最小

The least absolute deviations are using widely used in engineering because of it s robustness,but the algorithm solving the least absolute deviation is not efficient.

最小一乘在稳健性上比最小二乘好，使得最小一乘在工程中得到广泛的应用，但求解最小一乘的算法并不理想；本文根据最小一乘的性质，把最小一乘问题变为组合优化问题。

Then, we construct a network model of the max-min spanning arborescence problem, we discuss the essential character of the max-min spanning arborescence and deduce an effective algorithm to solve this problem based on the relationship between the minimum in-arc circuit and the max-min spanning arborescence.

3最大最小树形图问题，即基于实际背景，建立求网络的最大最小树形图的模型，研究最大最小树形图的基本性质，并以最小入弧回路与最大最小树形图的关系为基石，介绍求网络的最大最小树形图的有效算法。

Our process capability: Plates: FR4, High TG FR4, high CTI FR4, high frequency materials, halogen-free materials, aluminum and other low-rise Materials :2-20 layer of finished copper thickness :0.5-5 OZ finished thickness: 0.2 -6.0mm Minimum line width: 3mil Minimum line spacing: 3mil smallest shape tolerances:+/-0.1mm minimum finished diameter: 0.1mm maximum thickness aperture ratio: 12:1 wide minimum solder bridge: 4mil characters minimum line width: 5mil Minimum height of characters: 30mil Solder Mask Color: Green, black, blue, white, yellow, purple characters such as color: white, yellow, black and other surface processes: spray tin, lead-free HASL, Electroless gold plating Shuijin, OSP, chemical Shen tin, silver and other chemicals Shen Process: Goldfinger, blue gum, Blind-via/Buried-via, characteristic impedance control, rigid-flexible combination of reliability testing such as: Open / Short testing, impedance testing, solderability testing, thermal shock testing, metallographic analysis of micro-slice curvature Isoptera: 0.7% flame retardant Level: 94V-0

我们公司的制程能力：板材：FR4、高TG FR4、高CTI FR4、高频材料、无卤素材料、铝基材料等层数：2-20层成品铜厚：0.5-5 OZ成品板厚：0.2-6.0mm最小线宽：3mil最小线间距：3mil最小外形公差：+/-0.1mm最小成品孔径：0.1mm最大板厚孔径比：12：1最小阻焊桥宽：4mil最小字符线宽：5mil最小字符高度：30mil阻焊颜色：绿色、黑色、蓝色、白色、黄色、紫色等字符颜色：白色、黄色、黑色等表面工艺：喷锡，无铅喷锡、化学沉金、电镀水金、OSP、化学沉锡、化学沉银等其它工艺：金手指、蓝胶、盲埋孔、特性阻抗控制、刚柔结合等可靠性测试：开/短路测试、阻抗测试、可焊性测试、热冲击测试、金相微切片分析等翅曲度：≤0.7%阻燃等级：94V-0

The relationship between the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was studied. Based on their relationship, the minimum zone circle and minimum circumscribed circle, maximum inscribed circle were transformed mutually.

本文研究了最小区域圆与最小外接圆、最大内接圆特征点的相互关系，实现了最小区域圆与最小外接圆、最大内接圆的相互转化，可有效解决最小区域圆的误差评定。

Thus, evaluation of the minimum zone circle could be solved effectively.Three methods of assessment of roundness error were proposed in this dissertation. Based on the criteria of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle and convex hull, a unified approach was proposed to evaluate roundness error of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle. Evaluation of the minimum zone circle, minimum circumscribed circle and maximum inscribed circle was fulfilled with rotation based the contact pattern. The minimum circumscribed circle and maximum inscribed circle were evaluated with curvature and the curvature circle.

本文提出了三种圆度误差评定的方法：根据最小区域圆、最小外接圆、最大内接圆在极坐标系下的判别准则，利用计算几何中的凸壳理论，提出了一种统一的评定方法，实现了对最小区域圆、最小外接圆、最大内接圆的误差评定；基于接触斑点的检验原理，利用旋转法，实现了最小区域圆、最小外接圆和最大内接圆的误差评定；利用曲率和曲率圆，实现了对最小外接圆和最大内接圆的误差评定。

The details as follow: 1.Based on rules about form error in GB, mathematical models of form error are established including straightness error on the base of minimizing zone method、least-squares method and two dots linked method ; flatness error based on minimizing zone method、lease-squares method、diagonal line and three dots method; circularity and cylindricity error based on minimizing zone method、lease-squares method、minimum circumscribed circle and maximum inscribed circle.

