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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。

Possible name derivation: Mellifluous="flowing or sweetened with honey,".

可能的命名来源： Mellifluous="流动或者甜美如蜜"。

The method of transformation between feature-based dimensions and engineering expression is proposed to change the complicated dimensions into basic-type dimensions which can be tested easily by means of dimension derivation, transformation, decomposition, and so on.

提出了基于特征与工程表达的尺寸转换方法，通过对尺寸特征、语义、图形特征的理解，将原来复杂的尺寸经过各种派生、分解等转换成易于检验的基本型式尺寸。

This paper brief introduce numerical method of algebraic equation,points out their shortcoming of missing multiple root and put forward one new kind of method--multiple derivation numerical method.

本文对通常代数方程的数值计算方法特点进行了简介并给以分析，指出了这些解法无法得出重根数的缺陷，提出了一种新的解决方法———多次求导数值计算法，使得数值计算法更加清晰、明了，且可得出重根数。

By an example of mutual inductance coupling circuit, it gaves the derivation and explains the physical meaning of each variable.

为了得到接近于矩形的频率响应特性，或因阻抗变换的需要，在佳二子技术领域里广泛地采用藕合振荡系统。

Sodium borate was chosen as the buffer andα- naphthylamine and NaBH3CN as the derivation agents. The optimal conditions were 60 mM pH 11 sodium borate buffer, 1.0 psi pressure injection for 90s. Compared with the normal CZE method, the detection sensitivity of glucose was enhanced by more than 20 times, and that of fructose nearly 60 times.

本文的最后一部分，选用硼砂作为缓冲液，以α-萘胺及NaBH3CN作为衍生化试剂，探索了采用场放大进样方法，用毛细管电泳对葡萄糖和果糖进行分离和富集的实验条件，最优的实验条件为60 mM，pH 11.0硼砂缓冲液，1.0 psi压力进样90s，和常规方法相比，葡萄糖的检测灵敏度提高了20多倍，果糖提高了近60倍。

It is also the base of structure optimization.According to main object characteristics of structural dynamics design,structuraleigenveetor sensitivity computation is,first,be studied.A Neumann series expansionmethod is proposed in accordance with the modal method and is developed to agreewith the structure with rigid body modes.A rapid Neumann series expansion methodfor eigenvector sensitivity is formed;it may greatly improve the efficiency ofcomputing eigenvector derivation.

本文根据结构动力学设计的主要目标特性，首先进行了结构特征向量灵敏度分析研究：形成了计算特征向量灵敏度的Neumann级数展开法，并将其扩展到适用于具有刚体模态的结构特征向量灵敏度分析；研究出计算特征向量灵敏度的快速Neumann级数展开法，该方法大大提高了特征向量灵敏度分析的效率；建立了无需K-1运算的结构特征向量灵敏度分析的共轭梯度迭代法。

With the energy equilibrium, we obtain therelations of oblateness e, period P, period derivation〓,surface magnetic field B, averge density ρ, and the evolutions of those quantities.

但对高速自转的脉冲星(如超新星1987A中0.5毫秒脉冲星)，由于自转的作用而成为扁形的椭球体，此时星体的形变能量就会起很大作用。

From its form the derivation of the word ocarina is said to be "small goose".

其名字据说来源于形状，为意大利语的"小天鹅"一语。

In the fifth chapter, the further derivation and demonstration of the VCA technique are made, and a new simple method to calculate the proper optimal step size in this condition is presented, which can improve the computational efficiency.

在第五章中，我们对VCA技术进行了进一步的更具一般性的推导论证，并在此基础上，推导出一种适用于该情况下的计算优化步长的公式，提高了数值计算效率，节省了计算时间。

I want to be a big fish in a small pond.

我要做一条在小池塘里的大鱼。

While the software functioned well, we did not feel the same about their customer support!

虽然该软件运行良好，我们没有同样的感觉他们的客户支持！