MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.

Synthesis, Spectroscopic Properties, and Stabilities of Ternary Europium Complex in SBA-15 and Periodic Mesoporous Organosilica: A Comparative Study

Ternary europium complex Eu(tta)(3)phen was covalently bonded with the general mesoporous. material SBA-15 and SBA-15-type of periodic mesoporous organosilica (PMO) material via impregnation of Eu(tta)(3)center dot 2H(2)O into phen-S15 and phen-PMO, respectively, through a ligand exchange reaction. The parent materials of phen-S15 and phen-PMO were synthesized by co-condensation of tetraethylorthosilicate (TEOS) or 1,2-bis(triethoxysilyl)ethane (BTESE) and the functionalized chelate ligand 5-(N,N-bis(3-triethoxysilyl)propyl)ureyl-1,10-phenanthroline (phen-Si) in the presence of Pluronic P123 surfactant as template, which were confirmed by SEM, XRD, FTIR, Si-29 CP-MAS NMR, and N-2 adsorption measurements.

Localization of the electric-field distribution in graded core-shell metamaterials

The local electric-field distribution has been investigated in a core-shell cylindrical metamaterial structure under the illumination of a uniform incident optical field. The structure consists of a homogeneous dielectric core, a shell of graded metal-dielectric metamaterial, embedded in a uniform matrix. In the quasistatic limit, the permittivity of the metamaterial is given by the graded Drude model. The local electric potentials and hence the electric fields have been derived exactly and analytically in terms of hypergeometric functions. Our results showed that the peak of the electric field inside the cylindrical shell can be confined in a desired position by varying the frequency of the optical field and the parameters of the graded profiles. Thus, by fabricating graded metamaterials, it is possible to control electric-field distribution spatially. We offer an intuitive explanation for the gradation-controlled electric-field distribution.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.