临界

Only with such characteristics, the movement equations can be expressed as matrices, and the idea of transforming the movement equations to the simplest form through a nonlinear transformation can be realized;(2) The form of Zi =Yi + YTH2i Y + Y7H3i Y(2)+ Y(2)T H4i Y(2)+ YTH5i Y(3) is adhibited in the nonlinear transformation, so that the multivalued problem caused by the nonlinear transformation is avoided, and the higher order transformation can be taken next;(3) The fourth order nonlinear transformation matrices H21,H31,H41 and H51 are derived, by which the original movement equations of electric power system is transformed to Jodan form in Z space;(4) By use of the fourth order nonlinear transformation, the approximate expression of the stability boundary is obtained, in Z space it is Z1= 0,in Y space it is Y1 + YTH21 Y + YTH31 Y(2)-i- Y(2) TH41 Y(2)+YTH51 Y(3)= 0;(5) The criterion used in this paper to judge whether the system critical unstable is simple and quick;(6) The method used in this paper is a direct method, and no need to construct an energy function.

正是由 于电力系统的运动方程具有这样的特性，才能写成矩阵的形式，通过非线性变换将电力系统的运动方程变换为最简单的线性形式的思想才能得以实现；（2）将通常运用于电力系统暂态稳定性分析的Normal Form变换的形式由 Yi＝ Zi＋ ZTh2riZ变形为 Zi＝ Yi＋YTH2iY＋YTH3iY（2）＋Y（2）TH4iY（2）＋YTH5iY（3），从而使得在对持续故障轨线实施同样的非线性变换以确定临界切除时间时，避免了非线性变换带来的多值性的问题，而只有在没有多值性问题的困扰下，才能采用较高阶的变换：（3）推导出了将原始电力系统系统的运动方程变换到Z空间的约当形式的非线性变换矩阵H21、H31、H41、HS1：（4）在运用四阶了「线性变换的情况下，给出了受扰动后系统的稳定边界的近似的解析表达，在Z空间为Z1=0，在y空间为： Y1+YTH21Y+YTH31Y(2)+Y(2)TH41Y(2)+YTH51Y(3)=0 （5）确定临界失稳的判据简单、快捷：对于一个复杂的电力系统，其稳定边界是相当复杂的一个高维曲面，即便是已知系统稳定边界的解析表达，要求出系统持续故障轨线何时与这一高维曲面相交，在数学上几乎是不可能实现的。

The results of bend loss measurements for polymer optical fiber composed of different cores and claddings are tes-ted.

测试了不同材料和纤芯半径的塑料光纤中弯曲损耗随光纤弯曲半径和弯曲圈数的变化规律，结果显示弯曲损耗呈现随弯曲半径增加而下降的趋势，纤芯直径越大，临界半径越大，弯曲半径小于临界半径时，弯曲损耗呈现指数规律。

The movement contrails of the mixer heads were founded. The critical angular velocity of partially circular motion was deduced for both single grain and a group of grains.

分析单个颗粒的圆周运动，得到了单个颗粒作部分圆周运动的临界角速度；分析颗粒群体的运动，得到了颗粒群体作完全圆周运动的临界角速度，结果表明该值与颗粒物料常数及充装系数相关。

Two parameters proposed by RILEM,the critical stress intensity factor K ICS and critical crack tip opening displacement CTOD C ,and third parameter of the characteristic length l ch are applied for investigation of fracture characteristics of concrete,which is with different size of coarse aggregate and different content of silica fume,and under different curring condition.

采用RILEM推荐的双参数临界应力强度因子和临界裂缝尖端张开位移，同时还采用了特征长度lch研究了不同粗骨料粒径、不同硅灰掺量以及不同养护条件下这3个因素对混凝土断裂特性的影响。

The results show that single structure parameters (width and depth of flow path/passage, and height, and angle of dentations) are local and difficult to represent the anti-clogging ability of emitters. Characteristic structure parameters(minimum size of cross section, hydraulic radius and dentitions spacing) can represent the anti-clogging ability of emitters in a sense. There are anti-clogging critical values under the test. Rated flow Qr and the ratio of diameter of labyrinth passage to diameter of particle η are well cor related to the anti-clogging ability and have anti-clogging critical values too.

