruction of output states, full quantum process tomography, and an evaluation of entanglement of formation prove very good performance of the gates.     

The kinetics of solid-phase microextraction measured for freshly added and aged hydrophobic compounds in two different soils

The proper choice of exposure times is critical if the freely dissolved concentration of chemicals in soil porewater is to be measured via the equilibrium solid-phase microextraction (SPME) as the times to equilibrium may vary depending on compound and soil properties. To reveal the effects of compound hydrophobicity, ageing and soil organic matter content on times to equilibrium, the SPME uptake was measured for five freshly added and aged hydrophobic organic compounds (phenanthrene, pyrene, lindane, p,p′-DDT and polychlorinated biphenyl (PCB) 153) in two contrasted soils (arable and forest soil). The tested compound-soil systems behaved kinetically different. Longer equilibrium times were observed with increasing hydrophobicity of compounds for aged compared to freshly added chemicals and for the forest soil in comparison to the arable soil. The calculated soil–porewater partition coefficients (i.e. sorption coefficients, K_d) of chemicals differed between soil types mainly due to various organic carbon (OC) contents as evidenced by the comparable K_oc values (i.e. K_d values normalised to soil OC content). Similar K_oc values were also found with the various extent of ageing, indicating that both the freshly added and aged compounds linearly partitioned between the soil organic matter and porewater. Our results suggest that, for a respective compound, variations in equilibrium times may be expected depending upon the residence time and the organic matter content in soil where the longest equilibrium times seems to appear for a combination of aged compounds and high organic soils. With regard to this outcome, the effect of the level of sample depletion due to the SPME extraction (LD_SPME) on equilibrium times was assessed. At LDs_SPME of up to 10%, equilibrium times increases linearly with LDs_SPME for p,p′-DDT and PCB 153. For phenanthrene (LD_SPME<10%), and for lindane and pyrene (1.2% < LD_SPME > 40%), no clear relationships were observed.