Banach空间上凸集的凸性

以Banach空间的一般凸集为研究对象,将Banach空间的凸性研究推广到了内部非空的凸集上．打破了从单位球出发研究Banach空间几何的具有局限性的研究方法,给出了严格凸集的若干特征刻画及性质,并得到了严格凸集和光滑集之间的对偶定理．     

Lame equation and asymptotic higher-order periodic solutions to nonlinear evolution equations

Based on an auxiliary Lame equation and the perturbation method, a direct method is proposed to construct asymptotic higher-order periodic solutions to some nonlinear evolution equations. It is shown that some asymptotic higher-order periodic solutions to some nonlinear evolution equations in terms of Jacobi elliptic functions are explicitly obtained with the aid of symbolic computation.     

Convergence of Solutions of General Dispersive Equations Along Curve

In this paper, the authors give the local L~2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R~+→R satisfies some suitable conditions and φ((-?)~(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L~2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper.     

ZrO2∶Tb3+纳米晶的离子交换法制备及其发光特性

以强碱性阴离子交换树脂为交换介质,采用离子交换法制备了稀土Tb3+离子掺杂的ZrO2:Tb3+纳米晶.通过XRD,TG-DSC,TEM,HRTEM等手段分析了样品制备过程的物相变化及晶粒形貌,用荧光光度计研究了样品的三维荧光光谱、激发光谱和发射光谱.结果表明:前驱沉淀物经800℃焙烧处理2 h,制备出近方型形貌,颗粒分散性好、尺寸约为40 nm的四方相ZrO2:Tb3+纳米晶.当焙烧温度升高到900℃以上时样品出现了少量单斜晶相,而经800℃焙烧处理的纯Zr02是以四方相和单斜相同时存在.说明稀土Tb3+离子的掺杂对ZrO2基质的四方晶相起到稳定作用.由ZrO2:Tb3+)的等角三维荧光光谱图显示Tb3+在ZrO2基质中的最佳激发波长为290 nm:在290 nm波长光的激发下观察到纳米ZrO2中Tb3+的发射峰位于491,545,582 nm分别对应于Tb3+的5D4→7F6、5D4→7F5、5D4→7F4、5D4→7F4能级跃迁,以491,545nm的发射峰最强,其中经800℃焙烧处理的样品其5D4→7F6跃迁发射与5D4→7F5跃迁发射强度几乎相同,说明该法制备的纳米ZrO2:Tb3+中5D4→7F6跃迁发射增强,使Tb3+发光的蓝色成分增加了.     

Synthesis,crystal structure and chemical bonding of the novel compound IrGa2

The crystal structure of the novel constant composition compound IrGa₂ was determined from X-ray single-crystal diffraction data. The compound crystallizes in the space group Cmcm with the lattice parameters a=3.9021(3) Å, b=12.9925(8) Å and c=10.8808(7) Å. Its structure represents a new type with the Pearson symbol oC36. Analysis of the electron localization function (ELF) showed that the d electrons of both iridium atoms in IrGa₂ are involved in the bonding and that the two crystallographically independent iridium atoms have different bonding character.     

Hydrothermal synthesis and structure characterization of two six-connected metal–organic frameworks based on the mixed ligands

Two metal–organic frameworks, namely, [Ni₂(BIMB)₂(ndd)₂·H₂O]_n (1) and [Zn₃(ndd)_2.5(μ₃-OH)(1,3-dpp)]_n (2) (H₂ndd = 2,2′-(naphthalene-1,5-diylbis(oxy))diacetic acid, BIMB = 1,4-bis[(1H-imidazol-1-ly)methyl]benzene, 1,3-dpp = 1,3-di(pyridin-4-yl)propane) have been synthesized under hydrothermal conditions and characterized by single-crystal X-ray diffraction and thermogravimetric analysis. Compound 1 presents a two-dimensional network with point symbol of (3⁶·4⁶·5³)-hxl topology. Moreover, compound 2 displays a novel 2-fold interpenetrated structure with the point symbol of (4¹²·6³)-pcu topology based on the hexanuclear [Zn₆(CO₂)₁₀(N)₄] unit as a six-connected node. Meanwhile, compound 2 shows good fluorescence property in the solid state at room temperature.     

抛物量子点中强耦合磁双极化子内部激发态性质

基于Lee-Low-Pines幺正变换,采用Pekar类型变分法研究了抛物量子点中强耦合磁双极化子的内部激发态性质,当考虑自旋和外磁场影响时,推导出二维量子点中强耦合磁双极化子基态的能量E0,声子平均数ˉN0以及第一激发态的能量E1,声子平均数ˉN1随量子点受限强度ω0,介电常数比η,电子-声子耦合强度α和磁场的回旋共振频率ωC的变化规律.结果表明,磁双极化子的基态能量E0和第一激发态能量E1由两电子的单粒子能量E E,两电子间库仑相互作用能E C,电子自旋与磁场相互作用能E s和电子-声子相互作用能E e-ph四部分组成;单粒子"轨道"运动与磁场相互作用导致了第一激发态能级E1分裂为E(1+1)1,E(1-1)1两条,而电子自旋-磁场相互作用的效应又使基态和第一激发态的各能级均产生了三条"精细结构";ˉN0和ˉN1随ω0,α和ωc的增加而增大,E e-ph的取值总是小于零,其绝对值随α,ω0和ωc的增加而增大;电子-声子相互作用的效应是束缚态磁双极化子形成的有力因素,而限定势和电子之间的库仑排斥能的存在不利于束缚态磁双极化子的形成;能量为E(1-1)1的磁双极化子要比能量为E(1+1)1的磁双极化子更容易且更稳定地处于束缚态.     

Asymmetric synthesis of N-phenylethyl-2-phenyldecahydroquinolin-4-ones via Lewis acid catalyzed imino-Diels–Alder reaction

The asymmetric synthesis of N-phenylethyl-2-phenyldecahydroquinolin-4-ones was performed via a Lewis acid catalyzed imino-Diels–Alder reaction between the enantiopure (R)-N-phenylethylbenzylideneimine and the trimethylsilyl enol ether of acetylcyclohexene. The regio- and stereoselective formation of intermediary bicyclic enoxysilanes, followed by their stereoselective protonation was evidenced. The initial stereoselectivity was kept only if the reaction mixture was treated using controlled basic conditions. Three enantiopure title compounds were isolated with a 5–15% yield.     

Survivor statistics and damage spreading on social network with power-law degree distributions

Damage spreading(DS) of the random graph networks with power-law degree distributions is investigated using Glauber dynamics. Various subgraphs defined by the probability of acquaintance show distinct features in DS as measured by Hamming distance. A heuristic understanding of the long-time value of damage is achieved through an analysis of the survivor statistics. All survivors are dynamical, flipping in unison for the controlled sample and the damaged sample. Verification of these dynamic survivors is achieved through the introduction of a new measure of self-damage.     

Suppression of Chaos and Phase Locking in Two Coupled Nonidentical Neurons under Periodic Input

Dynamical behaviour of two coupled neurons with at least one of them being chaotic is presented. Bifurcation diagrams and Lyapunov exponents are calculated to diagnose the dynamical behaviour of the coupled neurons with the increasing coupling strength. It is found that when the coupling strength increases, a chaotic neuron can be controlled by the coupling between neurons. At the same time, phase locking is studied by the maxima of the differences of instantaneous phases and average frequencies between two coupled neurons, and the inherent connection of phase locking and the suppression of chaos is formulated. It is observed that the onset of phase locking is closely related to the suppression of chaos. Finally, a way for suppression of chaos in two coupled nonidentical neurons under periodic input is suggested.