混合型随机变量期望的求法及应用

讨论了混合型随机变量的数学期望的一般求法,并给出了其在保险精算中的应用.     

基于轴棱锥产生近似无衍射Mathieu光束的新方法

提出了一种基于轴棱锥产生零阶近似无衍射Mathieu光束的新方法,利用轴棱锥聚焦具有椭圆高斯振幅调制的平面波,得到近似零阶无衍射Mathieu光束.根据椭圆高斯平面波经轴棱锥衍射的衍射积分公式,对光强分布进行了数值模拟,依据几何光学模型计算了近似无衍射Mathieu光束的最大无衍射距离,并设计了实验对理论模拟的结果进行了验证.实验采用柱透镜和准直扩束系统变换圆高斯光束产生具有椭圆高斯振幅调制的平面波,用轴棱锥聚焦该平面波后得到近似无衍射Mathieu光束,实验结果与理论模拟和计算相符.     

Effects of N doping on photoelectric properties of along different directions of ZnO bulk and nanotube

The electronic structures and optical properties of N-doped Zn O bulks and nanotubes are investigated using the firstprinciples density functional method. The calculated results show that the main optical parameters of Zn O bulks are isotropic（especially in the high frequency region）, while Zn O nanotubes exhibit anisotropic optical properties. N doping results show that Zn O bulks and nanotubes present more obvious anisotropies in the low-frequency region. Thereinto, the optical parameters of N-doped Zn O bulks along the [100] direction are greater than those along the [001] direction, while for N-doped nanotubes, the variable quantities of optical parameters along the [100] direction are less than those along the[001] direction. In addition, refractive indexes, electrical conductivities, dielectric constants, and absorption coefficients of Zn O bulks and nanotubes each contain an obvious spectral band in the deep ultraviolet（UV）（100 nm～ 300 nm）. For each of N-doped Zn O bulks and nanotubes, a spectral peak appears in the UV and visible light region, showing that N doping can broaden the application scope of the optical properties of Zn O.     

核酸酶催化放大传感体系的设计及其在铅离子比色检测中的应用

基于8-17 DNA酶的催化切割特性和类辣根过氧化物酶DNA酶的氧化还原反应催化特性,发展了一种新型核酸酶催化放大传感体系,并用于Pb2+的比色检测。考察了K+浓度,pH值及反应时间对检测体系的影响。ABTS吸光度变化与Pb2+浓度在5.0～100 nmol/L范围内呈良好的线性关系,检出限为3.0 nmol/L。此外,因Pb2+酶的特异性,本方法对Pb2+具有良好的选择性。     

催化不对称[8+2]环加成反应构建环庚三烯并吡咯烷-3,3'-吲哚酮

设计了azaheptafulvenes作为偶极子与N-Boc-3-烯基吲哚酮反应,用来构建螺环[吡咯烷-3,3'-吲哚酮]衍生物.在1mol%手性氮氧-Ni(II)配合物催化剂条件下,该不对称[8+2]环加成反应以高的收率(90%~99%收率),好的非对映选择性(高达97∶3 dr)和优异的对映选择性(92%~99%ee)得到手性环庚三烯并螺环[吡咯烷-3,3'-吲哚酮]衍生物.     

Orientation of azobenzene molecules in polymer films induced by all-optical poling

A model of the alignment of azobenzene molecules in polymer film induced by all-optical poling is proposed and verified by experiment. We found that when the writing beams of frequencies ω and 2ω are both linearly polarized with their polarization directions parallel to each other, azobenzene molecules tend to reorient to the direction perpendicular to the writing beams polarization. At the end of the writing process, more molecules orient to the direction perpendicular to the writing beams polarization than those which orient to the parallel direction. The alignment of molecules parallel or perpendicular to the polarization of the writing beams is characteristic of polarity or no polarity, respectively. The alignment of molecules along the polarization of writing beams results in the second order nonlinearity in the polymer film. According to the model, a new method to improve the optical poling efficiency is put forward.     

TTA-Phen-吐温20胶束体系荧光分析法测定地质试样中的痕量钐和铕

本文研究了2-噻吩甲酰三氟丙酮(TTA)-邻菲绕啉(Phen)-吐温20胶束体系荧光法测定钐、铕时钙离子的熄灭效应和草酸钙共沉淀法的最佳条件。方法已用于水系沉积岩和塘积物等地质试样中痕量钐、铕的测定并得到满意的结果。     

强烈阳极氧化法快速制备多孔氧化铝模板

In the electrolyte of oxalic acid/alcohol/aqueous solution, highly-ordered porous anodic aluminum oxide(AAO) template was fabricated by hard anodization. The surface morphology and the structure of AAO template were characterized by Field-Emission Scanning Electron Microscope(FE-SEM) and XRD, respectively. The effects of different factors including alcohol type, ratio of alcohol to water, and oxalic acid concentration on the ordering degree and pore diameter of AAO template were investigated. Under the glycol to water ratio of 1∶1(by volume) with an oxalic acid concentration of 0.5 mol·L^-1, and voltage at 160 V, the obtained AAO template was hexangular arrangement with pore diameter of 80 nm and pores spacing of 120 nm, the growth rate was 51.9 μm·h^-1.     

一个包含伪Smarandache函数及 Smarandache可乘函数的方程

对任意正整数n,著名的伪Smarandache函数Z(n)定义为最小的正整数m使得n整除m(m 1)/2,或者Z(n)=min{m:m∈N,n│m(m 1)/2},其中N表示所有正整数之集合.而Smarandache可乘函数U(n)定义为U(1)=1,当n1且n=pα11 pα,22…pαss为n的标准素因数分解式时,定义U(n)=max{α1p1,α2p2,…,αsps}.本文的主要目的是利用初等方法研究方程Z(n)=U(n)及Z(n) 1=U(n)的可解性,并获得了这两个方程的所有正整数解.     

柱透镜聚焦高阶Bessel光束产生焦散光束

研究了高阶Bessel光束经过柱透镜后的光场分布特性.在广义惠更斯-菲涅尔衍射积分理论基础上,推导出高阶Bessel光束透过柱透镜后的衍射光场分布表达式;并利用MATLAB和MATHCAD模拟了不同传播距离处的光强分布.实验上,利用轴棱锥和螺旋相位板产生不同阶数的高阶Bessel光束,并使产生的高阶Bessel光束经过柱透镜,最后用CCD记录下不同距离处的衍射光场.研究结果表明,高阶Bessel光束经过柱透镜形成唇状的焦散光束.