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We study the properties of multifunction operators that are contractive in the Covitz-Nadler sense. In this situation, such operators T possess fixed points satisfying the relation x∈Tx. We introduce an iterative method involving projections that guarantees convergence from any starting point x0∈X to a point x∈XT, the set of all fixed points of a multifunction operator T. We also prove a continuity result for fixed point sets XT as well as a “generalized collage theorem” for contractive multifunctions. These results can then be used to solve inverse problems involving contractive multifunctions. Two applications of contractive multifunctions are introduced: (i) integral inclusions and (ii) iterated multifunction systems. 相似文献
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The trisilanol 1,3,5‐(HOi‐Bu2Si)3C6H3 ( 7 ), prepared in three steps from 1,3,5‐tribromobenzene via the intermediates 1,3,5‐(Hi‐Bu2Si)3C6H3 ( 8 ) and 1,3,5‐(Cli‐Bu2Si)3C6H3 ( 9 ) forms an equimolar complex with trans‐bis(4‐pyridyl)ethylene (bpe), 7 ·bpe, whose structure was investigated by X‐ray crystallography. The hydrogen‐bonded network features a number of SiO? H(H)Si and SiO? H hydrogen bridges. Evidence was found for cooperative strengthening within the sequential hydrogen bonds. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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We demonstrate significant enhancement of four-wave mixing in coherently driven mercury isotopes to generate vacuum-ultraviolet radiation at 125 nm. The enhancement is accomplished by preparation of the mercury atoms in a state of maximum coherence, i.e. maximum nonlinear-optical polarization, driven by Stark-chirped rapid adiabatic passage (SCRAP). In this technique, a pump laser at 313 nm excites the two-photon transition between the ground state 6s21S0 and the target state 7s 1S0 in mercury. A strong, off-resonant radiation field at 1064 nm generates dynamic Stark shifts. These Stark shifts serve to induce a rapid adiabatic passage process on the two-photon transition. During the process a coherent superposition of the two states is established, which enhances the nonlinear-optical polarization in the medium to the maximum possible value. The maximum coherence permits efficient four-wave mixing of a pump laser and an additional probe laser at 626 nm. The efficiency is further enhanced, as the SCRAP process allows to stimulate the complete set of different mercury isotopes to participate in the frequency conversion process. This enlarges the effective atomic density of the medium. Thus, we observe the generation of vacuum-ultraviolet radiation at 125 nm enhanced by more than one order of magnitude with respect to conventional frequency conversion. Parallel to the frequency conversion process, we monitored the evolution of the population in the medium by laser-induced fluorescence. These data demonstrate efficient coherent population transfer by SCRAP. 相似文献
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Frank Abild-Pedersen Ole Lytken Jakob Engbk Gunver Nielsen Ib Chorkendorff Jens K. Nrskov 《Surface science》2005,590(2-3):127-137
We have, theoretically and experimentally, investigated the dissociation of methane on the terraces and steps of a Ni(1 1 1) surface. Using Density Functional Theory (DFT) total energy calculations combined with Ultra High Vacuum (UHV) experiments, we find that the steps exhibit a higher activity than the terraces. We have, furthermore, investigated how carbon and sulfur present on the surface will deactivate the steps, leaving only the terraces active. We find the intrinsic sticking probabilities of methane on the steps and terraces at 500 K to be 2.8 × 10−7 for the steps and 2.1 × 10−9 for the terraces, in complete agreement with our calculated difference in activation energy of 17 kJ/mol. 相似文献
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We consider solutions bifurcating from a spatially
homogeneous equilibrium under the assumption that the associated
linearization possesses continuous spectrum up to the imaginary
axis, for all values of the bifurcation parameter, and that a real
eigenvalue crosses the imaginary axis. For a model we investigate
the nonlinear stability of the trivial solution with respect to
spatially localized perturbations, prove the occurrence of a
pitchfork bifurcation of equilibria and the nonlinear stability of
the bifurcating equilibria, again with respect to spatially
localized perturbations. 相似文献
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