函数变量

The theory of functions of a complex variable is the extension of calculus to complex variables.

复变函数是微积分的内容从实变量到复变量的扩展。

Equal forms with multiobjective function optimization of composite structure,which is suitable for genetic algorithm solving, is constructed.

用评估函数法构造了适用于遗传算法求解的复合材料结构多目标优化问题的等价表达形式，给出了离散变量与连续变量混合优化问题解的染色体表示。

Equal forms with multiobjective function optimization of composite structure,which is suitable for genetic algorithm solving, is constructed. Expression of optimal problem with chromosome including discrete mixed with continuous variables are established.

用评估函数法构造了适用于遗传算法求解的复合材料结构多目标优化问题的等价表达形式，给出了离散变量与连续变量混合优化问题解的染色体表示。

We firstly look back thebirth of SD method,and then present the SD scheme presented by Johnson et.al.forlinear problem to explain the basic idea and implementation:At step 1,we change the testfunctionwhere(1,β)t is the streamline or character direction decidedby hyperbolic operator of the continuous problem,therefore the SD method belongs tothe Petrov-Galerkin method;At step 2,we adopt time-space finite element space,whoseelement is only continuous in space variables x but discontinuous in time variable t.

首先回顾了SD方法的产生过程，然后以线性问题为模型，描述了SD方法的基本思想和具体实现：第一步，将标准有限元方法的检验函数ν改成其中(1，β)t是连续问题的双曲算子部分所确定的流线方向。换言之，SD方法是一种Peterov-Galerkin有限元方法；第二步，采用时空有限元空间，其元素关于空间变量x是连续的，但关于时间变量t仅分段连续。

If mark the probability density function of continuous random variable X and continuous random variable leave each other, then when,there is , there is inverse function of .

Theorem 如果将连续型随机变量和连续型随机变量的概率密度函数分别记为，则时有：，这里是的反函数。

And then the approach is extended to continuous random variable. The optimal rule of general group decision-making is drawn by the new approach, which turns out to be a generalized weighted majority rule. The weight allocated to a decision-maker should be equal to the information quantity he provides.

鉴于Boltzmann—Shannon熵难以直接用来度量群体决策中信息的变动情况，我们提出了一种对离散随机变量的新的信息度量方法，证明了该信息函数仍然满足等状态时信息量最小这一性质；随后将其推广到了连续随机变量。

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence. Second, the relations among some types of convergence are studied. Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

Firstly, the difference of per capita GDP tends to convergence between the Western region and the Eastern region.

文章摘要：本文假设我国西部与东部地区的能源消费强度差异是西部与东部地区人均GDP差异的函数，然后同其他回归变量一起检验这两个变量之间的关系，并通过使用面板数据计量经济学模型进行实证估计。

According to induced response method, the expression in frequency domain of pressure response at the end of pipeline is derived using impulse response method and convolution theorem. The expression indicates that that transfer function is only related to the characteristics of pipeline system and the Fourier transform of flow variable only depends on the operating characteristics, and the pressure response in frequency domain is linear with the Fourier transform of flow variable.

基于激励响应法，应用脉冲响应方法和卷积定理得出了管道末端压力响应在频域中的表达式，此式表明：传递函数只与系统的特性相关，流量变量的傅立叶变换只与操作特性相关，且压力频域响应与流量变量的傅立叶变换为线形关系，根据此式在理论上能够得到管道泄漏点的重要信息。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。