函数的最小

The optimization algorithms are commonly used to approach the minima of the roundness objective functions through iteration when a microcomputer is applied to assess roundness errors by minimum zone, minimum circumscribed circle, and maximum inscribed circle methods.

引言在用计算机求最小区域、最小外接圆和最大内切圆评定法求圆度误差时，广泛采用最优化算法，通过迭代去逼近目标函数的极小值。

Firstly, this paper investigated roundly the basic theory of the ambient vibration method, analyzed systematically the main methods of ambient vibration identification, and discussed their advantages and disadvantages. Then we established the finite element model of structural dynamics and test model and analyzed their mutual relation, improved MUSIC method and correlation function method in the harmonic identification, and gave the subspace method and correlation function method based on continuous model, which is multi-harmonic retrieve technique. And then, this paper also puts forward least-squares method to estimate directly structural physical and modal parameters; this approach replaced the derivative operator in the continuous time model with an equivalent approximation, and estimated the physical parameters of structures by the least-squares method. And then, we discussed the approximation methods of derivative and their convergence. Finally, this paper researched the modal parameters of a frame structure by the simulation and test. The results demonstrated that subspace method, correlation function method and the least-squares method are effective and stable respectively.

全面地研究环境振动识别方法的基本理论，系统地分析环境振动识别方法的主要方法，讨论它们的优点和不足；建立结(来源：6666AB44C论文网www.abclunwen.com)构动力学的有限元模型和试验模型，分析有限元模型与试验模型之间的相互关系；改进谐波识别中的MUSIC识别方法和相关函数识别方法，给出大型结构模态识别的连续型的子空间分解识别方法和相关函数识别方法，这个方法是多元谐波识别方法；提出直接识别结构的物理参数和模态参数的最小二乘方法，这个方法利用导数的近似值代替导数值，并运用最小二乘方法识别结构的物理参数，讨论导数近似值的选择方法，分析算法的收敛性；通过仿真计算和模型实验，研究高层框架结构的模态参数识别，验证子空间分解识别方法、相关函数识别方法和最小二乘识别方法的有效性，算法的稳定性；从理论和试验两个方面分析和研究噪声对识别精度的影响，影响识别精度的因素，以及部分模态成分的模态参数不能够被识别的原因。

However, the BER cost function is highly nonlinear, so constraint selection is difficult.

本文提出了一组新的约束条件，证明了在该约束条件的约束空间里误码率代价函数的最小点是唯一的。

The unique existence theorem for minimal determining set of completerational choice function is obtained,and the sufficient condition is used to show avery simple proof of Arrow Impossibility Theorem.

构造并证明了完全理性选择函数的最小决定集的存在惟一性定理，同时应用该定理的充分性条件给出了Arrow不可能性定理的一个简单证明。

By the minimum risk Bayes decision theory, this paper develops a new way of image segmentation: establish the mathematics model of image segmentation; estimate the probability density of grey scales and figure out its math-expectation and square difference that accord with normal distribution and the loss function; and judge the every pixel dot in the image according to the minimum risk Bayes decision theory and determine whether it is of target or non-target images, thereby realizing the extraction of the target image.

依据最小风险贝叶斯决策理论，提出了一种基于最小风险贝叶斯决策的图像分割方法。首先建立图像分割的最小风险贝叶斯决策模型，对灰度级类条件概率密度估计出其符合正态分布的数学期望和方差以及损失函数，再依据最小风险贝叶斯决策理论对图像中的每一像素点进行目标图像和非目标图像的类别判断，从而实现目标图像的提取。

It is assumed that the reinsurer's risk must be less than a given constant and in such a condition the optimal reinsurance contract in order to minimize the insurer's risk is found out.

对于原保险人的风险度量，本文采用了方差风险函数、半方差风险函数和最小一乘L_1风险函数，并且分别讨论了这三种风险度量下最优再保险函数存在的充分条件。

The exact expressions of minimal martingale measure and the minimal entropy martingale measure for jump diffusion semimartingale are gained,with the specific changes of intensity and density function processes in these measures.

在跳扩散半鞅模型中，引进了跳的强度过程与跳的概率密度函数过程，研究了测度变换对跳的强度与密度函数过程引起的变化、研究了跳扩散半鞅的最小鞅测度与最小熵鞅测度。

In chapter 1, the achievement on multiple-valued logic at home andabroad is introduced briefly. In chapter 2, some decisions for theminimal covering of the regular separable sets in partialmultiple-valued logic is studied under the condition of σ=e andm=2 . We reach some conclusions that certain regular separable setsmustn't be the minimal covering of Pk under some conditions.

第一章，简要介绍了国内外在多值逻辑方面的研究成果；第二章，对部分多值逻辑中，当σ=e时，二元正则可离函数集最小覆盖之判定作了研究，并得出了当σ=e时，一些满足一定条件的二元正则可离函数集不是Pk 之最小覆盖成员的结论。

So we have in the dissertation: 1. First we proposed the minimal singular blending function, and established the minimal singular blending functions of power form、Bernstein form and Bézier form.

提出了最小奇异混合函数，研究了它的建立方法，给出了各种形式的最小奇异混合函数，有幂形式、Bézier基形式及Bernstein-Bézier基形式。

In allusion to the above-mentioned problems, considering the self-adaptive regulative ability of the visual system to natural perceptive information and the feedback between visual cortexes, a bidirectional NNSC model is proposed, which is based on the robust principal component analysis and the priors of receptive fields of simple cells in V1. And using the (Polak-Ribiere-Polyak) PRP conjugate gradient descent algorithm, the minimum optimization problem of the objective function can be realized.

针对上述问题，考虑视觉系统对外界感知信息的自适应调整机制和视皮层之间的反馈连接，本文提出了一种基于稳健 PCA 和 V1区简单细胞感受野先验知识的反馈非负稀疏编码模型，并且使用 Polak-Ribiere-Polyak共轭梯度下降优化算法实现了目标函数的最小化问题。

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。