波函数

Antiplane responses of a scalene triangular hill or structure, an isosceles triangular hill or structure, an isosceles triangular hill with a subsurface cavity to incident SH waves are studied in this paper based on methods of wave function expanding, complex function, moving coordinates and by employing idea of assistant function.

本文在"分区"和辅助函数思想的指导下，综合利用了波函数展开、复变函数、移动坐标三种方法，研究了等腰三角形凸起地形和坝体结构、非等腰三角形凸起地形和坝体结构、浅埋圆孔附近等腰三角形凸起地形等三类问题对SH波的散射。

Week 15 Experiment law of hydrogen atomic spectrum, Bohr hydrogen atom theory, wave -particle dualism of matter, de Broglie waves, uncertainty relation, wave function and its statistical explanation, standard condition of wave function, Schrodingger equation in one dimension, simple introduction of quantum mechanics.

第15周氢原子光谱的实验规律，氢原子的玻尔理论；波粒二像性，德布罗意波，不确定关系；波函数及其统计解释，波函数的标准条件，一维薛定谔方程，量子力学简介。

Dirac equation can be separated into an angular equation and a radial equation with the help of separation variable.

通过分离变量得到Dirac方程相应的角向方程和径向方程，得出了用广义连带勒让德多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数；获得了精确的束缚态能谱方程并对结果作适当讨论与结论。

The digital algorithms of integral and discrete wavelet transform are presented for purpose of electric power system protection, based on the analysis of wavelet transform for sampled digital signals under the Shannon sampling theorem.

从电力系统继电保护应用的角度，结合香农采样定理，深入探讨了连续信号和离散信号的小波变换的关系，给出了离散信号的积分小波变换和离散小波变换的数字计算方法。从理论上研究了信号小波变换的误差与尺度函数和小波函数的关系。

The preliminary chromatogram data were resolved with Mallat algorithm of wavelet analysis theory. This method that resetting the high frequency signals, reconstructing low frequency and then correcting the background signals in the original signal was to avoid the data skewness with negative digital points after background correction and achieve the baseline correction; according to the study and analysis of simulated data including curve background and real data of the needle-plate and free metal partials insulation defects, the method is effective; the best wavelet function of the background correction is Db5 and the best resolution times of the background correction is 8 for chromatogram data of SF_6 decomposition products, based on the calculation with different wavelet functions and resolution times.

在初步获取的气相色谱数据基础上，运用小波分析技术中的Mallat算法对色谱数据进行小波分解，采取将高频信号置零，重构低频背景信号，再用原始信号扣除背景信号的方法，并对背景信号进行纵向平移以避免扣除后出现负数据点造成色谱峰失真的题目及达到色谱图基线校正的目的；通过对含曲线背景信号的模拟色谱数据和针-板、自由金属微粒缺陷下的真实数据的计算研究表明，该方法的应用是有效的；并通过对不用小波函数和不同分解次数的背景扣除计算，确定了SF_6气体放电分解组分色谱背景扣除所选用的最佳小波函数为Db5小波和最佳分解次数为8次。

First of all, the basis of the MRTD method is studied. In Chapter 2, wavelets analysis and multiresolution analysis, the mathematical basis, are introduced, and the characteristics of the wavelets basis functions, including orthonormality, compact support, multiresolution and so on, are also introduced. The advantages of the applications of these functions to the numerical electromagnetic calculations are discussed. In Chapter 3, the algorithm basis of MRTD: the combination of the wavelets and the method of moments is studied. This Chapter shows that the MoM based MRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

First of all, the basis of the MRTD method is studied. In Chapter 2, waveletsanalysis and multiresolution analysis, the mathematical basis, are introduced, and thecharacteristics of the wavelets basis functions, including orthonormality, compactsupport, multiresolution and so on, are also introduced. The advantages of theapplications of these functions to the numerical electromagnetic calculations arediscussed. In Chapter 3, the algorithm basis of MRTD: the combination of the waveletsand the method of moments is studied. This Chapter shows that the MoM basedMRTD method is the combination of wavelets and MoM using Galerkin sampling.

文中首先讨论了 MRTD 的建立基础，其中第二章介绍了其数学基础－小波分析及多分辨分析，讨论了小波基函数的性质包括正交性、紧支撑性、多分辨性等及其应用于电磁场数值计算的优势；第三章讨论了其算法基础－小波与矩量法的结合，阐述了以矩量法作为算法基础，以 Galerkin 离散采样的方式与小波函数结合而产生了 MRTD。

Our conclusion is that we propose to have found a concrete and distinct mathematical form for the thing-in-itself in the Quantum Mechanics regime, which may serve as the non-sensible noumenal cause for an appearance of a body.

对於复数函数波函数的不可观测性，我们也做了详细的论述。我们的结论是：在量子力学的范畴里，已经找到了康德物自体的一种明确而具体的数学形式，即复数函数的波函数。

As same as the above-mentioned reason, because theconditions at the inside straight boundary of the binarycomposite material can not be easily satisfied, here, anelastic circular inclusion with large radius is used to replacethe upper half space of the binary composite material, so the〓mary binary composite mater ial problem can be changed〓the scattering problem of a circular elastic inclusion andto the scattering problem of a circular eastic inclusion and〓circular cavity in an infinite space to the steady incident〓wave.

与前面两个问题的理由一样，同样，由于问题中双质复合材料的内部直边界上的边界条件不易解析满足，为此，本文采用了一个半径很大的弹性实夹杂来代替问题中双质复合材料的上半空间部分，而将原来的双质复合材料问题转化成了无限大空间中一圆形弹性夹杂和一圆孔对稳态P波的共同散射问题，根据该问题的特点写出了弹性夹杂内外波场中波函数的一般形式解，利用该问题中夹杂和圆孔处的位移和应力的连续条件，并采用复数傅立叶级数展开技术将其化为一个仅包含问题波函数中未知系数的无穷线性代数方程组，在满足一定计算精度的前提下，通过有限项截断进行近似求解，进而讨论了双质复合材料中圆孔边界处的动应力集中系数随不同入射角、圆孔的不同位置、以及入射波的不同无量纲波数的变化和分布情况。

From theoretical analyses and calculations, it has been confirmed that the local strains around Cr〓 in SrTiO〓: Cr〓 are about twice the bulk ones. It is found that the change of Dq〓 with pressure makes main contribution to PS of ground-state g factor of SrTiO〓: Cr〓. It is the admixtures of basic wave functions that cause the strain-induced splittings of t〓E and t〓A〓 levels of SrTiO〓: Cr〓. It is found that there are non-vanishing matrix elements of operators C , C and C between wave functions with positive M〓 and those with negative M〓 and the shortcomings in previous literature have been overcome.

通过微观理论分析与计算，证实了SrTiO〓：Cr〓中Cr〓周围的局域应变大约为整体应变的两倍；阐明了基态g因子随压力的变化主要来源于Dq〓的变化；发现波函数的混合对单轴压力导致的SrTiO〓：Cr〓t〓E和t〓A〓态的分裂是至关重要的；C、C和C算符在Ms为正的波函数与M〓为负的波函数之间的矩阵元不为零，纠正了过去文献对此的错误处理。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。