用标准件对梯度磁场定标

就标准厚度卡片在霍尔传感器的定标方面的应用作了有益的探讨。在纵向测量微小长度时,霍尔片处于磁场边缘位置,其对磁场的梯度更大,即灵敏度更高,且靠中心位置的线性更好。     

利用杨辉三角形对称性推导高阶运动微分方程

利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系，发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程，并讨论了理想约束系统下的高阶运动微分方程. 关键词： 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束     

A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

Maximum Shannon Entropy, Minimum Fisher Information, and an Elementary Game

We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.     

颜色视觉匹配中明度阈值的评价

为了对颜色视觉匹配中的明度阈值特性进行评价,采用在阴极射线管显示器上获得的颜色刺激,在5个不同明度的中性色背景下,标准刺激的明度L*从5到95以5个CIELAB单位为变化步长,共对19个不同明度的中性标准颜色进行视觉匹配实验。通过对实验结果的处理和分析,验证了关于颜色刺激视觉辨别明度阈值与背景明度之间相关性的韦伯法则和crispening效应,同时利用颜色视觉匹配数据对基于CIELAB的相关色差公式进行了评价和比较,CIEDE2000具有最好的明度差预测性能,CMC次之,CIELAB和CIE94最差。     

关于NA情况下重对数律收敛速度的一般形式

研究了NA序列重对数律收敛速度的一般形式，把Davis和Gut的结果推广到了NA的情形，并使梁汉营等人关于对数律一个结果成为特例；作为推论，得到了关于NA序列重对数律收敛速度的充分条件．     

Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

Density-Functional Theory Calculations of Normal Modes and Raman Intensities for Tetraazaporphin

The structure, harmonic frequencies, and nonresonance Raman intensities for porphin, tetraazaporphin (TAP), and three of its isotopomers are calculated by the density-functional theory of B3LYP/6-31G(d). Scaling of force constants for porphin in nonredundant natural coordinates is performed. The scaling factors obtained were used to predict the force field and normal modes of TAP and three of its isotopomers. Two alternative methods are used to carry out reliable assignment of the TAP frequencies: wavenumber-linear scaling method and frequency-shift method. There is good agreement between the frequencies predicted within the framework of the three methods used. The conservativeness of the out-of-plane B _2g - and B _3g -modes for porphin and TAP is examined. The Raman spectrum for TAP is simulated. A refinement of the assignment of the experimental frequencies for TAP of even symmetry types on the basis of the calculations performed is made.