本文给出调和函数极值原理的一种推广。
The note gives an extension of extremum principle for harmonic functions.
判别函数极值的方法是数学分析中的重要组成部分。
Extreme function analysis of the mathematical method is the important component.
微粒群优化算法是求解连续函数极值的一个有效方法。
Particle Swarm Optimization (PSO) algorithm is a powerful method to find the extremum of a continuous numerical function.
摘要函数极值是应用数学解决实际问题的一个重要方面。
The function extreme value is an important aspect that applied maths solves the practical problem.
使用遗传算法实现关于函数极值问题的求解，函数已给出。
The use of genetic algorithms achieve about extremal function of problem solving, function has been give.
利用二次型的理论，给出解决多元函数极值问题的另一种方法。
Through the quadratic form theory, another solution to the extremum problem of function of several variables is given.
以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
本文给出了利用梯度判定多元函数极值的判别法，并提供了若干范例。
In this paper we give a method of test, which makes use of the gradient, to verify the extreme value of multivariate function, and give some typical examples.
本研究所建立的冲线模式是依据多变数函数极值法与静力学力矩平衡原理设计而成。
The loom finish modeling in this research is designed according to the extreme of function and the statics moment balance theory.
经典的粒子群优化算法是一个在连续的定义域内搜索数值函数极值的很有效的方法。
The classical Particle swarm optimization (PSO) algorithm is a powerful method to find the minimum of a numerical function, on a continuous definition domain.
利用函数极值和旅行商问题分别对方案的资源耗费、运行速度的有效性进行了验证。
The optimal solution of function and classical travel sales problem are used to verify the effect of the schemes on resource consumption and running speed.
通过利用泰勒公式推导出判断三元函数极值存在的充分条件和极值不存在的必要条件。
By using Taylor's formula, the article deduces the sufficient condition of the existent extreme value and the necessary condition of the inexistent extreme value of trinary function.
动态规划法是运筹学中的一种常用的优化算法，可以用来求解约束条件下的函数极值问题。
Dynamic programming is an optimal arithmetic which is commonly used in operational research and can be used to solve the extreme value of the function in restricted condition.
利用多元函数极值的定义和偏导数的定义公式证明二元函数与一元函数在某点取得极值的关系。
This article use the diverse function extremum and the local derivative's definition formula to prove the relation between extremum obtained by the two function and the dollar function at some point.
本文中，利用目标函数或约束条件的几何性质，提供了某些多元函数极值或最值问题的几何解法。
In the paper, it provides the geometrical solution to extreme value of many variables function by geometric properties of objective function or constraint condition.
通过对两类特殊三元函数极值问题的探讨，得到了由其系数来判别它们能否取得极值的充分条件。
Via the discussion about the extremum question of two kinds of special ternary function, Obtain the sufficient condition of judging if they can get the extremum by their coefficients.
从函数几何意义入手，通过巧妙地构造几何图形，建立几何模型，可以简明扼要地求出函数极值。
This article discusses the methods of how we can find the function extreme valve by subtly constructing geometric figures and geometric models from the function geometric meaning.
对“抢渡长江”问题进行了分析，建立了一种函数极值的数学模型，分析了解题思路和初等求解方法。
In this paper, the problem of Crossing Speedily the Changjiang River is analysed, and a type of functional extreme value model is built, then its analysis and elementary solution is illustrated.
本文利用积函数极值法，从地震作用的角度出发，推导并建立了已建立交桥桥墩的基底剪力的表达式。
In this paper, the method of extremum of the product function is used to analyze upper bound seismic base shear force of the existing overpass and the calculation formulas are gotten.
研究一种多变量非线性函数极值的通用数值解法，并将这种算法应用于石英晶振热敏网络温度补偿系统中。
An universal numerical algorithm of extremum for multivariate nonlinear function is discussed, and is used in the calculate system of compensation for thermistor net.
将一元函数和二元函数极值的部分判别方法推广到多元函数极值的判别，提出了判定多元函数极值的几个方法。
The extreme conditions for the monovariate functions were applied to the multivariate functions and then an effective method to decide the extreme values for the multivariate functions was presented.
本文利用二次型理论给出了二次函数最值的一个充分条件及求法 ，定义了二元齐次多项式的正定性 ，并基于定义给出了二元函数极值的一个充分条件。
This paper is mainly devoted to provide a supplementary analysis of extreme value problem of bivariate functions, in which a new sufficient condition and its concise proof when critical case is given.
摘要李文学用拉格朗日函数提出求条件极值的充分条件，但他的证明却是错误的。
Wenxue li put forward a sufficient condition of conditional extreme value with Lagrange function but his proof is wrong.
传统风煤比寻优通常采用求解燃烧函数解析式，再求极值得出最佳风煤比，这一方法可靠性差而且工作量大。
In traditional ways, the optimal air coal ratio is obtained by solving combustion function and finding out the extremum, which is time consuming and unreliable.
用特定系数法、换元法、配方法探求二元二次函数的极值公式。
The extremal formula of binary quadratic functions is studied by using method of undetermined coefficients, substitution method and method of completing the square.
同时，在具体反演中使用快速模拟退火算法，可以克服目标函数局部极值的限制，从而获得全局最优解。
Meanwhile, we use a fast simulation annealing algorithm in the inversion, which can overcome the limitation of the local extremum of objective function, and acquire a global optimum result.
对屈服条件与屈服函数的极值条件进行了讨论，在不需要流动法则的情况下建立了速度方程。
The extreme conditions of yield condition and yield function are discussed; and a velocity equation is established under the condition that no flow rule has been required.
对屈服条件与屈服函数的极值条件进行了讨论，在不需要流动法则的情况下建立了速度方程。
The extreme conditions of yield condition and yield function are discussed; and a velocity equation is established under the condition that no flow rule has been required.
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