从多种角度看线性相关系数

1引言 在科学研究中,我们不但要了解一个变量的变化情况,更要进一步了解一个变量与另一个变量之间的关系．变量之间的常见关系有两种：一是确定性函数关系,变量之间的关系可以用函数表示;二是非确定性相关关系,变量之间有一定的关系,但不能完全用函数表达,变量间只存在统计规律．相关和回归是研究变量间线性关系的重要方法．但两者研究的角度不同．回归是研究变量间的因果关系的,力图把非确定性相关关系化归为确定的函数关系,达到通过自变量的已知值来预测因变量的未知值的目的．     

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对所研制的质谱测量与分析系统进行了性能测试。烘烤后系统的极限真空达到了7.3×10-7Pa,总漏气率为3.84×10-9Pa.m3.s-1。上下球室之间的气体压力,以及漏孔的漏气率与高分辨四极质谱计的氦分压力均呈现了良好的线性关系。结果满足动态流导法真空校准的技术要求,为氘、氦混合气体的测量与分析提供了条件。     

Memristance controlling approach based on modification of linear M–q curve

The memristor has broad application prospects in many fields, while in many cases, those fields require accurate impedance control. The nonlinear model is of great importance for realizing memristance control accurately, but the im- plementing complexity caused by iteration has limited the actual application of this model. Considering the approximate linear characteristics at the middle region of the memristance-charge （M-q） curve of the nonlinear model, this paper pro- poses a memristance controlling approach, which is achieved by linearizing the middle region of the M-q curve of the nonlinear memristor, and establishes the linear relationship between memristances M and input excitations so that it can realize impedance control precisely by only adjusting input signals briefly. First, it analyzes the feasibility for linearizing the middle part of the M-q curve of the memristor with a nonlinear model from the qualitative perspective. Then, the lin- earization equations of the middle region of the M-q curve is constructed by using the shift method, and under a sinusoidal excitation case, the analytical relation between the memristance M and the charge time t is derived through the Taylor series expansions. At last, the performance of the proposed approach is demonstrated, including the linearizing capability for the middle part of the M-q curve of the nonlinear model memristor, the controlling ability for memristance M, and the influence of input excitation on linearization errors.     

基于TOPSIS的二级分压线路的线性分析

采用TOPSIS方法分析了二级分压线路的输出电压与粗、细调电阻比值的变化规律.结果表明,粗、细调电阻比值为10/1时,输出电压既能很好地满足线性关系,又有一定的调节范围.     

几种吡啶酮偶氮类化合物吸收半峰宽的预测研究

利用Gaussian98程序包，对几种吡啶酮偶氮类化合物的基态和最低激发态构型分别用密度泛函的B3LYP法和CIS法进行优化，然后用TD-DFT方法计算它们的最高吸收波长λmax和发射波长λmax^＊，最后将此二波长差的绝对值S与吸收半峰宽Δλ1/2。进行回归分析，得到了较好的线性关系．利用这一关系对其它同类化合物的吸收半峰宽进行预测，结果与实测值比较吻合．     

用不同散射角模拟研究石蜡厚度响应初探

为改进检测油垢厚度方法,本文用石蜡模拟油垢,用γ射线垂直照射距源为25cm处的石蜡样品.在与石蜡样品25 cm的距离处,以不同的散射角和同一探测立体角接收散射光子数.发现散射γ光子计数与被测石蜡厚度之间存在不同的线性关系.本实验测得最佳线性相关系数平方值为0.9859,平均测量精度为2.14 mm.     

丙酮肟1H核磁共振溶剂效应的研究

测定了丙酮肟在四氯化碳、氯仿、二氯甲烷、苯和甲苯溶剂中随丙酮肟摩尔浓度变化的¹H NMR谱,观察到在氯代甲烷溶剂中,丙酮肟分子中两个甲基和氯代甲烷的质子共振峰随丙同肟摩尔浓度增加而逐渐移向高场,而羟基共振峰却逐渐移向低场。其两个甲基表现为单峰。在芳烃溶剂中,丙酮肟分子中两个甲基和芳烃质子共振峰随丙酮肟摩尔浓度增加逐渐移向低场,且两个甲基表现为双峰,得到了所有化学位移与丙酮肟摩尔浓度呈线性关系。     

Surface-Induced Melting of Metal Nanoclusters

We investigate the size effect on melting of metal nanoclusters by molecular dynamics simulation and thermodynamic theory based on Kofman‘s melt model. By the minimization of the free energy of metal nanoclusters with respect to the thickness of the surface liquid layer, it has been found that the nanoclusters of the same metal have the same premelting temperature Tpre = To - To(γsu - γlu - γsl)/(ρLξ) (To is the melting point of bulk metal, γsu the solid-vapour interracial free energy: γlu the liquid-vapour interracial free energy, γsl the solid-liquid interracial free energy, p the density of metal, L the latent heat of bulk metal, and ξ the characteristic length of surface-interface interaction) to be independent of the size of nanoclusters, so that the characteristic length ξ of a metal can be obtained easily by Tpre, which can be obtained by experiments or molecular dynamics (MD) simulations. The premelting temperature Tpre of Cu is obtained by MD simulations, then ξ is obtained.The melting point Tcm is further predicted by free energy analysis and is in good agreement with the result of our MD simulations. We also predict the maximum premelting-liquid width of Cu nanoclusters with various sizes and the critical size, below which there is no premelting.