求解

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。

The dynamic characteristics of stochastic truss structures and stochastic frame structures are analyzed by using Random Factor Method. Then, from the expressions of structural random response of the frequency domain, the computational expressions of the mean value, variance and variation coefficient of the mean square value of the structural displacement and stress response under the stationary random excitation or non-stationary random excitation are developed by means of the random variable's functional moment method and the algebra synthesis method.

考虑压电智能桁架结构物理参数、几何参数、结构阻尼和外荷载、闭环系统控制电压分别或同时为随机变量，构建了结构在随机力作用下的动力响应分析模型，提出了求解方法，推导出结构动力响应随机变量的数字特征计算表达式，通过算例验证了所建模型和所提求解方法的正确性和有效性。

On the algorithm research, several techniques and strategies are developed so as to reduce the complexity and meliorate the quality of the solutions.

在设计算法的研究方面，本文针对不同问题与阶段，研究了运用知识改善求解质量与降低计算复杂度的多种求解技术与策略。

Because the large-scale supply chain design problem is a NP-hard problem, so we used the meta- heuristic algorithm as simulated annealing algorithm to solve it.

针对大规模的供应链设计问题难以求解的特性，提出使用现代优化算法—模拟退火算法进行求解。

In this paper, based on the rational transfinite interpolation, a set of global approximation method namely rational macro-element method was proposed.

基于有理超限插值，提出了一种在求解域边界布点的全域求解数值方法－有理宏单元法。

This paper details the basic idea and main point of perturbation method in slo-ving complex mathematical problem, in which the characteristics of perturbation method are put stress on.

本文简要说明了摄动法在求解复杂数学问题中的基本思想和要点，着重分析摄动法在求解泡沫塑料气泡膨胀数学模型中的应用。

The processing of the middle point incremental method of resolution in particular is discussed.

论述了求解非线性有限元方程的方法，主要讨论了中点增量法求解的具体过程。

Firstly, we apply block AOR method to find the least square solution of minimal norm to the rank deficient linear systems where A is a complex m*n matrix with rank k.

首先，我们把求解线性方程组的块加速超松弛迭代法应用于求解亏秩线性方程组的最小范数最小二乘解，其中线性方程组的系数矩阵A是秩为k的m*n复矩阵。

The uncertainty of travel time of road network is depicted by means of scenario union firstly,then a path finding modal applied minimax theorem is constructed for obtaining most reliable path of all scenarios.

该方法通过场景集描述网络旅行时间的不确定性，应用Minimax理论构建求解所有场景下可靠路径的数学模型，并设计了问题求解算法，分析了算法的时间复杂性，最后通过典型算例对算法进行了验证。

In this paper, an algorithm based on heuristic function for minimum set covering problem is presented, as well as the definition of complete strategy concept and the method to structure heuristic function.

本文给出了求解NP困难问题的完备策略的概念，在此基础上提出了一个求解集合覆盖问题的启发函数算法SCHF（set－coveringheuristicfunction），文中对该算法的合理性、时间复杂性以及解的精度进行了分析，本文的主要创新点是用已知的完备策略建立启发函数，并用该启发函数进行空间搜索求出优化解。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。