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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。

Secondly, the problem of linear prediction for Qy in the original model and its transformed model is considered, the notion of linear sufficiency and the problem of comparison of linear models with respect to prediction problems are proposed and the corresponding necessary and sufficient conditions for the transformation to be linearly sufficient and for one model to be superior over another are given, respectively.

其次，我们讨论了原始模型和变换模型下Qy的线性预测问题，提出了在该预测问题意义下的线性充分性和模型比较的概念，分别给出了变换Fy是线性充分的、以及一个模型优于另一个模型的充分必要条件，此外还得出了一些特殊结论。

The basic characteristic of the linear model is the unknown parameter of the model is linear and it also includes the linear random error.

线性模型的基本特征是，模型的未知参数是线性的，同时又线性的包含了随机误差项。

The optical element comprises: a plurality of rectangular prisms for dividing linear visual field, and is characterized in that the effective work area of each rectangular prism is a linear narrow slit, which can perform visual field division of the light beam from a long linear geographical object and turn the divided visual field into separate light beams for the rational space arrangement of the subsequent optical elements.

光学组件包括：用于分割线型视场的多个直角棱镜，其特征在于：各直角棱镜中的有效工作区域均为一线型窄缝，可将长线型地物目标光束按需要进行视场分割，并将各分割后的视场形成空间分离的光束，以便于后续光学组件的空间合理排布。

In chapter two, we analyzed the methods for single linear Diophantine equations: Rosser algorithm and Fortenbacher algorithm; the methods for linear Diophantine equations: EMAS algorithm and Contejean algorithm.2. In chapter three, the DLU and IILX algorithms for linear Diophantine equations are given based on the ABS algorithms.

第三章在ABS算法的基础上给出了求解线性丢番图方程组的整隐式LU算法和整隐式LX算法，讨论了相应的ABS性质，并讨论了复杂性分析及其应用。

Using the properties of base solution vectors of the linear restriction equations, a condition to maintain the same discriminant result between the sampled observations of changed and unchanged was obtained: the disturbed row vector of sampled observations was satisfied all linear equations whose coefficients were the base solution vectors of linear restriction equations.

利用约束条件方程组基础解向量的性质得出了使数据变化前后的判别分类结果保持不变的条件：数据扰动行向量必须满足所有以约束条件方程组的基础解向量为系数的线性方程组。

Using the result for non-restricted model, we transform the restricted model to common model, and multi collectivity model to single collectivity model, thus, the necessary and sufficient conditions that nonhomogeneous linear estimators for Sβ are admissible in the class of nonhomogeneous linear estimators are obtained which filled the blank for admissibility for restricted linear model.

对线性等式约束的共同均值线性模型，利用无约束单总体模型的现有结果，通过适当变换，把等式约束模型向无约束转换，并把多总体转换为单总体，在矩阵损失下找到了均值参数β的条件可估函数Sβ的线性估计∑mAiyi+a在非齐次线性估计类中可容许的充要条件，填补了等式约束的共同均值线性模型可容许性方i=1面的空白。

By use of first-order linear expansion of Taylor series, the linearization process of both nonlinear constraints and objective function of long-term optimal scheduling model are performed and an optimal scheduling model based on seccessive linear programming is built; an approach to solve Optimal scheduling of cascade hydropower station problem by seccessive linear programming is put forward, the scale-down factor of iteration step length is used to ensure that the algorithm can converge to the optimal solution of optimization problem quickly and accurately.

通过采用泰勒级数一阶描述形式，对优化调度目标函数和约束条件中的非线性约束进行线性化处理，建立了基于连续线性规划算法的优化调度数学模型，提出了用连续线性规划技术求解梯级水电站优化调度问题的算法，并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。

Ln this paper, a new learning method is presented which is based on analyzing a set of linear separable structures. The most important benefit of this method is all binary neurons belong to one or more types of linear separable structure sets. If those linear separable structure sets have clear logical meaning, the whole knowledge of binary neural networks can be dug out.

该文提出了一种基于线性可分结构系结构分析的学习算法，采用这种方法对布尔空间的样本集合进行学习，得到的二进神经网络隐层神经元都归属于一类或几类线性可分结构系，只要这几类线性可分结构系的逻辑意义是清晰的，就可以分析整个学习结果的知识内涵。

The PID parameter tuning of non-linear control system is set as the engineering background. The aim is the optimal design of PID parameter. On the basis of the design and research of the advanced PID parameter tuning, the mathematical model-transfer functionis developed through correlation analysis on statistical method.And with the optimization algorithm under constraint condition, the non-linear, Isqnonlin is set as object function. Then with connection of the non-linear constrain optimization algorithm and simulink technique, a set of adjust parameters which fit the performance index of the control system are found. And optimization design process and steps are provided.

本文以非线性控制系统PID参数整定为工程背景，以PID参数的优化设计为目标，在分析和研究国内外PID参数先进整定方法的基础上，运用相关分析实验统计方法建立对象的数学模型——传递函数，把PID参数设计问题转化为一种非线性优化设计问题，借助于约束条件下的优化算法，以非线性最小平方指标为目标函数，将非线性约束优化算法同Simulink仿真技术相结合，找出符合控制系统品质指标的一组调节参数。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。