临界点

The AE rate and rising time can be employed to predict two "critical points" of wood fracture damage. The first point means the material is in the state of slight danger and the second point means the material is in the state of serious danger.

4声发射信号的声发射率和上升时间可以预测材料开始断裂进入危险期的和材料大量纤维断裂进入严重危险期的两个&临界点&。

Seen from the philosophy angle, death is a process from quality change to quantity change after physiology condition descend the threshold, then die cant avoid.

从哲学角度看，死亡是从量变到质变的过程，病人在生理状况下降到临界点之后，死亡也就不可避免，实际是完成了生死过程中的第一个质变，安乐死仅仅是缩短死亡进程。

Find critical points, zeros, asymptotes, intervals of monotonicity, convexity, and points of inflection.

画出f=(x^4 - 3)/x的草图，找出临界点、零点、渐近线、单调区间、凸性和拐点。

It is proved that the cavitated bifurcation equation is equivalent to a class of normal forms with single-sided constraints near the critical point by using singularity theory.

用奇点理论证明了，空穴分岔方程在临界点附近等价于具有单边约束条件的正规形。

Then the paper presents a novel-working mode of Boost-Forward single-stage Power Factor Correctors based on the analysis. And get the principle of the conduction mode and the method to control the voltage of the buck capacitor after the analysis of the boundary mode of the PFC converter and the DC-DC converter.

在此基础上，本文首次提出了一种全新的临界工作模式下的单级功率因数校正电路，在对PFC变换器及DC/DC变换器工作在连续及不连续的边界条件进行了讨论后，得出了电路工作状态的精确解并提出了控制储能电容电压的临界点工作方式。

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。

The transition point of the bilayer antiferromagnet is also determined by bond-operatormean-field theory and the result is consistent with the strong coupling expansion.

此外，本文还采用键算符平均场理论计算了反铁磁双层Heisenberg模型中相变的临界点，计算结果与微扰论一致。

The fermion environment is considered from zero temperature to the critical temperature. It is show that the decoherence of the two-level system may also act as the witness of the environments phase transitions, which is similar to the relation between quantum phase transitions and decoherence in the former study.

对于一维XY自旋链系统，二粒子系统的纠缠度会在自旋链的量子相变临界点附近发生剧烈的变化，这种剧烈的变化正是量子相变的一种外在体现。

Here on Earth the critical point can't be reached because the liquid quickly pools at the bottom of the container, leaving a foam with odd flat-sided bubbles and only about 5% liquid content floating on top.

在地球上，泡沫不能达到临界点，因为液体很快就流淌在容器的底层，泡沫中只剩下畸形的扁平气泡飘浮在顶部，其液体含量只有大约5%。

Firstly two characteristic points of the open-loop frequency are identified based on relay feedback experiments: the ultimate point and the bandwidth point.

通过继电反馈辨识系统开环带宽度点和临界点，利用带宽点的信息建立一阶加纯延迟模型。

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。