A characterization of the optimal sets for self-similar measures with respect to the geometric mean error

Let μ be a self-similar measure on ? ^q associated with a set of contractive similitudes ${\{S_{i}\}}_{i=1}^{N}$ and a probability vector ${(p_{i})}_{i=1}^{N}$ . Assume that ${\{S_{i}\}}_{i=1}^{N}$ satisfies the strong separation condition. In terms of the n-optimal sets for a finite number n∈?, we give a characterization for the n-optimal sets for all n∈? in the quantization for μ with respect to the geometric mean error. As an application, we determine the convergence order for the logarithmic difference of the asymptotic geometric mean error. This characterization also allows us to show that the μ-measure of every element of an arbitrary Voronoi partition with respect to an n-optimal set is uniformly comparable with n ^?1, provided that μ vanishes on every hyperplane in ? ^q .     

Boussinesq-Burgers方程的分岔及一些有界行波解

利用平面动力系统理论研究了Boussinesq-Burgers方程,讨论了方程在行波变换后所对应的平面动力系统的分岔行为,并基于相平面上特定的相轨道求出了该方程的扭结波、孤立波及周期波的解析表达式.数值模拟进一步验证了所得结论的正确性.     

一类具偏差变元的Duffing方程周期解的存在唯一性(英文)

本文允许线性项x′(t)前的系数β(t)可变号的条件下,研究如下一类具偏差变元的Duffing方程:x″(t)+β(t)x′(t)+g(t,x(t-τ(t)))=p(t).获得了周期解的存在唯一性新结果.     

一个新混沌系统及其电路仿真

提出了一个新的三维自治混沌系统,并对系统的基本动力学特性进行了深入研究, 得到系统的Lyapunov指数和维数,给出了系统数值仿真图、Poincaré 映射图、Lyapunov指数谱和分岔图, 重点分析了不同参数变化对系统动力学行为的影响.最后,设计了该混沌系统的硬件电路并运用Multisim软件 对该电路进行仿真实现,数值仿真和电路仿真证实了该混沌系统与以往发现的混沌系统并不拓朴等价, 是一个新的混沌系统.     

微波法合成离子液体1-乙基-3-甲基咪唑四氟硼酸盐的研究

离子液体(ionic liquids)是在室温下液态的一种熔融盐,又称为室温离子液体,一般由有机阳离子和无机阴离子或者有机阴离子构成,可以通过调节阴阳离子的种类来改变离子液体的性能,因此敢称为一种"可以设计的溶剂".     

Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function

By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.     

合金化成分对NiTi合金M_s点影响的正电子湮没研究

用双探头符合系统测量了金属Fe、Co、Ni、Al、Nb、Cu、Ti和NiTi合金的多普勒展宽谱,计算了其S参数和W参数,分析了合金中d-d金属键的作用.结果表明,当用Fe、Co或Al原子加入NiTi合金时,都将使合金中参与形成d-d金属键的d电子减少,从而使金属键减弱;而用Cu或Nb原子加入NiTi合金时,对合金中d-d电子作用的影响很小,合金中共价键的成分变化不大.在NiTi合金中加入合金化元素可以改变其电子结构,进而影响Ms点.     

Catalytic ability of MgO to break CH bonds during slurry oil carbon deposition

Although MgO has been widely used for the MgO-templated synthesis of carbon materials, little attention has been paid to MgO’s catalytic function during carbon deposition. Here, a systematic analysis of the products of slurry oil (SO) carbonization with and without MgO templates present indicates that MgO catalytically promoted the breakage of CH bonds by immobilizing heavy oil molecules on MgO surfaces and the attractive interaction between hydrogen and MgO. Compared with the carbonization of SO alone, a notably higher H₂ concentration and a lower hydrocarbon concentration was observed in the tail gas, a higher solid yield and a lower degree of graphitization of the carbon product were observed when MgO was also present. Furthermore, treatment at 900 °C in the presence of MgO efficiently enhanced the capacitance and rate capability of the as-obtained porous carbon when tested as an electrode material for supercapacitors. These results suggest that the catalytic function of MgO could exist in all MgO-templated syntheses and in the heat treatment of porous carbons and graphene.     

硅酸盐熔体团粒结构类声子振动的高温拉曼光谱研究

硅酸盐熔体是典型的近程有序,远程无序的准稳定态分数维体系,文章采用X射线小角散射(SAXS)、低波数拉曼光谱(LWRS)及高温拉曼光谱(HTRS)实时、原位分析等技术,对高温熔融法和溶胶凝胶法合成的CaO-Al₂O₃-SiO₂和Na₂O-Al₂O₃-SiO₂系列低维非晶硅酸盐试样进行了团粒结构粒度及其类声子振动频率的定量测定,获得了低温硅酸盐凝胶、高温硅酸盐熔体及其淬火玻璃相均具有纳米级(几个纳米至几十纳米)自相似团粒结构和类声子振动模的重要结论,进而建立了测定高温熔体介观团粒结构粒度的HTRS测定法,结果表明硅酸盐熔体的团粒结构粒度在高温下均会比其室温玻璃相的团粒尺度小,且高温熔体的网络结构基元也向桥氧数减少之基元转变。这些结论为探索自然界岩浆的地球化学特征、岩浆的结晶和演化以及低维硅酸盐材料结构性能的改进提供重要理论依据及信息。