A novel carbon source coated on C-LiFePO<Subscript>4</Subscript> as a cathode material for lithium-ion batteries

The poor electronic conductivity and low lithium-ion diffusion are the two major obstacles to the largely commercial application of LiFePO₄ cathode material in power batteries. In order to improve the defects of LiFePO₄, a novel carbon source polyacrylonitrile (PAN), which would form the hierarchical porous structure after carbonization, is fabricated and used. This work comes up with a simple and facile carbothermal reduction method to prepare porous-carbon-coated LiFePO₄ (C-LiFePO₄-PC) composite and to study the effect of carbon-coated temperature on ameliorating the electrochemical performance. The obtained C-LiFePO₄-PC composite shows a high initial discharge capacity of 164.1 mA h g^?1 at 0.1 C and good cycling stability as well as excellent rate capacity (49.0 mA h g^?1 at 50 C). The most possible factors that improve the electrochemical performance could be related to the enhancement of electronic conductivity and the existence of porous carbon layers. In a word, the C-LiFePO₄-PC material would become an excellent candidate for application in the fields of lithium-ion batteries.     

Existence of pseudo-almost automorphic solutions for nonlinear differential equations

In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy~ and the results also hold for some nonlinear equations with the form x＇（t） = f（t,x（t）） ＋ λg（t,x（t））, where f,g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem.     

一类具非线性边界条件的高阶方程的双参数奇摄动问题

研究了一类含双参数的非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐近解,并运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.     

Improving the precision of fluorescence lifetime measurement using a streak camera

Streak camera has high temporal resolution and high sensitivity, and is a powerful tool in biomedical study to measure fluorescence lifetime and perform fluorescence lifetime imaging. However, nonuniformity of the gain in the streak tube and nonlinearity of the sweeping speed limit the precision of fluorescence lifetime measurement, particularly when fluorescence lifetimes are short. We have constructed a two-photon excitation fluorescence lifetime measurement system that is based on a synchroscan streak camera and have developed accordingly a method to correct the effect of gain nonuniformity and nonlinearity of sweeping speed on the measurement precision. A continuous-wave laser of high stability is used to calibrate the gain of the streak camera, and a Fabry-Perot etalon is used to calibrate the nonlinearity of the sweeping speed. Fitting algorithms are used to correct the gain of the streak camera and nonlinearity of the sweeping speed respectively, which significantly improves the measurement precision of the system, as characterized through the fluorescence lifetime of the short-lived fluorescence dye, Rose Bengal. Experimental results show that the measurement fluctuation of the lifetime has been improved from more than 10% to 2% after correcting the effects of gain nonuniformity and sweeping speed nonlinearity.     

High-Q exterior whispering-gallery modes in a metal-coated microresonator

We propose a kind of plasmonic whispering-gallery mode highly localized on the exterior surface of a metal-coated microresonator. This exterior (EX) surface mode possesses high quality factors at room temperature, and can be efficiently excited by a tapered fiber. The EX mode can couple to an interior (IN) mode and this coupling produces a strong anticrossing behavior, which not only allows conversion of IN to EX modes, but also forms a long-lived antisymmetric mode. As a potential application, the EX mode could be used for a biosensor with a sensitivity high of up to 500 nm per refraction index unit, a large figure of merit, and a wide detection range.     

一致超图谱半径界的改进结果

利用张量理论研究一致超图的谱半径.首先,利用对角相似张量与原张量同谱的性质,结合张量特征值的圆盘定理,给出谱半径的上界,这一上界严格小于最大度;其次,通过超图的度向量给出谱半径的下界.改进了超图谱半径上下界的原有结果.     

光学元件亚表层裂纹成核临界条件研究

基于压痕实验和连续刚度测量法得到了熔石英材料硬度和弹性模量随压入深度的变化曲线, 系统分析了材料由延性到脆性转变的过程, 确定了熔石英晶体在静态/准静态印压和动态刻划时产生裂纹的临界载荷和临界深度。渐变载荷刻划实验结果表明, 划痕过程诱发的裂纹对法向载荷有很强的依赖性, 载荷较小时材料去除方式为延性域去除。随着法向载荷的增加, 首先产生垂直于试件表面的中位裂纹和平行于试件表面方向扩展的侧向裂纹, 而在试件表面上并没有产生明显的特征。载荷进一步增加后, 侧向裂纹扩展并形成了明亮区域, 最终诱发了沿垂直于或近似垂直于压头运动方向扩展的径向裂纹, 实现了材料的脆性去除。     

-extension of Lie triple systems

In this paper, we introduce the notion of T^*-extension of a Lie triple system. Then we show that T^*-extension is compatible with nilpotency, solvability, and it preserves in certain sense the decomposition properties. In addition, we investigate the equivalence of T^*-extensions using cohomology. Finally, we show that every finite-dimensional nilpotent metrised Lie triple system over an algebraically closed field is the T^*-extension of an appropriate quotient system.     

考虑晶粒尺寸效应的超薄(10–50 nm) Cu电阻率模型研究

结合Marom模型与实验数据, 给出了晶粒尺寸与金属薄膜厚度的关系式. 基于已有的理论模型, 针对厚度为10–50 nm Cu薄膜, 考虑到表面散射与晶界散射以及电阻率晶粒尺寸效应, 提出一种简化电阻率解析模型. 结果表明, 在10–20 nm薄膜厚度范围内, 考虑晶粒尺寸效应后的简化模型与现有实验数据符合得更好. 相对于Lim, Wang与Marom模型, 所提模型的相对标准差分别降低74.24%, 54.85%, 78.29%. 关键词： 表面散射 晶界散射 晶粒尺寸效应 平均自由程