极值点

An modified BFGS algorithm o solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

It can not only overcome the disadvantage of easily getting into the local extremum in the later evolution period,but also keep the rapidity of the previous period.

所提出的算法将粒子群优化算法和混沌算法相结合，既摆脱了算法搜索后期易陷入局部极值点的缺点，同时又保持了前期搜索的快速性。

A hybrid particle swarm optimization algorithm based on the chaos search is proposed. It can not only overcome the disadvantage of easily getting into the local extremum in the later evolution period, but also keep the rapidity of the previous period.

所提出的算法将粒子群优化算法和混沌算法相结合，既摆脱了算法搜索后期易陷入局部极值点的缺点，同时又保持了前期搜索的快速性。

The algorithms based on two necessary condition is monotone decreasing, for multi-extreme point in solution space, the distribution of final codebook seriously depend on that of initial codebook, it is difficult to cast off if get in local optimality.

然而这些算法本身属单调梯度下降算法，在解空间存在多极值点时，最终码书的分布较大依赖初始码书分布，一旦落入局部最优区域，很难摆脱。

The approach first chooses three continuous data points in turn when the data points in time series are scanned. According to the angle formed by these three data and the extreme value in monotone sequence, the method then records key points reflecting the sequences changing feature.

该算法在扫描数据的过程中利用单调序列中三个连续数据形成的夹角和非单调序列中的极值点，从序列中挑选反映趋势变化的关键点，实现时间序列的线性拟合。

Simulation results on a set of benchmark functions show that the algorithm can properly find all the optima.

一组测试函数的仿真计算结果表明了所提出的算法能准确地找到全部极值点。

Moreover,these algorithms are very sensitive to the initialization and easy to get trapped into local optima.

此外这类算法还存在对初始化敏感，易陷入局部极值点等弱点。

Based on the array signal processing and the eigenstructure decomposition method, the signal subspace and the noise subspace are achieved by reconstructing and decomposing the data matrix collected by the array sensors. By using the orthogonal properties of the two subspaces, the information about the velocities and bearings of spatial moving targets can be exactly obtained.

本文提出一种超分辨的二维谱估计方法，它利用的是阵列处理技术，对天线接收数据进行本征分析，将信号数据张成一个空间并对其进行分解，根据正交原理分割成信号子空间和噪声子空间，构造出噪声本征矢量，利用信号子空间与噪声子空间的正交性，在空间谱上形成极值点，从而达到对方向和速度的二维高分辨率估计。

The parabola equation that can be fixed to the test curve and has reliable physical meaning was given.

该方程的极值点确定了最佳掺杂含量与晶体结构和制备方法之间的定量关系，进而得到了一个最佳掺杂含量的表达式。

The study found that it is not symmetrical convex parabolic type, left and right sides are not equal to the minimum axial velocity near the rod at the minimum axial velocity is small in the different condition from water to the various solution of HPAM chroma in the vertical eccentricity annuli with wide gap at pipe.

研究发现不同介质的流体在螺旋流条件下，其在偏心环空中的轴向速度分布不是左右对称的凸抛物线型，而是中间有凹陷且左右不对称的抛物线型，其轴向速度的极值点向模拟油管内壁偏移。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。