线性

In this paper,pose representation by quaternions are researched.With the basic quaternion algebra,the "quaternion based rotations combination theorem" is introduced and proved theoretically.On the basis of this theorem,a method for compute of pose nonliear state transfer function and its linearization is purposed.Then,the computing of the measurement function and the linearization is studied.With the Extended Kalman Filter,the pose is tracked and estimated.

研究用四元数表示物体的姿态，在四元数基本运算法则基础上提出并证明了"基于四元数的多个旋转运动合成规则"，然后将此规则为依据，推导出一种用来计算姿态非线性状态方程系数的方法，对非线性状态转移函数进行线性化，并且研究了测量方程函数的确定及线性化，借助扩展Kalman滤波实现了对姿态的跟踪。

The questionnaire method and the interview menthod were used to gain the tourist data, the quota sampling method was used in sampling survey, the principal component analysis method was used to measure the various variables, the statistical methods such as linear regression analysis, multivariate linear regression analysis, single factor variance analysis and logistic regression analysis were used to analyzes the relationship between various variables.

具体来说，在获取游客数据时采用了问卷调查法和访谈法，在抽样调查时采用了配额抽样方法；对各变量进行测度时使用了主成分分析法；在分析各变量之间相互关系时采用一元线性回归分析、多元线性回归分析、单因素方差分析及Logistic回归分析等统计方法。

The analytical results of radio frequency glow discharge optical emission spectrometry further proved that the content of each element in this series of stainless steel reference materials had good graded distribution. The linear investigation of characterisation elements indicated that the linearity was also good.

射频辉光放电发射光谱的分析结果进一步证明：本套不锈钢标准样品的各元素成分含量有良好的梯度分布，对定值元素进行成线性考查，线性关系良好。

In this paper we have found the main component s in a n -dimension random vector X , the so called main compon ents don′t contain linear relation and the others of X can be expressed as the linear combination of the main component s.

本文提供了在多维随机变量中寻找主成分的一种方法，证明了其余分量均可表示为主成分的线性组合，解决了多维随机变量的各个分量之间所存在的线性关系问题。

The variation of pH and conductivity of various phosphate solution with the solution temperature were obtained based on the physical chemistry theory and ionization equilibrium theory in electrolytic solutions, and be testified experimentally under radiation of ultrasonic wave. The pH was a linear function with the reciprocal of thermodynamic temperature, and the conductivity was a linear function with the temperature in phosphate solution.

三、超声波对双水相系统组成物质、两相组成及溶质分配影响的研究根据物理化学原理和电解质溶液电离平衡理论分析推导和实验验证，揭示了超声波作用下不同组成磷酸盐溶液的pH值和电导率随溶液主体温度变化的规律：磷酸盐溶液的pH值与溶液主体绝对温度的倒数成线性关系，磷酸盐溶液的电导率与溶液主体温度成线性关系。

Firstly, the coefficient matrix is put into Excel so as to see the possible solution to the linear equation groups; then the reciprocal matrix of the coefficient matrix is obtained; lastly the solution to the linear equation group is gotten.

首先在Excel中输入系数矩阵，并判断线性方程组是否有解，然后求出系数矩阵的逆矩阵，最后求出线性方程组的解。

Two linear objective programming models are established under the situations where the decision maker has preference information on alternatives, which takes the form of reciprocal judgement matrix and complementary judgement matrix respectively, and a method based on the models is presented for ranking alternatives in MADM.

在决策者对方案的偏好信息以互反和互补判断矩阵这两种形式给出的情况下，分别建立了一个线性目标规划模型，并提出了一种基于线性目标规划模型的多属性决策法。

In the last chapter, by introducing the isochronous center of real systems into complex planar and defining complex center and complex isochronous center, a concise linear recursion formula for period constants is given, necessary and sufficient conditions of complex isochronous center (the Time-Angle Difference Theorem) proved, conditions of real systems with linearizable center and saddle treated unitedly and the isochronous center conditions discussed fully for a class of real planar cubic systems.

在第七章，通过把实系统等时中心引入复平面研究，定义了复中心和复等时中心，给出了等时中心周期常数计算的简明的线性递推公式，证明了等时中心判定的充分必要条件，统一地处理了实系统具有可线性化的中心和鞍点条件，并对一类实平面三次系统的等时中心条件进行了完整研究。

The conditions with periodic solution are discussed in detail relating to fractional linear recursive relation of first order and some useful conclusions are obtained.

对一阶分式线性递归关系具有周期解的条件进行了详细讨论，得到若干有用的结论；对二、三阶分式线性递归关系，分别列举了一个具有周期解的例子，并对解的周期性进行了验证。

For a seemingly unrelated regression system consisting of m equations, we propose a new type of estimator called pre test ridge regression estimator by combining the idea of preliminary test and ridge regression methodology and establish some statistical properties of PTRRE.

对于由 m个相依线性回归方程组成的线性回归系统，本文作者基于岭回归估计和预检验估计，提出了回归参数的一种新型估计，即预检验岭回归估计。并讨论了它的统计性质。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