线性的

By utilizing an exponential transformation and piecewise linearization technique,transforming the exponential terms into the sum of absolute terms,and linearizing each absolute term,the original problem can be transformed into a linear programming problem which can be easily solved.

使用指数变换及利用分段线性化技术转变每个指数项为一些带绝对值项的和，再将绝对值项线性化，最终将原问题转化为一个线性规划问题。

It separated 3-D space, 2-D space, temporal space and abstract space (focused on the first 3). 3-D space/2-D space belong to the same category in syntactic model; but 2-D space/ temporal space /abstract space share the same category when we talked about how to confirm the spatial direction. 2. It investigated a spatial system proposed by Mr. Qi Huyang, and argued that there is necessity to modify this system. 3. It enumerated a series of grammatical forms which are involved in the "Spatial System", and pointed out that there exits a relation among these forms: words representing "Spatial and Locative"→ phrases representing "Spatial and Locative"→ sentences representing "Spatial and Locative".

第三章研究"空间系统"的子系统。1、分出立体空间、线性空间、时间和抽象空间几大领域，在句法上，立体空间/线性空间是一类；但在如何确定方向场的问题上，线性空间/时间/抽象空间是一类。2、省视了齐沪扬先生已提出的一个空间系统体系，指出很有改进的必要。3、归纳了"空间系统"所涉及的各种语法形式，并指出它们构成"表示空间方位意义的词→表示空间方位意义的短语→表示空间方位意义的句子"的层次关系。4、辨析各种语法形式的语义域及其语义结构，并考察语法意义与语法形式的对应情况。

Finally by constructing an auxiliary problem, using addition theorem and applying an iterative process based on results obtained for the linear problem, the existence and uniqueness of the weak generalized solution of the nonlinear problem is proved.

解决了线性问题后，本文构造了辅助问题，利用迭加原理，并基于线性问题的主要结论运用迭代过程，最终证明非线性问题存在唯一广义弱解。

The admissible input of 2-D linear discrete singular general model is discussed more deeply, some very effective new criteria for the 2-D singular general model to accept all the input sequence have been developed, and a new algorithm that determines the admissible input sequence of the 2-D singular systems has been proposed.

在线性广义2-D系统可解性方面，首先研究了线性广义2-D连续—离散系统的可解性问题，给出了可解的条件，并给出了等价的判别条件；其次深入研究了线性广义2-D离散系统的允许输入序列问题，给出了系统接受所在区域上的所有输入的新的非常有效的判别方法以及确定系统允许输入序列的新的方法。

That is by introducing the switch function, the linear dynamical part is separated by a simple algebraic operation, then a new linear model can be achieved.

即通过引入开关函数，将线性动态部分分离处理，辨识得到新的线性模型。

The mechanism is composed of two ball screws, U-type linear rails, linear bearings and flexible couplings. The permanent magnetic direct current motors are used as actuators. The rotary encoder is used to measure the angular position of the DC motor. The digital controller is implemented on the personal computer and a motion control card (EPCIO-6000). The objective of this thesis is to realize precise positioning control using a real-time motion control system on an X-Y table.

机械结构包括有滚珠导螺杆、U型线性滑轨组、线性轴承及可挠性连轴器等；致动器是采用永磁式直流马达(permanent magnetic direct current motor)；感测器是使用光学式旋转型编码器来量测马达旋转的角度；控制器则是以个人电脑为控制核心，搭配运动控制轴卡(EPCIO-6000)所组成。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

For the models by MMFI is a nonlinear differential equation with variable coefficients and the 'nonlinearity' brings discommodiousness to analyse the nature and quantification of a control system, it applies brim linearization method to better MMFI. By transforming 'triangle wave' membership functions of the base elements into 'rectangle wave' membership functions, we get three models which represent different aspect respectively. By simulating second order system and analysing the errors of the results, a conclusion is drawn, that is, the model obtained by brim linearization method has a good precision in contrast with the real model.

由于模糊推理建模法得到的模型是变系数非线性微分方程，这种&非线性&对该控制系统的某些定性或定量分析带来不便，因此应用边缘线性化方法对模糊推理建模法进行改进，将基元的隶属函数由&三角波&改成&矩形波&，从而得到了三个模型，这三个模型各有侧重，通过对二阶系统进行仿真，分析仿真结果，从而给出了关于边缘线性化方法的结论，即由边缘线性化方法得到的系统模型对该系统的真实模型有较高的逼近精度。

Harmonic frequencies and infrared spectra intensity for these clusters are given in order to aid in the characterization of the ground states. The results show that Si2CmN(m=2-10) clusters form linear structure, which are doublet states. The Si atoms favor to bond at ends of C and N linear chain. The ground state energies of clusters are nearly in proportion to increased m. The stability of Si2CmN(m=2-10) clusters with even m are greater than that with odd m.

结果表明，m=2-10的团簇为线性结构，随着m的增大，团簇的自旋多重度均为2，Si原子在C与N原子形成的线性链端部成键，团簇的基态能量近似线性增大。m为偶数的Si2CmN团簇比m为奇数的更为稳定。

As applications of the method, the linear wave making problems of Wigley hull and Series 60 hull are solved, with less collocation-points than that in traditional panel method, and the Kelvin wave-patterns calculated are in accord with the test data. Reasonable Kelvin wave-pattern and wave resistance of a high-speed round-bulge ship with transom stern are obtained by enforcing a condition, resembling Kutta-type condition, of smooth flow detachment at the transom stern. In addition to that, the linear solution of a catamaran is also presented.

本文运用该方法求解了Wigley船型与系列60船型的线性兴波问题，以较少的配置点计算出了与实验结果相近的Kelvin波系及合理的波形阻力；以在方尾部强加类似于库塔条件的光滑分离边界条件求解了高速圆舭型方尾船的线性兴波问题，得到了合理的三维波型及波形阻力；另外还求解了双体船的线性兴波问题。

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。