线性的

The bilinear form of BBM equation has known, so we can similiarly get the bilinear form of associated DGH equation, then we can get the bilinear form of DGH equation and 1-soliton by a approciate method.

BBM方程的双线性已知，通过恰当的设法可以类似得到关联DGH方程的双线性形式，即得到了DGH方程的双线性形式，并由此得到了DGH方程的1—孤子解。

In chapter three, the new concepts of the bifurcation point and asymptotic bifurcation point of compact continuous operators in Menger PN-spaces are introduced. Some sufficient conditions for the existence of the bifurcation point and asymptotic bifurcation point are obtained. And the problems on the intrinsic value and intrinsic element of compact continuous operators are studied in Menger PN-spaces. A series of theorems on the existence of the intrinsic value and intrinsic element are obtained.

第三章，在概率赋范线性空间中提出非线性算子的歧点和渐近歧点的新概念，获得了非线性算子存在歧点和渐近歧点的充分条件；讨论了Menger概率赋范线性空间中非线性算子的固有值和固有元问题，得到了非线性算子存在固有值和固有元的一系列充分条件。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

The constraints with different linearity in this model are dealt with by an approach that combines successive linearization with piecewise linearization, and in the solving process the security and stability constraints of transmission lines are directly considered to avoid the low-efficiency of both model and solution due to the passive calibration and modifying working constraints in Newton method.

对模型中线性度不同的约束，采用逐次线性化和逐段线性化相结合的方法处理。在求解过程中直接考虑线路安全稳定约束，避免了牛顿法被动校验和变更约束带来的模型和求解的低效性。

Linear differential equations of the principle of superposition theory of linear differential equations play an important role, especially in solving linear differential equations of the nature and structure of play to solve the problem of reducing the complexity and difficulty of the role.

请帮忙翻译一下摘要，跪谢线性微分方程解的叠加原理在线性微分方程理论中占有重要地位，尤其是在解决线性微分方程解的性质和结构问题中起到了降低解决问题的复杂度以及难度的作用。

Linearizing a nonlinear power system with TCSC and applying the linear optimal control technique which possesses the quadratics index to the linearlized system, a TCSC stability controller is designed.

运用逆系统方法将含可控串联补偿电容器的非线性电力系统线性化，并且对该线性化的系统运用具有二次型性能指标的线性最优控制方法设计了 TCSC的稳定控制器。

In addition, the nonlinear processes such as cross-phase modulation, non-degenerate two-photon absorption, and stimulated Raman scattering must also be considered for double wavelengths propagating in waveguide.

在归纳分析了SOI对光信号处理的研究进展的基础上，进一步完善了超快脉冲在脊形硅波导中演变时所满足的线性和非线性传输方程，在此非线性方程中包括波导线性损耗、群速度色散和三阶色散等线性效应；同时也包含了自相位调制、简并双光子吸收、自由载流子吸收和自由载流子色散等非线性过程；当双光场在波导中传输时，脉冲之间的交叉相位调制、非简并双光子吸收和受激拉曼散射效应等非线性效应也被考虑。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

Not only should cryptographically strong sequences have a large linear complexity, but also the change of a few terms should not cause a significant decrease in linear complexity.

密码学意义上强的序列不仅应该具有足够高的线性复杂度，而且当少量比特发生变化时不会引起线性复杂度的急剧下降，即具有足够高的k-错线性复杂度。

A novel least squares algorithm based on anti-WKB method and linear segment interpolation,which is called prediction-verification method, is proposed.This method takes the values calculated by anti-WKB and linear segment interpolation as approximation,then uses the least squares fitting,and after that compares the linear segment interpolation based on the anti-WKB method with it.

提出一种基于反WKB法与分段线性插值的最小二乘拟合方法来确定离子交换玻璃波导的横向折射率分布，它将反WKB法与分段线性插值所计算出的结果作为近似值，然后进行最小二乘拟合，并与基于反WKB的分段线性插值方法进行比较。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。