具体内容如下：根据国标中形状误差的相关规定建立了各种要素评定方法的数学模型包括：直线度的最小区域法、最小二乘法、两端点连线法；平面度的最小二乘法、最小区域法、对角线法、三远点法；圆度和圆柱度的最小区域法、最小二乘法、最小外接圆法、最大内切圆法。

The results showed that:(1) The characteristic frequency of IC neurons of house mouse was increased with increasing recording depth, and the masker intensity used was positive relevant to the IC neurons\' minimum threshold. When the minimum threshold was high, the masker intensity needed was loud, vice versa.(2) According to the masking rate at MT+10dB of IC neurons to frequency modulation and tone burst, the IC neurons were classified as three types: type I neurons ( 72/113, 63.7%), in which the masking effect of TB was better than frequency modulation ;type II neurons (32/113, 28.3%), in which the masking effects of the two maskers were same; type III neurons( 9/113, 8.0%), in which the masking effect of FM was better than TB.(3) Type I neurons, the minimum threshold of which was low, but the Q_(10) and DR values of which were large; in type III neurons, the minimum threshold was high, the Q_(10) and DR values were narrow; in type III neurons, the MT Q_(10) and DR values were in between.(4) Both FM and TB could make the MT of type I neurons shift upward distinctively, but the effect of TB was more significant than FM.(5) The Q_(10) values of type I neurons became narrower under the influence of TB, were unaffected under the influence of FM.

结果显示：(1)小鼠下丘神经元的特征频率随着记录深度的增加而增高，掩蔽声强度与神经元的最小阈值呈正相关，即对高最小阈值的神经元进行掩蔽时需要的掩蔽声强度高，对低最小阈值神经元进行掩蔽需要的掩蔽声强度低：(2)根据调频声(frequency modulation， FM)和短纯音(tone burst， TB)对下丘神经元阈上10dB处反应的掩蔽，将小鼠IC神经元分为三类：Ⅰ类神经元(72/113，63.7％)，短纯音的掩蔽效果比调频声更好；Ⅱ类神经元(32/113，28.3％)，两者对神经元声反应的掩蔽率相同；Ⅲ类神经元(9/113，8.0％)，调频声的掩蔽效果更好；(3)Ⅰ类神经元的最小阈值低、Q_(10)值和动态范围大，Ⅲ类神经元最小阈值高、Q_(10)值和动态范围小，Ⅱ类神经元的最小阈值、Q_(10)值和动态范围介于Ⅰ和Ⅲ类神经元之间；(4)短纯音和调频声都可以使Ⅰ类神经元声反应的最小阈值明显上移，但短纯音使神经元最小阈值的上移更显著：(5)短纯音使Ⅰ类神经元的Q_(10)值变小，调频声使神经元的Q_(10)值增大不显著，短纯音与调频声对神经元Q_(10)的影响差别显著；(6)短纯音与调频声都使神经元的动态范围减小，并且作用显著，但短纯音的效果更显著：(7)短纯音与调频声都使神经元反应的潜伏期延长，效果显著，但TB的延长作用更为显著；(8)随着探测声强度的升高，短纯音和调频声对Ⅰ类神经元声反应的掩蔽率都降低，但在各个探测声强度短纯音的掩蔽率都比调频声高。

This thesis introduces the basic principle of the least square data fitting.. According to the least square data fitting ,the paper studies and analyzes the linear least square fitting ,the quantic least square fitting and nonlinear least square fitting respectively . By using the mathimatic instrument Matlab , this paper shows a lot of examples of interrelated questions. Using Matlab makes the theory of data fitting easier to be understood.

本文介绍了最小二乘数据拟合法的基本原理，并根据最小二乘数据拟合方法，分别针对线性最小二乘拟合、多项式最小二乘拟合，非线性最小二乘拟合（lsqcurvefit、nlinfit、lsqnonlin、以及非线性的线性化）、多元最小二乘拟合进行了分析和研究，并通过数学工具Matlab实现了对相关问题的举例应用，使相关数据拟合理论更加生动易懂。

The solutions of ProblemⅠ,ⅡandⅢare discussed by using the generalized conjugate gradient method. When the equation is consistent, the solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are successfully found; When the equation is inconsistent, the least-squares solutions such as symmetric, skew-symmetric, centrosymmetric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric are also found successfully. The generalized conjugate gradient method has the following traits:(1) It can judge automatically the information of solutions.

利用广义共轭梯度法，讨论了问题Ⅰ、Ⅱ和Ⅲ解的情况：当方程相容时，研究了方程的一般解、对称解、中心对称解、自反矩阵解、双对称解、对称次反对称解及其最佳逼近等问题；当方程不相容时，研究了方程的最小二乘一般解、最小二乘对称解、最小二乘中心对称解、最小二乘自反矩阵解、最小二乘双对称解、最小二乘对称次反对称解及其最佳逼近等问题。

At each level, the parameters, hyper parameters and model parameters are adjusted to minimize the Kullback-Leibler divergence between their posteriors and real distributions so that the variable free energy can approach the real free energy.

在指出证据框架和自由能最小化方法等贝叶斯推理方法的局限性的前提下，通过对比证据框架的方法，提出了自由能框架的概念，将通常难以求解的自由能最小化过程分解成参数自由能最小化、超参数自由能最小化、模型参数自由能最小化等层次，在每个层次上调节参数、超参数和模型参数，使其后验分布为其真实分布之同的Kullback-Leibler距最小，以使可变自由能逼近真实自由能。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。