Affine embeddings and intersections of Cantor sets

Let E,F⊂R^d$E,F\subset {\mathbb{R}}^d$ be two self-similar sets. Under mild conditions, we show that F   can be C¹$C^1$-embedded into E if and only if it can be affinely embedded into E; furthermore if F cannot be affinely embedded into E  , then the Hausdorff dimension of the intersection E∩f(F)$E\cap f(F)$ is strictly less than that of F   for any C¹$C^1$-diffeomorphism f   on R^d${\mathbb{R}}^d$. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of E and F if F can be affinely embedded into E  . As an application, we show that _dimH?E∩f(F)<min?{_dimH?E,_dimH?F}${\dim }_H?E\cap f(F)<\min ?\{{\dim }_H?E,{\dim }_H?F\}$ when E is any Cantor-p set and F any Cantor-q   set, where p,q?2$p,q?2$ are two integers with log?p/log?q∉Q$\log ?p/\log ?q\notin \mathbb{Q}$. This is related to a conjecture of Furstenberg about the intersections of Cantor sets.     

Magnetic Properties and Magnetoresistance of CdMnS：Au Based Structures Prepared by Co-evaporation

Polycrystalline CdMnS and CdMnS：Au films with hexagonal structure on Si（111） substrates are prepared by co-evaporation, and exhibit ferroelectric and ferromagnetic properties, respectively. Under optimized growth conditions, CdMnS：Au samples with an average crystallite size of 90nm and Mn concentration of 5.0at.% are obtained, and an all-semiconductor spin valve device of Co/Au/CdMnS：Au/CdMnS/Pt is fabricated. Electrical measurement of the device reveals the clear dependence of resistance on applied magnetic field, with a relative magnetoresistance of 0.06% and a switching field of 100 Oe at 77K.     

纳米TiO2的光生电荷迁移特性研究

利用场诱导光电压谱(简称FISPS)和瞬态光伏(简称TPV)技术研究了TiO₂的光生电荷的产生和传输机制.发现光生电荷在体块TiO₂上的迁移机制不同于在纳米TiO₂上的迁移机制，也不同于在结界面空间电荷区的迁移机制. 400 ℃处理的TiO₂颗粒表面具有大量的表面态，光生电荷被表面态捕获-释放机制控制着光伏行为的过程是慢过程. 800 ℃处理的TiO₂已经形成了完整的能带结构，光伏响应除了表现带-带跃迁外,还有一个在带边的自由激子带，光生电荷被表面自建场驱动进行传递的过程是快过程. 600 ℃处理的TiO₂混晶由锐钛矿型和金红石型两种构型组成，在两相之间存在着较低势垒的结界面．它的光伏响应受控于两种机制 ：光生电荷在两相间结界面空间电荷区的传输和在表面自建场驱动下的传输.当激发光强较小时，界面空间电荷区的光生电子由于积累的浓度较小而不能隧穿过结界面，这种场助隧穿只有在外场作用下才能发生.     

Design of a curved surface constant force mechanism

A new curved surface constant force mechanism which mainly consists of a roller and a curved surface has been proposed. The magnitude and the direction of normal force caused by squeezing between the roller and the curved surface satisfy a certain relationship, thus the decomposed force of the normal force keeps constant in a certain direction all the times. According to the envelope theorem, the trajectory of the roller center and the profile of the curved surface are obtained by ignoring friction. Then, the influence of the friction is discussed in detail. In addition, the simulation is performed to verify the theoretical calculation. The simulation results show that the output force is relatively constant and the friction has little effect on the output force.     

On a Statistical Framework for Estimation from Random Set Observations

Using the theory of random closed sets, we extend the statistical framework introduced by Schreiber⁽¹¹⁾ for inference based on set-valued observations from the case of finite sample spaces to compact metric spaces with continuous distributions.     

Multifractal Formalism for Almost all Self-Affine Measures

We conduct the multifractal analysis of self-affine measures for “almost all” family of affine maps. Besides partially extending Falconer’s formula of L ^q -spectrum outside the range 1 < q ≤ 2, the multifractal formalism is also partially verified.     

Mg-Al-NO_3层状双氢氧化物的制备及性能研究

制备了带正电荷的Mg-Al-NO_3层状双氢氧化物（LDH）,并对其组成、形貌、 电性能、离子交换性能等各种性质进行了表征。实验结果表明,所制备的正电纳米 颗粒具有可调控的层间自由空间。该方法为进一步研究聚合物/纳米复合材料提供 了一个合成前驱体的方法。     

Studies on Zero Point of Charge and Permanent Charge Density of Mg-Fe Hydrotalcite-like Compounds

The theoretical analysis on the zero point of charge (ZPC) and charge density of colloidal particle possessing permanent charges indicates that ZPC determined directly by means of potentiometric titration (PT) should be zero point of net charge (ZPNC) and the permanent charge density (σ_P) can be obtained from the adsorption amount of H⁺ and OH^-(Γ_OH--Γ_H+) at ZPNC. ZPNC does not change with the electrolyte concentration while the zero point of variable charge (ZPVC) changes with the electrolyte concentration. When σ_P is zero, ZPNC equals to ZPVC, and only under this condition is ZPC measured directly by PT equal to ZPVC. The relationship between ZPNC, ZNVC, σ_P, the variable charge density (σ_V)5 or the total net surface charge density (σ_T) with pH or electrolyte concentration is derived.     

氰基乙烯基苯胺衍生物的电化学行为

本文利用循环伏安法研究了电子给-受体模型化合物——氰基乙烯基苯胺衍生物的电化学行为,并对推电子取代基团—NH_2和—N(CH_3)_2与吸电子取代基团氰基乙烯基对化合物电化学行为的影响进行了较为详细的讨论.提出了这些化合物的电氧化态和电还原态的结构,通过分析比较叔、仲和伯自由基对化合物电化学行为的影响,探讨了电极反应机理.     

磺化酞菁铜分子膜／SiO2／Si界面电荷转移机制的研究

在具有不同氧化层厚度的p型硅基片上修饰2层磺化酞菁铜分子膜.利用时间分辨表面光电压谱技术,对该膜系的界面电荷转移机制的光电开关特性进行了研究。结果表明,用时间分辨表面光电压谱技术研究界面电荷转移过程具有明显优越性.