证明

Through establishing the priori estimates for the approximation solutions, we pove the existence of global generalized solution by using the compactness principle and obtain the global property for the generalized solutions in the space L〓. At the last, a new method is used to prove the uniqneness which is a good results, at some extense, under generalize conditions.

运用De Giorgi的最大模估计方法，证明了解的整体上界估计和准衰减型的估计，进一步，在边值和初值具有正的下界条件下，证明了解的一致下界估计，得到了深刻结果。

This thesis investigates the profile extraction and shape optimization on the result of topology optimization of planar compliant mechanisms. The main context includes the following work:(1) summarizing and analyzing the recent research status, some harvest and unsolved problems;(2) analyzing the conceptual design of planar path-generating compliant mechanisms and its mathematical model and tools;(3) Modifying the method of density contour as the method of profile extraction, and developing a method to optimize the density function in the profile extraction according to the requirement of the design of compliant mechanism;(4) developing a method to abstract the compliant mechanism into a form of links and joints by using the principle of connectivity on topology;(5) developing a method of shape optimization of planar path-generating compliant mechanisms, by representing the profile of the abstracted compliant mechanism as simple curves such as straight lines and arcs, establishing the models of the size optimization of the parameters of these curves, so that the compliant mechanism has a machinable shape;(6) At last, proving the feasibleness and effectiveness of the design method by making simulation design and validating it in FEA software.

主要工作包括：(1)分析了柔顺机构拓扑优化和形状优化的研究现状，分析了目前柔顺机构的研究重点、主要成果和尚未解决的问题；(2)分析了基于SIMP的柔顺机构概念设计方法及其相关工具和模型；(3)针对柔顺机构轮廓提取的特殊要求，提出了密度等值线法的改进方案，对密度函数插值点密度值进行优化，提出优化模型和选择优化算法；(4)根据轨迹输出平面全柔顺机构自身的形状特点，提出了轨迹输出平面全柔顺机构的抽象方法，即应用拓扑学上的连通性原理将柔顺机构抽象成杆件和结点形式，并对相应的数学原理进行了证明；(5)提出了平面全柔顺机构的形状还原和尺寸优化方法，对抽象的柔顺机构进行还原，将其轮廓还原成简单曲线的连接，从而建立尺寸优化模型，对机构进行尺寸优化设计，在得到可加工的机构轮廓的同时又能对关键部位进行特别处理；(6)进行了柔顺机构的数值仿真设计，并将所得设计结果导入商用有限元软件中进行仿真实验，证明了设计方法的可行性和有效性。

Introduced in the third chapter with 区间套 theprinciple, the true principle, the fluxionary calculus proved threemethods have carried on the proof to a zero theorem; Then introduces azero theorem the promotion; Finally introduced the zero theorem twoapplications.

在第三章中介绍了用区间套原理、确界原理、微积分证明三种方法对零点定理进行了证明；接着介绍零点定理的推广；最后介绍了零点定理的两个应用。

The second is the subjectivity and immaterialness in the applicability. The third is the advance of the content development. The forth is the formal neutrality and essential orientation and the last is the single goal and multiple arrangements.

针对有限的法学理论上关于证明标准特征的几种具有代表性的理论总结出本文所认为的民事诉讼证明标准在法学理论中所具有的特征，即内容上的客观性与确定性、适用上的主观性与无形性、内容发展中的历史前进性、形式的中立性与实质的倾向性、目标的单一性与层次设计的多元性。

Facts have incontrovertibly proved that the decision to begin reform and opening up is vital to the destiny of contemporary China that reform and opening up are the only way of developing socialism with Chinese characteristics and rejuvenating the Chinese nation, that only socialism can save China and that only reform and opening up can develop China, socialism and Marxism.

事实雄辩地证明，改革开放是决定当代中国命运的关键抉择，是发展中国特色社会主义，事实雄辩地证明，改革开放是决定当代中国命运的关键抉择，是发展中国特色社会主义，实现中华民族伟大复兴的必由之路；只有社会主义才能救中国，只有改革开放才能发展中国，发展社会主义，发展马克思主义。

Insection 4.3, semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are constructed. The convergence and stability for the schemes are proved, and the error estimates are obtained.Chapter 5, consider the damped coupled generalized nonlinear wave equations. In section 5.2, by coupled a priori estimates and Galerkin method, prove the existence and uniqueness of the global smooth solution for the periodic initial value problem and obtain the existence of global attractors.

第四章，考虑一类具耗散的广义KdV方程组的周期初值问题，在第二节中证明了整体光滑解的存在性和唯一性，得到整体吸引子；在第三节中构造了半离散和全离散的Fourier谱格式和拟谱格式，在整体光滑解存在的条件下，证明了这些格式解的收敛性，并得到了误差估计。

The model is used to count several engineering example.Comparing the 2D numerical results with electrical simulations,it is proved that the seepage model can count the seepage surface and the location of search results in dam well and truly.Comparing 3D results with 2D results at close section,the results are tally well except the difference of meshes and the interceptive position of section.So the model is credible and has upper practicality value.In the projects,the spending of account is increasing because of the bigger account field.

将饱和—非饱和渗流模型用于几个工程实例，其二维模拟结果同渗流电模拟实验结果进行了对比，证明本文的渗流模型完全能够准确计算坝内的渗流浸润线以及逸出面位置；三维数值模拟的结果在相近剖面处与二维结果作了比较，考虑三维网格剖分及剖面截取位置的差异，三维结果与二维结果吻合的较好，证明本文的饱和—非饱和渗流模型在三维计算中是可靠的且具有较高的实用价值。

Although there is fair evidence that articial disc replacement is similarly effective compared to fusion for single level degenerative disc disease and that an interspinous spacer device is superior to nonsurgical therapy for 1- or 2-level spinal stenosis with symptoms relieved with forward exion, insufcient evidence exists to judge longterm benets or harms.

尽管已有相当的证据证明人工椎间盘置换治疗单节段脊柱退变疾病具有和融合手术类似的疗效，也有相当的证据证明棘突间支架治疗1～2个节段伴间歇性跛行的椎管狭窄的疗效优于非手术治疗，但以上都缺乏长期随访的证据。

Since the commutators of both sing-ular integral operators and fractional integral operator with BMO functions areone of the special cases of〓,so the discussion of the boundedness of〓notonly gives a new proof of the boundedness of the two commutators,but al-soweakens some of restrictions into discuss the problem,thus it impro-vessome of results inwith the method of complex analysis,show-ed boundedness of〓,then directly obtained boundedness of the commutato-rs of fractional integral operator with BMO functions.

既然奇异积分算子和分数次积分算子与BMO函数的交换子是其特殊情形，所以〓的有界性的讨论不仅给出了中关于这两类交换子有界性的一个新的证明，而且减弱了中讨论这一问题时对齐型空间所作的限制，从而改进了中的结果（利用复分析的方法，先证明〓的有界性，从而直接得到分数次积分算子与BMO函数的交换子〓的有界性。

The key to that is an abstract proof, a mathematical sleight-of-hand that shows irrefutably that Goldbach, a mathematics professor in St Petersburg who went to Moscow as tutor to the family of Tsar Peter II, got it right.

问题的关键是需要有一个绝对的证明，即利用数学技巧来证明哥德巴赫所提出的这一猜想是无可辩驳的。哥德巴赫本人是圣彼德堡的数学教授，他曾在莫斯科被沙皇彼得二世聘为家庭教师。

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。