临界的

In chapter 5,we persue the ctiticality and complexity of thecritical sets.We describe carefully the Whitney's example in 1935.Meantime,we introduce some rsults about the critical sets and thecritical value sets,in particular,on W-sets and C-sets.And usingthe Lebesgue density theorem and the Vitali covering lemma weprove a rank zero theorem with Hausdorff measures.Finally wegive some examples to prove our results are sharp in the sense thatthe numbers k,m,n,s,〓,etc.,in the hypothesescan not be improved.

第五章研究临界点集的临界性和复杂性，并详细地描绘了Whit-ney在1935年的例子，同时也介绍了关于临界点集和临界值集的一些结果，尤其是W-集和C-集的一些结果，并利用Lebesgue密度定理和Vitali覆盖引理证明了一个与Hausdorff测度相关的秩零定理，最后举例证明我们的结果在定理的假设中的那些数字如k，m，n，s，a，r+/等不能被改进的情况下是最佳的。

Using the method of linear response theory in lattice dynamics on the basis of Tyson's model, the response displacements of atoms on cleavage plane at the incipience of brittle fracture was derived and an expression for evaluating brittle fracture surface energy of metals was found.

本文在Tyson模型的基础上，应用点阵动力学线性响应的理论方法，导出了脆断发生时解理面上原子的响应位移，并进而给出金属脆断表面能的计算公式。这种处理方式既保持了解理断裂面是结晶的表现，避免了局域"熔化"和"沸腾"模拟脆断的简单模型中出现的非晶化问题，也对解理面上原子临界位移做了合理估计，避免了人为规定临界位移的随意性，同时，从理论上得出的脆断时产生的声发射信号与实际探测到的量级相近。

The experimental results show that hydrophobic association increases obviously with increasing polymer concentration, hydrophobe content, hydrophobic side chain length and temperature. The Critical aggregate concentration of P(AM/NaAA/C_8AM) with different hydrophobic content is 1.5-3g/L. Strong ass...

结果表明，随聚合物浓度、疏水单体摩尔分数、疏水侧链长和温度的增加，疏水缔合作用增强；不同疏水单体含量的P(AM/NaAA/C8AM)的临界缔合浓度为1.5~3.0 g/L；表面活性剂十二烷基硫酸钠与P(AM/NaAA/C8AM)发生了强烈的疏水相互作用，形成混合胶束，得到SDS的临界胶束浓度为8×10-3 mol/L；由于聚合物链上羧基的存在，使其具有良好的 pH敏感性，随 pH值的增大，P(AM/NaAA/C8AM)的疏水缔合作用呈现先减弱后恒定再增强的变化。

The experimental results show that hydrophobic association increases obviously with increasing polymer concentration, hydrophobe content, hydrophobic side chain length and temperature. The Critical aggregate concentration of P (AM/NaAA/C8AM) with different hydrophobic content is 1.5~3g/L. Strong association between surfactant sodium dodecyl sulfate and P (AM/NaAA/C8AM) occurs through the formation of mixed micelles. The CMC of SDS is 8×10^(-3)mol/L. Moreover, because of the presence of-COOH group, the terpolymers have pH-responsive characterization. The hydrophobical association changes greatly with increasing pH.

结果表明，随聚合物浓度、疏水单体摩尔分数、疏水侧链长和温度的增加，疏水缔合作用增强；不同疏水单体含量的P(AM/NaAA/C8AM)的临界缔合浓度为1.5~3.0g/L；表面活性剂十二烷基硫酸钠与P(AM/NaAA/C8AM)发生了强烈的疏水相互作用，形成混合胶束，得到SDS的临界胶束浓度为8×l0^(-3)mol/L；由于聚合物链上羟基的存在，使其具有良好的pH敏感性，随pH值的增大，P(AM/NaAA/C8AM)的疏水缔合作用呈现先减弱后恒定再增强的变化。

Chapter four studies the chaotic responses in a system consisting of simple pendulum and harmonic oscillator under bounded noise excitation. Firstly, the Melnikov function of the two-degree-of-freedom system under Hamiltonian perturbation is derived. The essential condition of the autonomous system for the probable onset of chaos is obtained, the Poincare maps of the system under small Hamiltonian perturbation and the effect of increasing perturbation on the Poincare maps are studies. Then for the non-autonomous system under damping and harmonic or bounded noise excitation, the largest Lyapunov exponent and Poincare maps are calculated. From the analysis of the largest Lyapunov exponent, the critical criterion for the onset of chaos, and the conclusion that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity parameter of Wiener process increases are obtained. The result from the analysis of Poincare maps is in agreement with that obtained from the Largest Lyapunov exponent. The effect of varying damping coefficient and intensity parameter of Wiener process is also analyzed.

