充分利用了的

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。

With the Ben Tal generalized algebraic operation of 2 , we obtained some necessary and sufficient conditions for the class of generalized convex programming, and the results generalize the corresponding ones for the convex Programming.

利用文〔2〕中定义的Ben－Tal广义代数运算，本文得到了这类广义凸规划的Kuhn－Tucker充分条件和必要条件，所得结果推广了通常凸规划相应的结

By using the difference inequalities, the asymptotic behavior of solutions to forced nonlinear neutral difference equations is studied.

利用差分不等式研究了具有强迫项的非线性中立型差分方程解的渐近性，得到了方程的解趋于零的充分条件

Then the eigenvalues of the closed loop system is studied and the necessary and sufficient condition for the closed loop system to be asymptotically stable is derived.

其次，对相应的闭环系统特征方程进行详尽的讨论计算，得到了系统本征值的分布特性，从而利用Lassel 不变原理得到了闭环系统渐近稳定的充分必要条件。

The sufficient conditions for the existence of the local bifurcations of two semi-trivial solutions (θr,0) and(0,θd) are proved,and stability of the local bifurcate solution from semi-trivial solution(θr,0) is obtained.

利用局部分歧理论及线性稳定理论，证明了两个半平凡解(rθ，0)和(0，θd)局部分歧解存在的充分条件，并且证明了半平凡解(rθ，0)产生的局部分歧解是无条件稳定的。

On condition that the nonlinear uncertain function is bounded, based on state observer and controller, we derive a sufficient condition for robust stability independent of delay by the Lyapunov functional theory.

在非线性不确定性满足有界条件下，通过构造增广系统，利用Lyapunov稳定性理论，给出了该不确定性系统基于观测器的鲁棒镇定的充分条件，并给出了相应的状态观测器和鲁棒控制器。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

Based upon the test and observation in the mine, the pre-weakening acting mechanism and the rule of the pre-blasting and the injecting water are explained, and by analyzed, it is get out that the row holes can be well utilized the mining pressure, the rational way to set the holes and the rational main technique parameters of pre-weakening are worked out for Honghui mines. These offer the technique basis for practice application.

根据现场试验和观测，分析论述了综放工作面坚硬顶煤预先爆破和注水的弱化作用机理和规律，认为采用按排布孔能较充分地利用矿压破煤作用，并进一步总结得到了红会矿区坚硬特厚煤层综放开采顶煤预先爆破粉碎区、裂隙区和裂隙发育区的范围及合理的布孔方式及其主要工艺参数，为现场实际应用提供了良好的技术基础。

A three-point boundary value problem for a semi-positone second-order differential equation is investigated.

研究了一类半正二阶非线性常微分方程的三点边值问题u +λf =0 ，u′(0 )=0 ，u(1 )=αu ，利用Krasnosel'skii不动点定理得到了正解存在的一个充分条

Using 〓-theory in partial differential equation,I find out a sufficient condition on A,B,under which ican be extended to andreplaced by a self-adjoint operator.

利用偏微分方程中的〓理论，我对算子A和B找到了一个充分条件，在该条件下，i可以扩张成一个自共轭算子。

We are in a real jam.

我们的麻烦大了。

Hey, it's Ahmet from India, that foreign exchange guy.

看，那是印度的阿曼特，国际交换生