含边界在内的一般极值的必要条件与拉格朗日乘数法

讨论包括定义域边界点在内的极值,称为一般极值.对可导的一元和多元函数给出了一般极值点的必要条件,这些必要条件与经典极值的必要条件是相容的.还利用一般极值的必要条件导出了条件极值的拉格朗日乘数法.     

The structure and the potential energy function of AlSO(C_S,X~2A″)

By using the B3P86/aug-cc-pvtz method,the accurate equilibrium geometry of the AlSO(CS,X2A″) molecule has been calculated and compared with available theoretical values.The obtained results show that the AlSO molecule has a most stable structure with bond lengths of R OAl = 0.1864 nm,R OS = 0.1623 nm,R AlS = 0.2450 nm,together with a dissociation energy of 13.88 eV.The possible electronic states and their reasonable dissociation limits for the ground state of the AlSO molecule were determined based on the principle of atomic and molecular reaction statics.The analytic potential energy function of the AlSO molecule was derived by the many-body expansion theory and the contour lines were constructed for the first time,which show the internal information of the AlSO molecule,including the equilibrium structure and stable point.The analysis demonstrates that the obtained potential energy function of AlSO is reasonable and successful and the present investigations provide important insights for further study on molecular reaction dynamics.     

The role of vacancy,impurity,impurity-vacancy complex in the kinetics of LiNH2 complex hydrides:a first-principles study

This paper studies first-principles plane-wave pseudopotential based on density functional theory of hydrogen vacancy,metal impurity,impurity-vacancy complex in LiNH 2,a promising material for hydrogen storage.It finds easy formation of H vacancy in the form of impurity-vacancy complex,and the rate-limiting step to the H diffusion.Based on the analysis of the density of states,it finds that the improvement of the dehydrogenating kinetics of LiNH 2 by Ti catalysts and Mg substitution is due to the weak bonding of N-H and the new system metal-like,which makes H atom diffuse easily.The mulliken overlap population analysis shows that H vacancy leads to the H local diffusion,whereas impurity-vacancy complexes result from H nonlocal diffusion,which plays a dominant role in the process of dehydrogenation reaction of LiNH 2.     

电多极矩跃迁选择定则的对称分析

只有由群的对称性才可能导出每个不可约表示的对称性波函数, 即对称化基函数.也只有由群的对称性才可能导出电子状态跃迁的最一般选择定则 , 即电偶极跃迁E1, 电四极跃迁E2 和 电八极跃迁E3跃迁的选择原则. 本文以 和 为例, 导出电多积跃迁的选择原则. 角动量的选择定则只是特例. 并用方法SAC-CI/6-31G 计算了 H2O和 CC的基态以及其激发态的激发能和振子强度.本文只适合单光子过程. 计算都与理论相合.     

介观系统中的几何位相和持续流

介观系统中的量子相干效应是一个在理论和应用方面具有重大意义的研究课题。本文系统全面地介绍包括Ａｈａｒｏｎｏｖ－Ｂｏｈｍ效应和Ａｈａｒｏｎｏｖ－Ｃａｓｈｅｒ效应在内的几何位相在介观系统中引发的诸如持续流等一系列新奇现象及其成因,详细讨论这些几何位相间的相互关系,评述了实验和理论研究的最新进展     

LiNH2储氢材料中间隙H与掺杂原子交互作用对其释氢性能影响机理研究

采用基于密度泛函理论的赝势平面波第一性原理方法,研究了LiNH₂缺陷及其掺杂原子交互作用对其释氢影响.通过对其进行优化求得它们的局域最稳定结构并计算了含间隙H原子缺陷的LiNH₂及其掺杂合金的结合能、间隙缺陷形成能、态密度和电荷布居.结果表明: 系统结合能不能反映LiNH₂及其掺杂合金的释氢性质;平衡时,LiNH₂中有一定的间隙氢原子存在,Mg,Ti掺杂使形成能大大降低,大大增大了间隙氢的浓度. 间隙H原子在带隙引入了缺陷能级使带隙大大减小,提高释氢能力.间隙H原子导致[NH₂]^-中N-H原子间相互作用减弱,容易释氢.间隙H与[NH₂]^-中N存在共价作用,可以解释LiNH₂释氢反应中NH₃的放出.当存在掺杂时,N-H键的键强不均衡,部分较弱,部分较强,较弱的N-H键中H容易放出. 关键词： 储氢材料 第一性原理 缺陷 释氢机理     

内源全息术的原理和数学描述

以往的全息术在对原子成像时,在相干光源、探测器空间分辨和信号强度三个方面遇到了难以克服的困难. 阐述了内源全息术克服这些困难的原理,研究了内源全息术的记录和再现全过程,推导出内源球面全息图的再现公式,并在散射因子球对称近似和能量无关近似下,推导出以δ函数表示原子全息再现像的解析表达式. 关键词： 内源全息术 同步辐射 晶体结构 傅里叶变换     

高效液相色谱指纹图谱及随机森林应用于湖南安化黑茶水溶性成分的研究

建立了适用于湖南安化黑茶的高效液相色谱指纹图谱分析方法。样品用水在90℃恒温水浴中浸提20min,以C18色谱柱(250 mm×4.6 mm,5μm)分离,甲醇-0.1%磷酸溶液为流动相梯度洗脱,检测波长为270nm,流速为1.0 m L/min,黑茶的各种组分得到较好分离,共确定18个色谱峰作为安化黑茶的特征指纹峰,并通过对照品分析对其中12个峰进行确证。运用相似度评价、主成分分析、正交偏最小方差判别分析(Orthogonal partial least squares discriminant analysis,OPLS-DA)和随机森林法对78个黑茶样品指纹图谱进行了化学模式识别研究和变量重要性判定。结果表明联合指纹图谱分析法和随机森林法可有效区分湖南安化黑茶和其他产地的黑茶。该方法操作简单,精密度、稳定性和重现性良好,为安化黑茶的鉴别和质量控制提供了实验依据。     

Field Emission from Silicon Nanocrystallite Films with Compact Alignment and Uniform Orientation

Patterned silicon nanocrystallite (SINC) films were fabricated on (100) orientation p-type boron-doped sificon wafer by the hydrogen ion implantation technique and the anodic etching method. The efficient field emission with low turn-on field of about 3.5V/μm at current density of 0.1μA/cm^2 was obtained. The emission current density from the SiNC films reached 1mA/cm^2 under a bias field of about 9.1V/μm. The experimental results demonstrate that there are great potential applications of the SiNC films for fiat panel displays. A surface treatment with hydrogen plasma was performed on the SiNC films and a significant improvement of emission properties was achieved.