虚点

The physical meanings of BEM are extended by the FBEM and FPFM. On the basis of solving plane problems sueessfully with FBEM and FPFM, the article recommends the fictitious boundary element method and fictitious point force method to solve three dimensions problem in solid mechanics.

本文对边界单元法进行了改进，提出了使用方便、灵活、物理意义清晰的虚边界单元法和点载荷法，较好地解决了局部数值解精度不高的问题，并将所提出的方法推广应用到求解三维问题，减少了问题的复杂性。

The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method, where the problem is formulated by distributions of fictitions fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically.

弹性半空间；本文用线载荷积分方程法研究嵌在弹性半空间的刚性变直径圆轴的轴对称扭转。利用将"半空间的点环力偶"这一虚的基本载荷沿对称轴的圆轴区间中分布就能使本问题归结为一个一维的非奇异的Ferdholm第一种积分方程，且很易用数值求解。文中给出刚性圆锥，圆柱，圆锥柱嵌在弹性半空间的扭转的数值计算的例并和他人的已知结果相比较。

By spectral analysis of the system, we find that 0 is the uniquespectral point of system on the imaginary axis.

同时通过研究系统算子的谱特征，证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱，进而得到系统的渐近稳定性，特别在范数意义下系统的动态解收敛到稳态解。

Based on two algebra Riccati equation method especially the structure of the system Hamilton matrix and system observability theory, the role of invariant zeros in constructing system reduced order controllers was given. That is, by the suitable selection of free parameters of the system H(subscript ∞) controller, some points which were symmetry with the unstable invariant zeros about the imaginary axis became the stable poles of the system controller which were not observable and could be reduced from the system, thus could get further reduced order controller.

基于2代数黎卡提方程方法，特别是系统Hamilton矩阵的结构特点和系统可观测性理论，论述了不变零点在构造系统降阶控制器中所起的作用，即通过选择控制器的自由参量，使某些不稳定的不变零点关于虚轴对称的点构成系统控制器不可观的稳定极点，从而实现了控制器进一步降阶。

Each of these complex points is composed of two numbers, the real part and the imaginary part.

这些复数点中的每一个都由两个数，即实部和虚部组成。

That is, the singular terms: signal, point, sample, and value, refer to the combination of the real part and the imaginary part.

也就是说，单一的术语：信号、点、样本和数值指的是实部和虚部的组合。

The zero-contours of the real and imaginary parts of complex amplitude are closed curves. The number of intersection points of the zero-contour of the real and imaginary parts is even, and positive and negative singularities are equal.

复振幅的实部和虚部零值线多为封闭的曲线，零值线交点的个数为偶数，并且正负相位奇异点的个数相等。

The concepts to be introduced include, but are not limited to, the random phase approximation, the mean field theory (aka saddle-point, or semiclassical approximation), the tunneling dynamics in imaginary time, instantons, Berry phase, coherent state path integral, renormalization group..

这些方法主要涉及如无规相近似、平均场理论(aka 鞍点或半经典理论)、虚时间中的隧道动力学、瞬子、贝里相、相干态路径积分及重整化群等概念。

Here, the meaning of virtual focus is a "point" from which rays of light seem to emanate but do not actually do so such as in the image in a plane mirror.

这里所指的虚焦点是一个"点"，从其中的光芒似乎产生，但实际上没有这样做（例如在图像在一个平面镜）。

Using the Updated Lagrange finite element method and the elastic-plastic large deformation finite element formula based on virtual work-rate principle of finite deformation, the author studies in detail the plastic flow rule of MPF, including the influence of the work hardening index, friction, thickness of sheet, material, number and position of the punch.

作者采用逐级更新Lagrange法以及有限变形虚功率增率原理的弹塑性大变形有限元法，详细研究了金属板材多点成形的塑性流动规律，包括加工硬化指数、摩擦系数、板料厚度、材料、冲头个数及位置等对成形的影响，同时探讨了分段成形时的金属流动规律。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。