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 extremum condition 极值条件(2)极值条件(2)
 极值条件
 We explain the economical meaning of all kinds of parameters,and analyze the extremum condition of the long-run cost function under constant factor production elasticity and factor price. 并对长期成本函数的重要参数给出了新的经济解释,分析了在投入要素的产量弹性和价格保持不变的前提下长期成本函数的极值条件,得出了企业最大长期成本出现的充要条件是各种生产要素等量投入。 短句来源 In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition is given. 本文首先介绍Rayleigh商定理，然后利用Rayleigh商定理给出无约束极值条件新的严格证明。 短句来源
 极值条件
 We explain the economical meaning of all kinds of parameters,and analyze the extremum condition of the long-run cost function under constant factor production elasticity and factor price. 并对长期成本函数的重要参数给出了新的经济解释,分析了在投入要素的产量弹性和价格保持不变的前提下长期成本函数的极值条件,得出了企业最大长期成本出现的充要条件是各种生产要素等量投入。 短句来源 In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition is given. 本文首先介绍Rayleigh商定理，然后利用Rayleigh商定理给出无约束极值条件新的严格证明。 短句来源

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 extremum condition
 For the unmodified and chill-modified eutectic microstructures it seems probable that the basic equation is applicable but that the extremum condition is not. The present measurements fit the extremum condition of the Hunt and Jackson theory of eutectic growth. We reject the extremum condition with respect to one of the order parameters in spin glass models. We show that it is possible to introduce an expansion at fixed magnetization amplitude in the inverse of lattice coordination number if the direction is selected by an extremum condition. When the extremum condition in the thermodynamical potential is imposed, a family of Bogoliubov transformations that give us a planckian spectrum is found, even in "pathological" cases such as the minimally coupled scalar field. 更多
 The unconstrained extremum conditions are the important parts of optimization theory, and have certain significance in the theory and practice. The optimality conditions for constrained problems become a logical extension of the conditions for unconstrained problems. One strategy for solving a constrained problem is to solve a sequence of unconstrained problems. In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition... The unconstrained extremum conditions are the important parts of optimization theory, and have certain significance in the theory and practice. The optimality conditions for constrained problems become a logical extension of the conditions for unconstrained problems. One strategy for solving a constrained problem is to solve a sequence of unconstrained problems. In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition is given. This proof is more concise than the old one, and it has considerably practical value in learning and grasping the optimization theory for those readers who are not familiar with the theory of limit of sequence. 无约束极值条件是最优化理论的重要组成部分，在理论上和实践上都有重要意义，约束问题的最优性条件是它的逻辑推广，解约束最优化问题的一种策略是解一系列无约束问题。本文首先介绍Ｒａｙｌｅｉｇｈ商定理，然后利用Ｒａｙｌｅｉｇｈ商定理给出无约束极值条件新的严格证明。这种方法比已有证法更简明，对那些不熟悉序列极限理论的读者，在学习和掌握最优化理论方面，有一定的实际意义。 The situation awareness is an important tache of C2 process in the cognitive domain, and the awareness sharing is a primary instrument to improve the situation awareness and decrease the awareness warp. Based on the analysis of situation awareness problem, the concept of discovery probability for tactical correlative factors, and the understan ling degree and warp for the situation awareness are put forward. The mathematic model for the quantitative evaluation of situation awareness is established, and the improvement... The situation awareness is an important tache of C2 process in the cognitive domain, and the awareness sharing is a primary instrument to improve the situation awareness and decrease the awareness warp. Based on the analysis of situation awareness problem, the concept of discovery probability for tactical correlative factors, and the understan ling degree and warp for the situation awareness are put forward. The mathematic model for the quantitative evaluation of situation awareness is established, and the improvement of battlefield situation awareness in condition of awareness sharing is analyzed. The relation between the discovery probability for tactical correlative factors and the number of members is given out, and the relative equation between the understand warp about tactical correlative factors and the number of members is advanced, and the extremum condition is also found out. 态势认识是指挥控制过程在认知域中的重要环节,认识共享是改进态势认识、减少认识偏差的重要手段。文中在分析态势认识的基础上,提出战术相关要素的发现概率、态势认识中的理解程度和理解偏差的概念,建立了用于态势认识的定量评估的数学模型,分析了认识共享对战场态势认识的改进程度,导出了团队合作时战术相关要素发现概率与个体数量的关系式,给出理解偏差与个体数量的联系方程并求出极值条件。 This paper analyzes the character of the long-run cost function with Cobb-Douglas production function.We explain the economical meaning of all kinds of parameters,and analyze the extremum condition of the long-run cost function under constant factor production elasticity and factor price.It is concluded that if the firm inputs the factor in equal quantity,then the long-run cost will be maximized.The paper points out that the firm must avoid the equal quantity of the factors inputting. 本文进一步深入研究任意多种生产要素的柯布-道格拉斯生产函数条件下的长期成本函数问题。并对长期成本函数的重要参数给出了新的经济解释,分析了在投入要素的产量弹性和价格保持不变的前提下长期成本函数的极值条件,得出了企业最大长期成本出现的充要条件是各种生产要素等量投入。论文最后指出企业在进行生产时,应严格避免各种生产要素的等量投入。生产技术应选择价格越高的要素的要素指数越小,最优的生产技术应是无限趋近于要素投入的边界点。
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