结果表明：用单一结构参数(流道宽度 W 、流道深度 D 、齿高度 h 和齿角度θ)表征其抗堵塞性能存在局限性；结构特征参数断面最小尺寸 min(D，W、水力半径 R 和齿间距 l 能较好反映滴头流道横、纵断面的结构特征，在不同程度上表征了流道的抗堵塞性能，且在试验条件下各自均存在抗堵塞临界值；滴头额定流量 Qr 和迷宫滴头径粒比η与抗堵塞性能相关性较好，且存在抗堵塞临界值。

By employing the Jordan-Wigner transformation and a modified mean field method, we are able to determine its ground-state quantum phase diagram approximately. The chapter IV is the main part of this Thesis. It contains the main innovations in our work. We propose and study in detail a S=1 Ising chain with the interplay of single-ion anisotropy and dimerization. The main results and innovations are the following: We show that the total number of the zero-component of spins at each site is a conserved quantity. This quantity, which may intuitively called as hole's quantum number, is hidden in the system. We show further that the hole's number in the ground-state is zero; By using the Jordan-Wigner transformation, we map this model onto a series of subsystems described by the spin 1/2 dimerized transverse Ising model. We solve the subsystems exactly, by presenting the exact wave functions and spectra;We show that this system exhibits a series of quantum phase transitions by varying the dimerization strength. We determine the quantum critical points exactly. We also show that the criticality is the same as that of the uniform S = 1/2 transverse Ising chain.

第四章是本文的重点及主要创新内容，我们具体研究了自旋为1的在横向单离子晶格场中的一维二聚化Ising链，我们得到的主要结果和创新之处是：(1)证明了这一模型具有一种隐藏的对称性，即自旋第三分量为零的格点数目是一个守恒量，并证明基态出现在空穴数目为零的子空间中；(2)利用Jordan-Wigner 变换将此模型变换到一系列自旋为1/2的横磁场中的二聚化Ising 模型，并给出了相应严格的波函数及能谱；(3)我们发现系统的基态随着二聚化强度的变化将呈现出一系列量子相变，我们得到了量子临界点的精确位置，并证明其临界性质与自旋为1/2的横磁场中的均匀Ising 链中的临界行为属于同一普适类。

As the plastic region expansion on circle plate under extemal pressure is smaller than that under equal internal pressure, it can be qualitatively reckoned that the critical pressure of in-plane instability under external pressure is higher than that under internal pressure with the same axial displacement load.

由于外压增量导致环板内塑性区域扩展的范围小于等值内压的影响，因此可以定性的认为，在同样的轴向压缩量下，波纹管的平面失稳外压临界压力大于内压临界压力。

Based on soil permeability and its two damage mechanisms (i.e. tensile failure and shear failure), a new method for determining critical thickness of base plate of foundation pit is presented based on elastic theory.

根据基坑底板土的渗透性及其破坏机制，基于弹性力学理论，按受弯拉裂破坏模式和剪切破坏模式计算确定基坑底板土层临界厚度，通过算例和分析，与传统确定临界厚度的计算方法进行了对比。

The main conclusions are those:(1) the cause of hot-dry climate before elevation of plateau is that the efficiency of atmospheric heat engine is lower than after the elevation owing to flatter global landform;(2) at the beginning of Oligocene Epoch,the horizontal scale of plateau reached the cr...

主要结论：（1）高原隆起前的干热气候是由于隆起前全球地势平坦，致使大气热机效率很低之故；（2）渐新世初高原的水平尺度达到了斜压大气地转适应的临界尺度，大气环流从南北两极&两涡对峙&突变成地球三极的&三涡鼎立&，气候发生突变；（3）分析了2.5Ma时高原抬升到2000m这一重要临界高度后大气环流的一系列相应变化；（4）计算、比较了最大冰期地气系统能量平衡与现代的差异，并由此分析了当时的气候状况

This analytical approach shows that, as increasing the wear flat of indenter, the maximum indentation force needed to develop critical plastic zone increases and its corresponding critical penetration depth also increases slightly, Note that the effect of wear flat will affect rock fracture behavior. In addition, regarding the simulation of the effect of doubled-indenters, result shows that two adjacent indenters may interact each other as reaching the transient/critical relative space between indenters of 2~3. It dicpicts that a proper spacing arrangement between indenters may enhance a efficient mechanical cutting due to the less required maximum indentation force and energy dissipation.

由数值模拟之结果得知，当楔尖磨耗增加时，岩材产生脆性破坏之初裂贯切力随之增加，而其对应之临界贯入深度则亦微幅增加，故磨耗效应确会干扰岩材脆性破坏机制之形成；而由双刀效应之模拟，可知两贯切刀楔互制影响之破坏裂缝生、衍行为，当双刀相对刀距为时，岩材之破坏特徵有明显变化，即定义此为临界相对刀距，并探讨其产生脆性破坏所需初裂贯切力之变动范围及应力重叠区，由此得知适当之刀距安排将有助於减少能量之耗损。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。