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Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

The terminal sliding mode controller is designed by using unit vector style; the switching function of the terminal sliding mode is designed by the quadratic optimal control theory.

采用单位向量控制形式的最终滑动模态控制器，并采用二次型最优控制理论设计最终滑动模态的切换函数。

Constructing a unitary matrix for transformation of coordinates by means of quadratic form theory,the Hamiltonian of the 3D coordinate-momentum coupling harmonic oscillator is transformed into diagonalmatrix,it not only offer a general mathematic method for solving this kind of problems,but also have an active effect upon upgrading students ability to solve physics problems by mathematical theory.

利用二次型理论构造一个幺正矩阵进行表象变换，将|x〉表象中的三模坐标-动量耦合量子谐振子体系的哈密顿量对角化，这不仅提供了一种解决该类问题的一般数学方法，同时对培养和提升学生运用数学工具解决复杂物理问题的能力也具有积极的指导作用。

Based on the proposed ORPF models, the quadratic optimal models of minimizing the total load curtailment are established to identify power flow unsolvability for AC and AC-DC power systems, and can be further used to identify system voltage instability with the modal analysis method.

算例表明：当离散内点法不存在收敛问题时，启发式混合离散内点法能快速地获取优化解，反之，则要使用启发式混合随机优化算法来保证解的质量，但需要牺牲部分计算速度。

By learning this course, students should proficiently use algebraic methods to solve geometric problems and practical problems, and proficiently grasp the basic ideas and methods of vector algebra and geometric properties of spatial line, plane and quadratic surface.

通过本课程的学习使学生熟练掌握运用代数方法解决几何问题并应用于实际问题之中，并熟练掌握向量代数的基本思想和方法，同时使学生熟练掌握空间的直线、平面和二次曲面及其各种几何性质。

The basic idea of the technique is to formulate the problem into semi-infinite quadratic optimization model with the minimization of the weight vector norm subject to a set of linear functional inequality constraints,wnich ensures unit gain for look direction and the desired sidelobe levels over the corresponding angula...

该约束条件保证瞄准方向为单位增益，并且在给定范围内旁瓣电平满足要求。该方法具有广泛的应用和实际意义。文中给出了设计例子以证明该方法的可行性和实用性。

In this paper the linear-quadratic optimal control theory is applied to the systhesis of yaw steering.

本文探讨应用最优控制理论设计横向导引规律的一种方法。

Based on the extended Huygens-Fresnel principle and the quadratic approximation of phase structure function, we have derived the analyticl expression of the spatial degree of coherence for partially coherent flattened beams propagating through the slant turbulent atmosphere with the help of tensor integral, then analyzed the effects of different zenith angle, propagation distance, coherence of source and outer scale of turbulence on the spatial degree of coherence on the receiver.

基于广义惠更斯-菲涅耳原理和相位结构函数的平方近似，运用张量积分的方法导出了部分相干平顶光束通过斜程湍流大气传输后接收面光束空间相干度的解析表达式，分析了不同天顶角、传输距离、光源相干性以及湍流外尺度对接收面光束空间相干度的影响。

In this way, we will be able to see abundancy patterns within the set of integers. Such visualizations are not only eye-catching, but also helpful in understanding the nature of the integers themselves.

这课题挺有意思的，可是这两天在那里数那些数字然后fit them with quadratic formulas已经有点头晕眼花了，不过还是看到了不少曙光，所以还是得坚持的。

Quadratic regression orthogonal rotational combing design was used to determine the optimal enzymatic hydrolysis process. Anthrone colorimetry's method was used to measure the carbohydrates content, pH-stat method to measure the degree of hydrolysis and Kjeldahl's method to measure the recovery of protein.

采用二次回归正交旋转组合设计优化直接酶解米糠制备短肽的工艺条件，其中总糖含量测定采用蒽酮比色法，水解度(degree of hydrolysis， DH)采用pH-stat法，蛋白质回收率采用凯氏定氮法。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。