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Open Linear Encoder includes main grating scale and optical encoder head. This optical encoder head includes LED light source, optical detector module, and secondary phase-grating. LED light will pass through the plano-convex lens and produces parallel light. As the parallel light pass through secondary grating, the quadratic image display on the main grating scale. And the Moire interference will be reflected from the main grating scale and detected by optical detector module, as there is a relative shift between the main and secondary grating. From detecting the periodic sinusoidal signal with phase difference 90°, the period represents the grating pitch, using the counter to detect the number of periodic signals to get the displacement, and we can adapt the technology of electron subdivide further to increase the resolution of measurement .

反射式光学尺包括主光栅尺及光学读头，光学读头包含LED光源、光侦测器模组及相位式副光栅，LED光源经平凸透镜，产生平行光穿透副光栅后，副光栅之二次成像投射在反射主光栅尺上，当主、副光栅因相对运对产生之Moire干涉经主光栅尺反射至光电检测器，检出相位差90°之周期性弦波讯号，其周期代表栅距，因此可用计数器检出周期性讯号数目得到位移量，可进一步采用电子细分割技术提高解析度。

The local error estimators respectively for velocity, density and Lagrange multi plier, are defined in the space of discontinue quadratic bump functions.

各变量的当地误差估算器定义在二阶非连续鼓包函数的空间中。

The method comprises the following: a step of calibrating a camera, which is to utilize a Taylor series model to calibrate an omni-directional vision sensor so as to obtain internal parameters of the camera; a step of obtaining epipolar geometric relation, which comprises the steps of calculating an essential matrix between binocular omni-directional cameras and extracting the rotation and translation component of the cameras; a step of correcting an outer polar line, which is to correct the outer polar line of a shot omni-directional stereo image so as to allow a corrected polar quadratic curve to coincide with an image scan line; and a step of three-dimensional reconstruction, which is to carry out feature point matching to the corrected stereo image and calculate the three-dimensional coordinates of points according to matching results.

该方法的步骤包括：相机标定：利用泰勒级数模型对全向视觉传感器进行标定，得到相机内参；对极几何关系求取：包括计算双目全向相机之间的本质矩阵，并从中提取相机的旋转和平移分量；外极线校正：对所拍摄的全向立体图像对进行外极线校正，使校正后的极二次曲线与图像扫描线重合；三维重建：对校正后的立体图像对进行特征点匹配，根据匹配结果计算点的三维坐标。

Basing on the coordinating equations of multivariate spline space, we firstly study the smooth connection problem of the bivariate quadratic polynomial spline functions which defined on the polygonal region with one interior net

最后说明了在一种类1—型三角剖分上二元二次样条函数s∈S_2~1的存在性及在其上曲面光滑连接的可行性。

Adopting homogenous experimental design and applying the response surface method,the effects of corn variety,screw speed and water content on radial expansion ratio and extrusion index were studied,and the quadratic polynomial mathematical models of expansion ratio and extrusion index were constructed.

采用均匀试验设计方法，应用响应面分析了玉米品种、螺杆转速和物料水分含量对膨化率和挤压指数的影响，并建立了膨化率和挤压指数的二次多项式数学模型。

At last the consistently symmetrical and positive definite properties between the energy matrices and the elastic matrices are clarified by using the theory of positive definite quadratic form of matrices.

最后，运用矩阵的正定二次型理论阐述了"能量矩阵与弹性矩阵"之间一致的对称性和正定性。

The physical meaning of the dynamical equilibrium relationships, velocity space-time distribution and energy propagation involved in the energy matrices can be described by the positive definite quadratic form of the energy matrices.

能量矩阵蕴含的动态力的平衡关系、速度的时间_空间分布和能量的传播及变化的物理意义，能够从能量矩阵的正定二次型特性表述出来。

The relation between the output phase differences and the losses of 2×2 and 3×3 optical fiber couplers with rotatory symmetry is deduced in this study, which is based on the characteristics of scattering matrix and Hermite positive definite quadratic form of the couplers.

前 言光纤耦合器用于诸如光纤干涉系统、光纤环、波分复用器件和光纤通信中的分集接收等场合时，除了要求适当的输出功率比以外，尚需考虑输出端光场间的相位关系［1～3］。

optical fiber coupler, scattering matrix ; output phase difference; Hermite quadratic form ; positive definite matrix

利用其散射矩阵为酉矩阵的么正性不难证明，2×2耦合器输出相位差恒为90°，与输出功率比无关，而耦合区具有旋转对称结构的3×3耦合器的输出相位差完全取决于输出功率比，特殊地，当等分功率输出时，输出

If A is a symmetric positive definite matrix, then the quadratic form x~ TAx can be written as a sum of squares. Equivalently, A is a sum of rank one matrices VV~T.

若A是对称正定矩阵，则二次型x~ TAx 能写成平方项的和，即A是秩为1的矩阵VV~T的和。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。