Normal halogen dependence of 13C NMR chemical shifts of halogenomethanes revisited at the four‐component relativistic level

The ‘Normal Halogen Dependence’ of ¹³C NMR chemical shifts in the series of halogenomethanes is revisited at the four‐component relativistic level. Calculations of ¹³C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four‐component relativistic theory of Dirac‐Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyall's basis sets of triple‐zeta quality or higher are to be used within the framework of the four‐component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non‐relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright © 2016 John Wiley & Sons, Ltd.     

Principal component analysis of the main factors of line intensity enhancements observed in oscillating direct current plasma

Enhancement of emission line intensities by induced oscillations of direct current (DC) arc plasma with continuous aerosol sample supply was investigated using multivariate statistics. Principal component analysis (PCA) was employed to evaluate enhancements of 34 atomic spectral lines belonging to 33 elements and 35 ionic spectral lines belonging to 23 elements. Correlation and classification of the elements were done not only by a single property such as the first ionization energy, but also by considering other relevant parameters. Special attention was paid to the influence of the oxide bond strength in an attempt to clarify/predict the enhancement effect. Energies of vaporization, atomization, and excitation were also considered in the analysis. In the case of atomic lines, the best correlation between the enhancements and first ionization energies was obtained as a negative correlation, with weak consistency in grouping of elements in score plots. Conversely, in the case of ionic lines, the best correlation of the enhancements with the sum of the first ionization energies and oxide bond energies was obtained as a positive correlation, with four distinctive groups of elements. The role of the gas-phase atom-oxide bond energy in the entire enhancement effect is underlined.     

基于主成分的改进雷达图及其在综合评价中的应用

本文从可视化角度出发,在总结传统可视化方法因优点与不足的基础上,将主成分分析、因子分析与雷达图结合,改进了传统的可视化方法。并将新的可视化方法引入到综合评价中,提出了一种基于雷达图面积的综合评价模型,实例验证该种方法切实有效。     

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.     

A physical mechanism based investigation on the elasto-plastic-damage behavior of anisotropic aluminum alloys under finite deformation

The elasto-plastic-damage behavior of anisotropic aluminum alloys is investigated under finite deformation using a physical mechanism based constitutive model. With an application to the structural calculation, the present model is used to describe and analyze the mechanical response of anisotropic 6260-T6 aluminum alloy extrusions. For the tensile specimens extracted along three different material orientations from the extruded aluminum profile, twelve simulations are carried out covering four different specimen geometries. The simulation results in force-displacement response and central logarithmic axial strain evolution are compared with experimental results. From the comparisons, it can be concluded that the present model has the capacity to describe the behavior of anisotropic material. From the force-displacement curves, the anisotropy is observed in different material orientations, and the physical mechanism of anisotropy is analyzed.     

-Weyl's theorem for operator matrices

If is a upper triangular matrix on the Hilbert space , then -Weyl's theorem for and need not imply -Weyl's theorem for , even when . In this note we explore how -Weyl's theorem and -Browder's theorem survive for operator matrices on the Hilbert space.

     

Natural bound in Kwiecinski's criterion for flatness

Kwiecinski has proved a geometric criterion for flatness: A morphism of germs of analytic spaces is not flat if and only if its fibre power has a vertical component, for some . We show how to bound using Hironaka's local flattener: If is not flat, then has a vertical component, where is the minimal number of generators of the ideal in of the flattener of .