极值的存在

The unsaturated and compacted soil triaxial test result under constant suction describes the unsaturated soil critical state surface in p-q-s three dimensional space: in p - q plane, the slope M of critical state line is independent of suction; the cross line of LC yield surface and critical state surface is a curve with extremum in three dimensional stress space, and its projection in p-s plane is located in quadrant 1 in triaxial compression state; its projection in q-s plane has asymptote, and there should also be asymptote in respect of the curve that stands for the function relationship between cohesive and suction.

基于局部变形测量的常吸力非饱和压实土三轴剪切试验结果，全面描述了非饱和土p—g—s三维应力空间中临界状态面的合理形态：在p—q平面，临界状态线斜率M是与吸力无关的物理量；临界状态面与LC屈服面交线在三维应力空间中是一条存在极值的曲线；该交线在p—s平面的投影曲线在三轴压缩应力状态下应位于第一象限；该交线在q—s平面的投影曲线应存在渐近线；反映凝聚力与吸力关系的函数曲线也应存在渐近线。

This paper considers existence of extreme solutions to first-order differential equations with a parameter by the method of lower and upper solutions with monotone iterations,and monotonic sequence is uniformly converged to the extreme value solution of nonlinear equation after being constructed.

文章利用上下解方法和单调迭代技术讨论了含有一个参数的微分问题极值解的存在性，通过构造单调序列使这个单调序列一致收敛于非线性方程的极值解。

The fact that solution of wave equation is equivalent to the extreme value of quadratic function solution was verified, and the existence and uniqueness of the quadratic function solution was also proved.

证明了波动方程的解和二次泛函极值解的等价性，以及二次泛函极值解的存在唯一性，为其在液压传动中流体瞬变分析的进一步应用提供了理论依据。

Due to the existence of local extremum, such traditionalmethods could not find the global extremum properly.

通过对系列60船的优化计算，发现了有局部极值的存在，而传统优化方法只能搜索到局部极值，通常不能得到全局最优解。

The conventional non-linear seismic inversion methods are low in convergence and sometimes will result in the problem of local extremum.

传统非线性反演方法存在着收敛效率低，有时会陷入局部极值的问题。

The conventional nonlinear seismic inversion methods are low in convergence and sometimes will result in the problem of local extremum.

传统非线性反演方法存在着收敛效率低，有时会陷入局部极值的问题。

In fact, negative skewness means that the risk for a substantial loss is bigger than the chance of a substantial gain. A high level of kurtosis means that the asset has a high probability of extreme events.

负偏度的存在使得资产收益下降的可能性大于上升的可能性；超出峰度的存在使得极值事件比在正态条件下更容易发生，从而增加风险，将其统称为高阶矩风险。

The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality.

首先证明了所构造泛函的强制性，从而证明了所构造的等价变分不等式解的惟一性，并根据椭圆型变分不等式解存在的充分条件论证了弹塑性接触问题解的存在性，为该问题的变分极值原理的建立莫定了数学理论基础。

The characteristics of genetic algorithm,global searching of Genetic Algorithm for complex,multi-apices,and nondifferentiable nonlinear function are applied to the Hopfield neural network,which results in the inputting pattern getting away from the attraction domain of fault pattern and the Hopfield neural network associative memory remaining high success rate while the noise to signal ratio is high.

0引言Hopfield神经网络模型在神经计算、优化求极值、联想记忆等方而取得了重大应用，联想记忆能够从不完整的或模糊的信息中联想出存储在记忆中的某个完整清晰的图像模式，但一般离散Hopfield模型存在很多伪稳定点[2]，这些伪稳定点的存在，不仅使真稳定点的吸引域变小，而且使网络

In chapter 3,we discuss the existence of solutions for impulsive differential equations with two-point boundary condition.

通过使用脉冲不等式和分析方法，得到了一阶脉冲微分方程周期边值问题新的比较结果，借助所给的新的上下解，结合单调迭代技巧，建立了一阶脉冲微分方程周期边值问题极值解的存在结果。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。