反过来，在某些条件下，满足局部-全局极值性的函数必是这些广义函数类之一。
Conversely, it is shown that, under some mild regularity conditions, functions for which the local-global minimum properties hold must belong to one of the classed of the functions introduced.
以光滑函数的一阶导数作为小波母函数 ，研究了管道泄漏特征信号拐点区间的敏感性 ，突出小波变换系数的局部极值性。
The differential coefficient of smooth function was taken as a mother wavelet for researching the sensitivity segment of inflexion of pipeline leakage signal.
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.
由于较粗尺度下目标函数呈现较强的凸性及较少的局部极值，很有利于收敛至优化解。
Objective function presents comparatively strong convexity and lesser local extreme values on wide scale which is favour of converging to optimized values.
运用此定理，在线性空间中建立了带广义不等式约束的向量极值问题的最优性条件。
By the alternative theorem, the optimality conditions of vector extremum problems with generalized inequality constraint are established in linear space.
最后，基于极限强度，将该组合方法用于评估散货船在极值弯矩作用下的船体梁安全性。
Then, the compound method is used to assess the hull girder ultimate strength reliability of a bulk carrier subjected to extreme bending moments.
在遗传算法中嵌入一个梯度下降算子，使得混合算法既有较快的收敛性，又能以较大概率得到全局极值。
Through embedding a gradient descend operator into the generic algorithm, a hybrid algorithm is achieved with fast convergence and great probability for global optimization.
先给出这些问题的提法，然后使用列紧性原理和极值原理证明了上述二阶椭圆型方程边值解的存在性和唯一性。
Fristly the boundary value problems for the equations is formulated, and then by using the compactness principle, the existence of solutions for the above problems is proved.
本文以极值统计学为理论基础，研究了该方法在洪灾损失风险计算中的适用性。
Based on the statistics of extremes, this paper studies the applicability of extremes in calculating hazard risk of flood damage.
近年来，凸性在许多应用数学领域的极值问题研究中已越来越重要。
Convexity has been increasingly important in recent years in the study of extremum problems in many areas of applied mathematics.
本文在一个不规则网路上离散拉普拉斯运算元的差分格式，不但能满足相容性及极值原理，而且还具有误差极少性质。
The paper gave disperse pattern of laplace function under in - uniform grid, which fulfills acceptance character and error maximization theory. it also has fulfills the character of extreme value.
在序线性空间中，利用次似凸映射的择一性定理，得出具有一般约束的向量极值问题的最优性条件。
Using the alternative theorem, the optimality conditions of vector extremum problems with generalized constraint are established in ordered linear space.
这种方法比传统极值方法更适用于无季节性变化的数据。
It seems that this method is more applicable than the traditional methods for those data without seasonal variations.
本文运用极值理论对鄂尔多斯北缘地震危险性作了估计。
The earthquake risk of the northern margin of Eerdosi has been estimated by statistica theory of extreme values in this paper.
在一个不规则网络上离散拉普拉斯算子的差分格式，不但能满足相容性及极值原理，而且还具有误差极小性质。
The paper gives disperse pattern of Laplace functor under in-uniform grid, which fulfills acceptance character and error minimum theory, extremes value principle.
该方法利用惯性矩是方位角的函数，且函数有极值的特征推出普遍性结论。
The general conclusion is derived by using the features that moment of inertia is a function of the Angle of rotation and the function has extreme value.
于是从语音产生模型入手，详细的分析了声门闭合时刻语音信号的性质，找到了浊音信号经过小波变换后周期性消失、极值点个数增多的原因。
Based on the speech produce model, we find the reason of periodicity disappearance and the extremum number increase by analysing the character of speech signal when the glottal closes.
对极值指数之矩估计量作了进一步的推广，并证明了其强、弱相合性。
The moment estimators are extended and their strong and weak consistency are proved.
仿真实验结果表明，新方法更准确地反映了水击极值点及整个动态过程，对保证水电站运行的安全性和经济性以及研究机组动态过程具有很高的理论和实际应用价值。
The results have shown that this method will benefit the security and economy of hydropower plant operation and help the study of the dynamic process of the unit.
利用这些概念，得到了总极值的最优性条件。
With these concepts, integral optimality conditions for global optimization are obtained.
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.
该模型来源于极值统计理论，并具有类似于确定性龚帕兹曲线函数的渐近性特性。
The proposed model can be derived from the statistical theory of extreme-value, and has a similar asymptotic property to the deterministic Gompertz curve.
本文采用求极值的数学方法，分别考虑了一次、二次作物产量函数。提出了不同产量函数下适时作业期限合理延迟天数的确定方法，以及依据作物产量函数计算适时性损失的方法。
A method to determine the reasonable prolongation of the proper operating time is proposed in this paper using the differential method according to the linear and parabolic functions of crop yields.
针对粒子群算法用于高维数、多局部极值点的复杂函数寻优时易陷入局部最优解现象，提出一种改进的带扰动项粒子群算法并进行收敛性分析。
Traditional particle swarm optimization(PSO) algorithms often trap into local minima easily when used for the optimization of high-dimensional complex functions with a lot of local minima.
针对粒子群算法用于高维数、多局部极值点的复杂函数寻优时易陷入局部最优解现象，提出一种改进的带扰动项粒子群算法并进行收敛性分析。
Traditional particle swarm optimization(PSO) algorithms often trap into local minima easily when used for the optimization of high-dimensional complex functions with a lot of local minima.
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