The Maslov P-index theory for a symplectic path is defined. Various properties of this index theory such as homotopy invariant, symplectic additivity and the relations with other Morse indices are studied. As an application, the non-periodic problem for some asymptotically linear Hamiltonian systems is considered. 相似文献
Rare-earth-based infinite coordination polymer (RE-ICP) spheres with diameters ranging from 50 nm to 2 μm have been prepared using meso-2,3-dimercaptosuccinic acid (DMSA) as ligand under hydrothermal conditions. RE2O2SO4 microspheres with similar morphology were obtained by calcining the corresponding RE-ICP spheres. However, as for Ce-ICP and Sc-ICP, CeO2 and Sc2O3 were obtained. The products were characterized using X-ray diffraction, scanning electron microscopy, thermogravimetric analysis, infrared spectroscopy, laser Raman spectrometry, and energy-dispersive X-ray spectrum. Elemental analysis and inductive coupled plasma atomic emission spectrometer were adopted to study the composition of the Eu-ICP. To explore their potential applications, several samples of the products were selected and their properties were investigated. The Eu-ICP and Eu2O2SO4 microspheres give strong red emissions when excited with a 394-nm ultraviolet light. Furthermore, the Eu-ICP displays a high selectivity for Fe(III). The obtained CeO2 has a strong absorption in the UV region and the Gd2O2SO4 microspheres show paramagnetic behavior.
In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible
QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessary to choose a problematic penalty
parameter. The new algorithm only needs to solve three systems of linear equations with the same nonsingular coefficient matrix.
Under some suitable conditions, the global convergence is established. Some numerical results are also presented. 相似文献
