极小条件

How to deal with the restrictions of deep excavation is a very difficult problem. This paper analyzes the restrictions of pile-support structure detailedly, uses a castigatory function to deal with the restrictions, and adds the castigation to the function. Now the problem has changed to solve a minimal problem, and GA can be used to the optimal design successfully.

束条件的处理是遗传算法应用到深基坑支护结构优化的难题和重点，本文详细分析了桩撑支护结构的约束条件，采用了罚函数法对约束条件进行处理并反映到适应度函数上，使其变为无约束的极小值问题，从而使遗传算法得以顺利实施。

On the basic that existing second-order sufficient condition for an isolated minimizer of order 2 for unconstrained multi-objective optimization, using the so called oriented distance from a point to a set, l-stable function and generalized second-order Peano direction derivative, some second-order sufficient conditions for an isolated minimizer of order 2 for constrained multiobjective optimization problems with l-stable functions are obtained.

在已有的无约束l-稳定函数多目标优化问题的二阶充分条件的基础上，借助定向距离函数和l-稳定函数的性质及引入的广义二阶Peano方向导数，进一步刻画了具有抽象约束的l-稳定函数的多目标优化问题的二阶孤立极小点的二阶充分条件。

Some relations between generalized KT-properly efficient solution and generalized H-local-properly efficient solution are obtained under appropriate conditions.

在实用中，由于在给定的约束条件下求得的目标函数的最优值，有时会不符合人们的要求，因此有必要考虑当目标函数的最优值作适当改进时，如何使约束条件进行极小扰动的问题。

Under suitable assumptions, the relationship is established between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the space of problem variables and the solution of the original constrained problem, and a relationship is also presented between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers and the solution of the original constrained problem.

在适当的条件下，我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

This method includes the method of profile data modeling in theory, bound searching method of expansion polar angle corresponding theoretical points and evaluation method of least-deviation profile error.

包括实现轮廓度测量的理论轮廓数据建模方法、对应理论点的扩展极角定界搜索方法以及满足最小条件的最小极偏差轮廓度误差评定方法。

Therefore, it's natural to estimate those values of operators such as 〓, log mf and so on in order to investigate the weighted inequalities for the minimal operator We discuss them under two conditions respectively: In one-weight case, we establish the relative weighted inequalities under the condition of A〓-weight and A〓-weight respectively, and the equivalent condition has been found between the strong -type weighted inequality and the property of W〓-weight; while in the case of two-weight condition, we characterize the equivalent relations between the weak type weighted inequality and the property of W〓-weight, the strong -type weighted inequality and the property of W〓-weight.

我们分两种情况分别加以讨论：单权情况下，我们分别刻画了A∞权和A〓权条件下关于〓，log mf等的强型加权不等式，并证明了关于鞅的极小算子的强型加权不等式与对应的W〓权性质之间的某些等价关系；在双权情况下，我们刻画了关于极小算子的弱型加权不等式与W〓权以及强型加权不等式与W〓权之间的等价关系。

It is also found that the spurious dipoles are unstable in different inverse problem solution.

反之，目标函数可以得到极小优化，但出现多余的伪偶极子，且这些伪偶极子在多次不同条件的反演结果中，处于不稳定状态。

It is concerned with the optimal design of cylindrical shell on minimax deflection and minimal compliancy with arbitrary axisymmetrical boundary conditions and radial pressure, under the condition of the volume being constant.

研究在任意轴对称边界条件下和任意轴对称分布载荷作用下体积保持常数的圆柱壳的两类优化设计问题：极小化圆柱壳的最大挠度和极小化圆柱壳的柔度。

Some solvability conditions, including sublinear ,subquadralic and superquadratic, and the corresponding existence results are summed up for periodic solutions of the second order Hamiltonian systems obtained by using the minimax methods.

本文综述了用极小极大方法得到的关于二阶Hamilton系统周期解的可解性条件及相关结果，包括次线性条件，次二次条件和超二次条件等方面的近期结果。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

在适当的条件下，我们建立了Hestenes-Powell 增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系，并且也给出了Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。