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The foundations of support vector machines are introduced. Four mathematics models of support vector classifications including linearly hard margin SVM, linearly soft margin SVM, non- linearly hard margin SVM and non-linearly soft margin SVM are discussed.

摘 要：介绍了支持向量机的基本思想，依据是否引入核函数，是否具有惩罚因子，支持向量分类算法被分为线性分界面硬间隔、线性分界面软间隔、非线性分界面硬间隔和非线性分界面软间隔四类，并讨论了它们的数学模型。

And it is shown that the dynamics equations of the system can be linearly parameterized. With the augmentation approach, we demonstrate that the augmented generalized Jacobi matrix can also be linearly parameterized.

对系统的运动学分析表明，联系两个机械臂末端运动速度与机器人关节角速度的增广广义Jacobi关系亦可以表示为一组惯性参数的线性函数。

We used coupling phototube convert the voltage of reflector voltages of klystron linearly to lower voltage, and convert the lower voltages of standing wave measuring line and crystal detector inputting power linearly to higher voltages by operation amplifier. Then we inputted these voltages to computer by analog-to-digital card and plotted the graphs of working characteristics of reflecting klystron with software .

利用光电耦合器将速调管反射极高电压线性转换为低电压，同时将驻波测量线测得电场强度的电压值和晶体检波器所测得的反射式速调管输出功率的电压值通过运算放大器线性放大，然后经过模数转换卡采集到微机中，利用软件绘制出速调管的工作特性曲线。

The authors used coupling phototube convert the voltage of reflector voltages of klystron linearly to lower voltage and converted the lower voltages of standing wave measuring line and crystal detector inputting power linearly to higher voltages by operation amplifier. Then inputted these voltages to computer by analog-to-digital card and plotted the graphs of working characteristics of reflecting klystron with software.

利用光电耦合器将速调管反射极高电压线性转换为低电压，同时将驻波测量线测得电场强度的电压值和晶体检波器所测得的反射式速调管输出功率的电压值通过运算放大器线性放大，然后经过模数转换卡采集到微机中，利用软件绘制出速调管的工作特性曲线。

First, the two convex hulls from the training set of approximate linear classification are similarly squeezed into the linearly separable ones, and based on the two similarly squeezed linearly separable convex hulls, an optimal separating hyperplane is figured out by using the method of halving the nearest points and the maximal margin method.

首先对近似线性分类中的训练集所形成的两类凸壳进行了相似压缩，使压缩后的凸壳线性可分；基于压缩后线性可分的凸壳，再用平分最近点和最大间隔法求出最优的分划超平面。

If the systems satisfy linearly degenerate or weakly linearly degenerate, the classical solutions to Cauchy problem for quasilinear hyperbolic system will exist as the initial data with compact support is small enough.

本章第一节，我们主要推导了波的分解公式，提出了弱线性退化、适配性条件和正规化坐标系的概念，并且给出了在正规化坐标系下一些关系式。

The empty set is linearly independent, for linearly dependent sets m ust be nonempty.

因为线性相依之集合必为非空集合，故空集合为线性独。

The empty set is linearly independent, for linearly dependent sets must be nonempty.

空集合為線性獨，線性相依集合必為非空集合。

A FDTD program was written and the electromagnetic fields for various polarized incident beams are calculated and the polarization states of the diffractive waves are extracted. The relation between the polarization state of the diffraction wave and the grating balzed angle and polarization angle for the linearly polarized incident wave is analyzed; In the spectral range of 1530 ~ 1570nm, the polarization dispersion is studied for the linearly and circularly polarized incident beam.

用时域有限差分程序计算出任意偏振方向线偏光经过闪耀光栅衍射后的电磁场分布，提取衍射波的S偏振和P偏振分量，分析它们与光栅闪耀角和入射光波偏振角的关系；分析在1530 -1570nm光谱范围内，入射光波为线偏振波和园偏振波时，衍射光波的偏振色散特性与光栅闪耀角的关系。

Loge CRP concentration was linearly associated with several conventional risk factors and inflammatory markers, and nearly log-linearly with the risk of ischaemic vascular disease and non-vascular mortality.

结果：厢式CRP浓度和一些常规的危险因素、炎性标记物呈线性相关，和发生缺血性血管疾病和非血管死亡率的风险大致呈线性关系。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。