10－5000 伏下电子被多原子分子CF4, CF3H, C2F4, C2F6, 及 C2H3F3散射总结面的计算

利用可加性规则和光学势方法计算了能量在10-5000 eV范围内电子被多原子分子CF4, CF3H, C2F4, C2F6, 及 C2H3F3的总结面，并与已有的实验结果和理论计算进行了比较，与这些结果符合得很好。对于CF4, CF3H, C2F4, C2F6, 及 C2H3F3在1000eV以上没有实验数据，本文对实验研究提供了对比和预测的数据。     

量子场论方法在电子与分子碰撞中的应用

这是一种利用量子场论所进行的探究性的研究方法,在文章中,我们设 计了一种新的较为简单的电子-原子碰撞模型,将量子场论方法与光学势方法中的可加性规 则结合起来.利用这种模型,我们计算了e-H,e-He和e-Li的微分碰撞截面,获得了较满意的 结果.     

Conditions for Choquet integral representation of the comonotonically additive and monotone functional

If the universal set X is not compact but locally compact, a comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is not represented by one Choquet integral, but represented by the difference of two Choquet integrals. The conditions for which a c.m. functional can be represented by one Choquet integral are discussed.     

Total cross sections for electrons scattering from simple molecules containing the larger atom sulfur at 30-5000eV

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds, is employed to calculate the total cross sections for electrons scattering from simple molecules （SO2, H2S, OCS, CS2 and SO3） containing the larger atom, sulfur, at 30-5000eV by using the additivity rule model at Hartree-Fock level. The quantitative molecular total cross section results are compared with those obtained in experiments and other calculations wherever available, and good agreement is obtained. It is shown that the additivity rule model together with the complex optical model potential modified by the concept of bonded atom can give the results closer to the experiments than the one unmodified by it. So, the introduction of bonded-atom concept in complex optical model potential betters the accuracy of the total cross section calculations of electrons from the molecules containing the larger atom, sulfur.     

On the evaluation of some distributions that arise in simultaneous tests for the equality of the latent roots of the covariance matrix

In this paper, the authors consider the evaluation of the distribution functions of the ratios of the intermediate roots to the trace of the real Wishart matrix as well as the ratios of the individual roots to the trace of the complex Wishart matrix. In addition, the authors consider the evaluation of the distribution functions of the ratios of the extreme roots of the Wishart matrix in the real and complex cases. Some applications and tables of the above distributions are also given.     

On a direct method for proving the Hyers-Ulam stability of functional equations

We study the stability of an equation in a single variable of the form

f(x)=af(h(x))+bf(−h(x))     

On the heat of formation of nitromethane

Two experimental values (?19.3 ± 0.3 and ?17.8 ± 0.1 kcal/mol) for the gas phase heat of formation (δ_fH) (298k) of nitromethane have been reported. Although these values differ by only 1.5 kcal/mol, substantially greater differences in theoretical and experimental results occur when these differing values are used to calculate thermodynamic properties. This is especially evident when these two values for the δ_fH of nitromethane are used to calculate thermodynamic properties of polynitro compounds. For example, when density functional theory (DFT) is coupled with the use of isodesmic reactions, the Δ_fH of octanitrocubane is calculated to be 160.6 or 172.6 kcal/mol, depending on which value is used. It should also be appreciated that several computational theories depend upon having access to reliable experimental data for testing and development. We have examined this discrepancy using several computational models and several levels of theory. Our results coupled with a comprehensive review of the literature support the lower (?19.3 ± 0.3 kcal/mol) experimental value. This is problematic because the higher value (?17.8 ± 0.1 kcal/mol) has been used in the development and/or testing of several semiempirical quantum mechanical models as well as ab initio Gaussian theory (G2 and G3). Copyright © 2008 John Wiley & Sons, Ltd.     

Carbon‐Centered Radical Addition and β‐Scission Reactions: Modeling of Activation Energies and Pre‐exponential Factors

A consistent set of group additive values ΔGAV° for 46 groups is derived, allowing the calculation of rate coefficients for hydrocarbon radical additions and β-scission reactions. A database of 51 rate coefficients based on CBS-QB3 calculations with corrections for hindered internal rotation was used as training set. The results of this computational method agree well with experimentally observed rate coefficients with a mean factor of deviation of 3, as benchmarked on a set of nine reactions. The temperature dependence on the resulting ΔGAV°s in the broad range of 300–1300 K is limited to ±4.5 kJ mol⁻¹ on activation energies and to ±0.4 on logA (A: pre-exponential factor) for 90 % of the groups. Validation of the ΔGAV°s was performed for a test set of 13 reactions. In the absence of severe steric hindrance and resonance effects in the transition state, the rate coefficients predicted by group additivity are within a factor of 3 of the CBS-QB3 ab initio rate coefficients for more than 90 % of the reactions in the test set. It can thus be expected that in most cases the GA method performs even better than standard DFT calculations for which a deviation factor of 10 is generally considered to be acceptable.     

Luminance-Type Additive Mechanism Produces Shading

It has been reported that the luminance mechanism mediates shadow perception of binary images. We evaluated the luminance additivity law to determine whether shading, which is produced by gradual intensity changes, is mediated by luminance or brightness using pictures with tones: two still lives and a painting. They were depicted by two colors-a reference color and a test color. The reference color was white with a constant luminance profile, and the test color was a mixture of red and green in various proportions. The observer’s task was to adjust the luminance of the test color in order that the impression of depth due to shading just disappeared (shading disappearance setting), where the intensity that produced the shading supposed to be equated between the test and the reference colors. The results show that the luminance additivity law holds for shading disappearance settings. This suggests that shading perception is based on luminance or a luminance-type additive mechanism as well as shadow.     

On oblique projection, rank additivity and the moore-penrose inverse of the sum of two matrices

The existence of certain oblique projectors is revealed by deriving onto-and along-space of a specific projector, namely the Moore-Penrose inverse of the product of two orthogonal projectors. The results are used to create a formula for the Moore-Penrose in-verse of the sum of two rank additive matrices, and to demonstrate relationships with already known facts.