一道高考题的解法探讨和变式引伸

2009年全国高考湖北卷（文、理）第10题是：古希腊人常用小石子在沙滩上摆成各种形状来研究数．比如：     

与“0”有关的几个问题解析

同学们,在数学中的零,即0这个数可真是个特别而又有趣的数!不是吗?当用它来表示物体的个数时,0就表示没有即一无所有!同时在实数中我们知道,数0又是唯一的一个中性数——既不是正数也不是负     

Preliminary Safety Assessment of Chinese ITER TBM Design with Helium-cooled Solid Breeder Concept

The China home team is developing an ITER TBM based on a helium-cooled solid breeder （HCSB） DEMO blanket concept . This blanket concept employs high-pressure helium （8 MPa） to cool down the blanket first wall （FW） and side wall （SW） structures and the interior of the blanket module, including the beryllium multiplier pebble beds and the Li4SiO4 breeder pebble beds （enriched lithium-6 of 80%）. The tritium breeder is purged by forced flow low-pressure helium （0.1 MPa） provided by the tritium extraction system （TES）. Low activation ferritic/martensitic steel is selected as the structural material for the TBM.     

基于Bootstrap的响应式企业网站设计

在以信息技术为支撑的新经济下,要想在竞争中取得胜利,企业就必须不断地进行更新信息,及时的将信息进行反馈,这必然就要求企业建立属于自己的网站管理系统。根据企业的需求,网站基于Bootstrap框架,能快速进行前端开发,能更好的兼容不同的终端设备,使Web网站页面风格一致,用户的体验始终一致。     

短路匝式角度传感器不同极数下输出特性对比分析

针对短路匝式角度传感器多极结构与其输出特性之间关系的问题,对比分析了四极、八极、十二极和十六极短路匝式角度传感器的输出特性参数。首先,通过对短路匝式角度传感器多极结构和工作原理的分析,建立了其输出特性与极数之间的方程式。其次,利用ANSYS Maxwell-3D软件对四极、八极、十二极和十六极短路匝式角度传感器的输出特性进行了仿真分析,得到了不同极数下传感器输出极内磁通量和输出电压的对比曲线。最后,通过搭建短路匝式角度传感器输出特性的实验测试平台,得到了其输出电压的实测结果,与仿真分析结果进行了对比。结果表明,极数大于八极的短路匝式角度传感器的制造和应用是没有实际意义的,且八极传感器工作在±4°内具有高的线性度和对称度。     

IMPLICIT DIFFERENCE APPROXIMATION FOR A TIME FRACTIONAL ADVECTION-DISPERSION EQUATION

In this paper, a time fractional advection-dispersion equation is considered. From the relationship between the Caputo derivative and the Grunwald derivative, the Caputo derivative is approximated by using the Griinwald derivative. An implicit difference approximation for this equation is proposed. We prove that this approximation is unconditionally stable and convergent. Finally, numerical examples are given.     

AsH(X~3∑~-)及AsH_2(X~2B_1)自由基的分子结构与解析势能函数

运用Gaussian 03程序包中的单双迭代三重激发耦合簇理论和相关一致五重基优化了AsH_2的基态结构,并在优化结构的基础上计算了它的离解能和振动频率.结果表明:AsH_2基态的平衡构型具有C_(2v)对称性,键长R_(As-H)=0,1508 nm,键角∠HAsH=91.2231°,离解能D_e(Has-H)=2.8795 eV,振动频率ν_1(α_1)=1013.3361 cm~(-1),ν_2(α_1)=2225.1347 cm~(-1),ν_3(α_1)=2233.7565 cm~(-1).这些结果与实验值较为相符.对H_2的基态使用优选出的cc-pV6Z基组、对AsH的基态使用优选出的cc-pV5Z基组进行平衡几何与谐振频率的计算并进行单点能扫描,且将扫描结果拟合成了Murrell-Sorbie函数.与实验数据及其他理论结果的比较表明,本文关于AsH(X~3∑~-)自由基光谱常数(D_0,D_e,R_e,ω_e,B_e,α_e和ω_eX_e)的计算结果达到了很高的精度并最为完整.采用多体项展式理论导出了AsH_2(C_(2v),X~2B_1)自由基的解析势能函数,其等值势能图准确再现了它的离解能和平衡结构特征.首次报导了AsH_2(C_(2v),X~2B_1)自由基对称伸缩振动等值势能图中存在的两个对称鞍点,对应于反应AsH+H→ABH_2,势垒高度约0.1512×4.184 kJ/mol.

Abstract：

The CCSD(T) theory in combination with the cc-pV5Z basis set is used to determine the equilibrium geometry, dissociation energy and vibrational frequencies of AsH_2 (C_(2v), X~2B_1) radical. By comparison, excellent agreement can be found between the present results and the experiments. The values obtained at present are of 0.1508 ran for the equilibrium bond length R_(As-H), 91.2231° for the bond angle ∠ HASH, 2. 8795 eV for the dissociation energy D_e (HAs-H) and 1013.3361 cm~(-1), 2225.1347 cm~(-1) and 2233.7565 cm~(-1) for the vibrational frequencies ν_1(α_1), ν_2(α_1) and ν_3(α_1), respectively. The equilibrium geometry,harmonic frequency and potential energy curve of the AsH(X~3∑~-) radical are calculated at the CCSD(T)/cc-pV5Z level of theory. The ab initio results are fitted to the Murrell-Sorbie function with the least-square method. The spectroscopic parameters are in excellent agreement with the experiments. The analytic potential energy function of the AsH_2 (C_(2v), X~2 B_1) radical is derived by using the many-body expansion theory. This function correctly describes the configuration and dissociation energy of the AsH_2 (C_(2v), X~2B_1) radical. Two symmetrical saddle points have been found at (0.160 nm,0.296 nm) and (0.296 nm,0.160 nm) ,respectively. And the barrier height is equal to 0.1512×4.184 kJ/mol.     

三维有限差分波束传输法:用于Ti∶ LiNbO_3方向耦合器的模拟

提出求解三维傍轴近似波动方程的交替方向隐式差分格式，并用它模拟Ｔｉ∶ＬｉＮｂＯ３方向耦合器