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Afterward Waldhausen ([7]) showed that this topological hypothesis was true. Besides, Stallings ([11]) gave another conjecture that was equivalent to Poincare"s Conjecture. Thus we know both conjectures made respec- tively by Traub and Stallings are equivalent to Poincare"s Conjecture.

另外Stallings([11])又提出了另一个代数的猜想并同时证明也证明了这个猜想与庞加莱猜想是等价的，由此可知Traub所给的猜想与Stallings的猜想都与庞加莱猜想是等价的，从而这两个代数的猜想也是等价的。

Based on equaling the semi-rigid connecting as the reduction of member end section bending stiffness,an optimization equivalent method is put forward on the principal of minimizing the error term between stiffness matrix of fined model and one of equivalent simple model.In this dissertation,structural fatigue cumulative damage and residual life assessment of wind-induced fatigue safety prewarning system is studied.S-N curve method and fracture mechanics method for fatigue analysis are discussed.

本文建立了高耸塔架结构中广泛使用的螺栓节点板联结节点的精细有限元模型，提出了一种优化等效的方法，以刚度矩阵的误差最小为等效原则，在把节点处杆件的半刚性联接等效为杆端截面抗弯刚度下降的基础上，得到了螺栓节点联结杆件的精细有限元模型与简化有限元模型的等效关系。

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

The elements of optical waveguide strain-stress measurement and fiber bragg grating strain-stress measurement system based on wavelength division multiplexing and spatial division multiplexing are emphatically discussed; the displacement regularity of stress field induced by roadway group excavating and short wall mining process is analyzed in detail; the concept of roadway "equivalent radius","correcting coefficient of coal and rock mass mechanical parameters",and "mining affecting coefficient" is put forward; the calculation method of "equivalent radius", the method of inversion of "correcting coefficient of coal and rock mass mechanical parameters", and the "mining affecting coefficient" determination method with the field measurement results and so on are provided.

重点研究了光波导应力应变测量原理，以及基于波分复用和空分复用技术基础上的布拉格光纤光栅应力应变测量体系；详细分析了近距离巷道群开掘工作和短壁体系回采工作诱发的应力场的重新分布规律；提出了巷道"当量半径"、"煤岩体力学参数修正系数"、"采动影响系数"等概念；给出了"当量半径"的计算方法、"煤岩体力学参数修正系数"的反分析求算方法、以及通过现

The equivalent damping and the equivalent stiffness of damper are in near-direct proportion to the damper load. Four remodelment of the damped blade system are performed for parametric studies.

为了对干摩擦阻尼器的性能参数进行研究，本文结合工程实际将凸肩阻尼叶片的参数做了相应的调整和变形，对调整参数后的系统进行了受迫振动响应的计算和分析。

To master thermal equivalent of food, thermal equivalent of oxygen, respiratory quotient, non-protein respiratory quotient.

熟悉影响能量代谢的主要因素：肌肉活动，食物的特殊动力作用，精神状态，环境温度。

Equipment: film or glass plates, metal plates, plastic stirring paddle, cheesecloth, gloves, safelight with light red filter (Kodak 1A or equivalent), 1 liter glass beaker or stainless steel bowl, 4 liter glass beaker or equivalent stainless steel bowl.

器具：透明胶片或玻璃板，金属板，塑料搅拌器，粗棉布，手套，安全灯，1升的玻璃大口杯或不锈钢杯，4升的玻璃大口杯或等大的不锈钢杯，以及一个药品搅拌勺也许会派上用场。

In the analysis the geology circumstance of 沁 water basin drills a hole data with what we control, we adopted to hang up to draw mountain west a set and too original set of the lord adopt coal seam to cover up deep equivalent line, the scaleboard elevation equivalent line the way of the diagram, appear the structure circumstance of research area at the diagram piece top body.

在分析了沁水盆地的地质情况和我们所掌握的钻孔资料，我们采用了勾绘山西组和太原组的主采煤层埋深等值线、底板标高等值线图的方式，来将研究区的构造情况在图件上体现出来。

To conclude the agreement to study at MSU you should submit to the department of international studies of the chosen faculty the following documents: Filled application form; Academic documentation, equivalent the academic documentation of Russian Federation, with the academic degree, the full list of learned subjects and full list of marks, with a notarized translation into Russian: For Bachelor studies: school-leaving certificate For Master studies: Bachelor's or Specialist's degree-certificate For Post-graduate studies (Candidate's degree): Master's or Bachelor's certificate Transcript (the document showing the list of the subjects with results) with a notarized translation into Russian; Evidence of the equivalent of the documentation about the education which was get abroad; Certification showing the results of your test in the Russian language.

总结协议在你应该对被选择的全体教员的国际研究部委托下列的文件的 MSU 学习：填写了申请表；学院的文件，同等物俄罗斯联邦的学院文件，藉由学院的程度，标志的有学问主题和完整目录的完整目录，藉由被证明的翻译进入俄语之内：因为学士学习：毕业证书因为主人学习：学士或专家的程度-证书因为在研究所之后的：主人或学士的证书进入俄语之内的有被证明的翻译的抄本(文件表现主题的目录用结果)；关于教育的等同于文件的证据是到达在国外；证明以俄国语言表现你的测试的结果。

This essay discussed and analyzed the equivalent self-Inductance Coefficient of two inductors connected in parallel,and solved the equivalent self-Inductance of perfect coupling with L Hospitcl rule .

文章分析和讨论了两个线圈分别在反并接和顺并接时的总等效自感系数，并用"洛必达法则"求解线圈在理想耦合状态下的自感系数。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。