第四章研究了有界噪声激励下的两自由度单摆—谐振子系统的混沌运动，首先推导了该两自由度系统仅在Hamilton扰动下的Melnikov函数，得到该自治系统可能产生混沌的必要条件；研究了该系统在小的Hamilton扰动和增大摄动情形下的Poincare截面；然后对有阻尼、谐和或有界噪声激励下的非自治系统数值计算了其最大Lyapunov指数和Poincare截面；从Lyapunov指数分析得到了这个两自由度系统产生混沌运动的临界条件及产生混沌的临界激励幅值随Wiener过程强度参数值的增大而增大的结论，Poincare截面分析的结果亦符合Lyapunov指数分析的结论；研究了Wiener过程强度参数、阻尼系数变化对Poincare截面的影响。

The article covers the full research on such aspects as mathematic description, numerical analysis method and their practical applications. The diphase heating surface is divided into a hot water section, a evaporation section and a micro overheat section , the problems of model switching are avoided successfully between subcritical and supercritical working condition in the model of The diphase heating surface, and the model can be used for between subcritical and supercritical working condition without causing the model stiff infinity prick up problem. The mathematical model and dynamic characteristic account is unified and predigested for the diphase heating surface of once—through boiler under subcritical and supercritical pressure, and propose that the working conditions at phase change point could be used as divide criterion between water region and steam region under supercritical pressure, the problems are solved successfully between water and steam phase change point under supercritical pressure.

本文在过程的数学描述、数值分析以及实际应用等方面进行了系统的研究分析，将双相受热面统一划分为热水段、蒸发段和微过热段三段，所建立的双相受热面模型不但成功地避免了超临界工况与亚临界工况间的模型切换，而且消除了由区段划分欠妥所引起的模型刚性无限加剧的问题，统一并简化了超临界及亚临界压力下直流锅炉双相区段的数学模型和动态特性计算，而且提出了利用相变点工况作为超临界压力下划分汽水区域的标准，解决了超临界压力下水与蒸汽的相变点问题。

This project was conducted starting with the three interrelated subjects the structural characteristics of desertification landscapes in different bioclimatic zones, desertification driving factors and their function mechanism, and the dynamic model of landscape space for the occurrence and development of desertification in representative desertification regions and on the basis of in-depth studies of the relations between landscape structural characteristics and processes of desertification and their stability; the driving force of different time-space scales of desertification and their proportion, manifestation form, and action mechanism in the desertification processes; and the establishment of threshold conditions for the surface wind erosion and has achieved important progress in the definition of desertification conception

本课题从三个相互联系的专题（即不同生物气候区荒漠化景观的结构特征、荒漠化驱动因素及其作用机理、典型荒漠化地区荒漠化发生与发展的景观空间动力学模型）入手，在深入研究荒漠化景观结构特征与过程的关系及其稳定性，不同时空尺度的荒漠化过程驱动力及其在荒漠化过程中所占比重、表现形式及作用机制，地表风蚀临界条件的确定等内容的基础上，虽未建立荒漠化景观空间动力学模型，但在沙漠化概念，末次间冰期以来沙漠化过程时间序列和特征冷暖时期沙漠、沙地空间分布格局，现代沙漠化过程中自然因素和人文因素的作用、贡献率、沙漠化土地对气候的反馈作用以及风蚀临界值，沙粒跃移轨迹参数和能量分布，我国沙漠化防治思路和对策，沙尘暴区划和沙尘暴指数等方面取得了重要进展。

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

In order to research the ship ultimate strength, the ultimate strength of stiffened panel must be considered. And the web buckling and the stiffener tripping are the two main failure forms of stiffened panel. Based on the two main failure forms in this paper, according to the six failure modes of stiffened panel, the ultimate strength is solved by programming, and the failure mode is presented.

船体梁可近似看作是由加筋板组成的薄壁箱型结构，要研究船舶的极限强度，必须考虑加筋板的临界应力，而腹板屈曲和扶强材侧倾是加筋板的两种主要失效模式，本文在分析这两种失效模式的基础上，根据加筋板的六种失效模式，编程求解加筋板的临界应力，并给出其失效模式。

The disturbances on power system are calculated and analyzed, and the conclusions show that self excited shunt excitation system with less rise time and overshoot has good quality in majority disturbances.

所选的项目也是发电机在运行中会遇到的扰动。临界切除时间和强励上升速度用以检查对暂态稳定的影响。较长的临界切除时间和较快的强励上升速度反映较优的暂态稳定性。

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。