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In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

In Chapter 2,a steady permeability identification problem in elliptic equa-tions for two-dimensional orthotropic medium is considered.We construct afunctional,obtain its first and second Gateaux differential,and prove that thefunctional is strictly convex on a convex admissible function set.We seek to iden-tify the permeability by minimization of the above functional.

第二章研究了二维稳态正交异性介质的渗透率反演问题，我们构造了一个泛函，求得该泛函的一、二阶Gateaux微分，证明了它在一个凸的容许集上的严格凸性，并使用极小化泛函即变分方法来求解此问题。

At the same time, we prove that the best linear unbiased prediction of a linear predictable variable Qy and the best linear unbiased prediction βn=(X"sV-1Xs)-1 X"sVs-1ys of regression coefficients of the finite populations βn=(X"V-1X)-1X"V-1y are admissible under matrix loss function and in the class of the linear predictions and the class that contains all predictions, and under quadratic loss function in the class of the linear predictions.

在线性预测类和一切预测类中是可容许预测，而在二次损失函数下其在线性预测类中是可容许预测。

We characterize the optimal value function as the viscosity solution of the associated Hamilton-Jacobi-Bellman equation and we prove that there exists an optimal barrier strategy which is optimal among all admissible dividend strategy in some special cases.

通过HJB方程的粘性解理论来刻画最优值函数，并证明了一些特殊情形下界策略在所有可允许的分红策略中是最优的。

Then we define the notion of adoptability of the diagnostic system and prove that the consistency-based diagnosis is adoptable.

为找到故障系统的真实诊断，讨论了候选诊断和真实诊断之间的关系，定义了诊断系统的可采纳性并证明基于一致性的诊断是可采纳的。

Only time can prove you are timeless, and only adulteration can demonstrate you are unadulterated.

在创造我的时候，你已将那形象铭刻于我记忆的母板，而只有时间才能显示你的永恒，只有沧桑才能显示你的纯粹。

Prove yourself as adventurer and embark on the journey of your lifetime.

证明自己的冒险家和开始的征途上你一辈子。

Even if software is free people still need advice and support that they may pay for. Also individuals can prove their skills and knowledge by working on free software, and use it to get other kinds of work.

IBM应用并且支持免费软件，即便是免费的实用软件，人们依然需要建议和帮助，而这些建议和帮助是需要付费的，也有个别人通过免费软件证明他们的技术和知识，并且通过这种方式作其他的事情。

The experimental results prove that the proposed method can get better visual effect,it is also shown that this method is robust to affine attacks.

实验结果证明，该方法可以获得良好的图像视觉效果，同时对于几何攻击具有很好的鲁棒性。

The businessman on the net is mentioned, oneself handle business license actively, the other side is informed besides needing to offer house property to prove, arrive even street affix one's seal.

有网上商家提到，自己主动去办理营业执照，对方告知除了需要提供房产证实外，还要到街道盖章。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了