平衡点

To be successful against both right and left handed players requires a well developed technique and a very good balance.

要想成功对抗左手和右手持拍的选手，需要好的发展的技术和非常好的一个平衡点。

We all know he's the premier point guard in the league, a lightning-rod who finds the perfect balance of distribution and scoring.

我们都知道他是联盟中最好的控球后卫，他总能在传球和得分之间找到最完美的平衡点。

The global stability of the positive equilibrium in this system is expounded by using the stability and qualitative theory of the ordinary difference equation,then the existence,the uniqueness and the global stability of the limit circle are proved,thus some former conclusions are extended.

利用微分方程稳定性和定性理论讨论该系统的正平衡点的全局稳定性问题，并得到了极限环的存在唯一性及其全局稳定性，推广了已有的一些结论。

To develop Linear Fractional Transformation model based on quasi-linear model for ground-to-air missile, state transformation method was used to establish quasi-Linear Parameter Varying model for missile longitudinal short-period dynamics by changing missile states along with an equilibrium trajectory decided by time-varying parameters. Based on the obtained quasi-LPV model, the LFT model of the missile was developed by use of MATLAB functions, and the missile dynamics were explicitly separated into certainty part and time-varying parameter part.

为了建立基于准线性化模型的地空导弹线性分式变换模型，采用状态替换方法将导弹的状态沿着一条由时变参数决定的平衡点轨迹进行变换，建立了纵向短周期动力学的准线性参数时变模型；基于所建立的准LPV模型，采用MATLAB函数建立了导弹的LFT模型，将导弹动力学明确描述为确定性部分和时变参数部分。

Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

课程的主题包括：非线性常微分方程组；二维自治系统；与课程相关的基本理论，如比卡迭代法，压缩映射定理，Bellman-Gronwall引理，平衡点稳定性分析的李雅普诺夫第一种方法和第二种方法，反馈的线性化；以及非线性电路和控制系统的实际应用。

Then consider the existence of a bionomic equilibrium. The optimal harvesting policy is studied by using Pontryagin's maximal principle.

讨论了这个系统的动力学行为和生态经济平衡点的存在性，最后得到了最优捕获策略。

The local and global stabilities are examined. The possibility of existence of a bionomic equilibrium is considered. The optimal harvesting policy is studied by using Pontryagin's maximal principle.

证明了系统的局部稳定性、全局稳定性和生态经济平衡点的存在性，最后得到最优的捕获策略。

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。

So it was a good bargain between man and microbe.

这就是人类与细菌一个和谐的平衡点。

The result indicates that equilibrium point that is temporary minimum is saddle point.

系统的平衡点即临时极小点为鞍点。

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。