线性

By means of Taylor's formulas and the extended homogeneous capacity method, the nonlinear equation is transferred into a linear homogeneous equation within an integral segment, which can be solved conveniently by the high precision integration method.

首先，借助Taylor级数展开，在一个积分步长内将非线性方程转化为线性非齐次方程，然后利用齐次扩容方法，进一步将其化为线性齐次方程组，便于用精细积分算法求解。

We consider the existence of positive solutions of second order impulsive boundary value problems by constructing the appropriate homotopy operator and applying the theory of fixed point index in cones. our results contain the conclusion when f ≥ 0 and J_k = 0([6]). Secondly, we discuss multiple positive solutions of the following impulsive boundary

其次，我们在§2.2中讨论了下面的脉冲微分边值问题多正解的存在性在这一部分的讨论中，利用不动点指数理论，在f既非超线性又非次线性的情形下，得到了两个正解的存在性定理，把文[7]的结果推广到脉冲微分边值

This invented simplified algorithm is to use sectional linear judgement method or looking-up table method to replace the hyperbolic tangent judgement. The substance is to use sectional linear judgement function L or judgement function T of looking-up table to approach the hyperbolic tangent function tanb.

为了解决这个问题，本发明的双层加权并行干扰对消算法的简化算法用分段线性判决方法或者查表法来代替双曲正切判决，其实质就是用分段线性判决函数L或者查表法的判决函数T逼近双曲正切函数tanh。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation. The difference between the original linear solution and the solitary wave theory results from the nonlinearity and dispersion of generated waves in the flume.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

This part constructed fuzzy linear support vector regression when the parameters of optimal hyperplane are fuzzy.

当最优超平面中的参数为模糊量时，建立了模糊线性支持向量分类机和模糊线性支持向量回归机。

Furthermore, it is possible to provide appropriate objects to design flight control systems for hypersonic vehicle.

针对高度非线性和强耦合的高超声速飞行器数学模型，引入了反馈线性化原理，将其非线性的数学模型转化成符合控制设计要求的等效线性模型。

Result:The linear of inosine is 0.040 1～0.721 8 μg,r=0.999 9,the limit of detection is 8.2 ng;The linear of hypoxanthine is 0.050 2～0.903 6 μg,r=0.999 9,the limit of detection is 7.4 ng.Conclusion:The peak ...

结果：肌苷的线性范围为0.040 1~0.721 8μg，r=0.999 9，最低检测限为8.2 ng；次黄嘌呤的线性范围为0.050 2~0.903 6μg，r=0.999 9，最低检测限为7.4ng；结论：各有关物质峰与肌苷峰能达到有效分离，且操作方法简便、准确、稳定，专属性强，可用于肌苷口服溶液有关物质的检查。

Then, breifly introduced the arithmetic of the Multiple Linear Regression and artificial neural networks, built up the Multiple Linear Regression model and artificial neural networks model on this foundation, and forecast ice jam water level distinguishly under experiment condition and natural condition.

然后，简要地介绍了多元线性回归和人工神经网络的数学算法，在此基础上建立了多元线性回归模型和神经网络模型，并依此分别对试验条件下和天然条件下冰塞的水位进行预测。

Furthermore, the advantages of the genetic algorithm and the above single layer neural network are combined to yield a new identification technique. The network topology is employed to replace the procedure for solving the governing equation when GA is used to identify the system parameters of both the SDOF system and the MDOF system with or without noise contamination. The comparison is made between the predicted acceleration and the measured one for each case.

另外，结合类神经网路与基因演算法於结构动力参数识别，首先应用前述之单层类神经网路架构做为系统动力模式，再藉由基因演算法搜索符合该系统之权重值，然后将权重值代入网路架构以取代解微分方程式求得系统反应，最后再与量测反应做比较；同时亦利用该方法应用於进行识别含杂讯之输出入资料的系统权重值，以验证该方法应用於单自由度线性系统及多自由度线性系统识别之可行性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。