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There is mutual contradiction between direction estimation of user's signal and power allocation among all users in the beamforming algorithm. A twice game beamforming algorithm based on game theory is proposed to deal with it. Beamforming game algorithm mathematics model is constructed. During the first game, direction of signal and power allocation are mapped the game theory as "player", which are modeled as the problem of maximin function and obtain direction estimation first. Then during the second game, power allocations of different users are described as a multi-user game. Power updated algorithm is designed. The existence and uniqueness of the Nash equilibrium in the twice game beamforming algorithm based on game theory are proved by mathematics derivation.

摘要针对波束成形算法中，用户的信号方向估计值和用户之间的功率分配存在着相互矛盾，本文提出了一种基于博弈论的二次博弈波束成形算法，构建了波束成形博弈算法数学模型，首先在第一次博弈的时候，将波束成形算法中的信号方向和功率分配映射为博弈论数学模型中的"局中人"，将其建模为函数的极大极小值求解问题，先求解出信号方向；然后在第二次博弈的时候，将不同用户的功率分配过程描述为一个多用户的博弈过程，设计了功率分配更新算法，通过数学推导论证了纳什平衡点的存在性和唯一性。

A deformable model is used to reconstruct the shape of the LV: first, the dynamic equation governing the surface deformation is deduced; secondly the image planes are mapped to the reconstruction coordinate system. From the slices data, the external force exerted on the surface is defined and the elastic force of the surface is constructed by mean curvature of the deformation surface. Finally, a level set method is applied to solve the dynamic equation for LV shape.

为了重建左心室的形状，使用基於形变模型的方法：首先建立变形曲面的动力学方程；再将成像坐标系中的图像平面映射到重建坐标系，根据图像数据构造外力，使用平均曲率构造变形曲面的弹性力，然后用水平集数值解法求解动力学方程以重建左心室的表面。

The MIDI standard specifies 16 channels. A MIDI device is mapped to a channel. Music data

MIDI标准规定可用16个通道来传输数据，每个通道对应一个MIDI设备。

The time series data can be mapped into the multidimensional points in multidimensional space.

对离群数据挖掘的研究往往可以使人们发现一些潜在的有用信息

A root can be mapped to multiple shared folders called root targets.

根目录可镜像到多种称为根目标的共享文件夹。

First, the short-range contacts between amino acids that are very close to each other were mapped, revealing the initial nonpolar folds.

首先描绘出邻近氨基酸之间的短程接触，揭示了最初的非极性折叠。

Furthermore, we prove that those relations mapped from XML are all in Third Normal Form.

在Web上进行数据交换时，我们往往要考虑进行数据交换的双方所要满足的XML模式约束。

Since a non-nullable value type can never be set to a null reference, when a class member of such a type is mapped to an XML element declaration, the

由于永远不能将不可为空值类型设置为空引用，因此，在将此种类型的类成员映射到XML元素声明时

This method returns null if no resource is mapped to the pathname.

如果没有资源映射该路径名，该方法返回null。

SQL NULL values are mapped to and from Python's NULL object, None.

SQL 的 NULL 值被映射为 Pyhton的 NULL 对象，也就是 None。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。