线性回归模型中一类式子的推导

线性回归中的最小二乘估计具有线性无偏估计类中方差最小的性质,而这个性质的证明较为复杂,许多文献都予以省略,复相关系数的定义更是直接给出,并未从统计意义上加以解释,回归方程显著性检验所给出的统计量往往是从约束最小二乘出发得到,本文利用简单方法来推导这些性质,并且导出检验统计量的分布,解释了复相关系数的统计意义,以及回归模型中不相关的推导.     

平面场的仿射对应及其在几何学中的应用

仿射对应在解决工程问题及几何问题中均是一种很有效的工具,为阐明这一认识,本文主要讨论了平面场的仿射对应在画法几何学及几何证明上的一些应用.     

基于反向随机投影的神经网络改进算法

提出基于反向随机局部投影的神经网络效率改进算法，通过降低深度学习中的网络规模，重点解决了从“局部连接”到“全连接”和随机节点抽取时输入端节点信息丢失的问题，从而提升网络的效率。在算法中设置缩减参数，提升了算法的可伸展性，以适用于不同数据集的学习。通过数据集ISO-LET进行实验，结果表明，基于反向随机局部投影的神经网络效率改进算法的准确率、效率分别平均提升了3.48%和105.21%?在迭代20次的实验中进行了缩减参数调节实验，当参数设置为1.4时其准确率则优于传统全连接网络2.61%，效率提升了272.78%，具有明显的优势。     

Mini-research Experience in Simple Linear Regression

Within the undergraduate mathematics curriculum, the topic of simple least-squares linear regression is often first encountered in multi-variable calculus where the line of best fit is obtained by using partial derivatives to find the slope and y-intercept of the line that minimizes the residual sum of squares. A markedly different approach from linear algebra, which could also be introduced in multi-variable calculus, obtains the regression line by vector projection. The latter viewpoint offers elegant proof of the equation relating the total, explained and unexplained variations. Consideration of data with the same regression line and correlation opens the door for a “mini-research experience” (MRE). A sequel MRE gives rise to an open Research Experience for Undergraduates topic to analyze reflection sequences and a fundamental connection between complex analysis and regression analysis. A few general guidelines and basic goals for MREs are included for those whose main interest is in undergraduate research.     

一类过程A的E｜_∞｜~2表现与估计

本文针对不同的停时类型讨论了一类典型过程Ａ的对偶可料投影Ａ～之Ｅ｜Ａ～∞｜２的表现，并由此表现得到了它的估计，从而对［１］中相应结论给出了有意义的修正。     

英语非限定动词的列表对比投影教学

本文阐述了列表对比投影辅助教学具有的系统性强、普遍性强、信息量大等特点,仔细探讨了这种教学方法在非谓语动词教学过程中所发挥的作用及其应注意的问题。     

二次曲线的射影与度量

度量几何中圆的切割线之间所确定的数量关系,推广到射影几何里一般二次曲线中,利用调和共轭元素之间的关系,更广泛地确定了极与极线的相互关系,着重介绍了二次曲线的度量性质与射影性质的内在联系。     

MM教育方式与高师解析几何教学

MM教育方式要求解析几何教学要作好与中学数学的衔接,注重与高等代数等其他数学分支的联系,注重改进教学的方式方法,要求教师加强创新意识和科研能力.     

Disturbance rejection control based on acceleration projection method for walking robots

This paper presents a disturbance rejection scheme for walking robots under unknown external forces and moments. The disturbance rejection strategy, which combines the inverse dynamics control with the acceleration projection onto the ZMP （zero moment point）-plane, can ensure the overall dynamic stability of the robot during tracking the pre-computed trajectories. Under normal conditions, i.e., the system is dynamically balanced, a primary inverse dynamics control is utilized. In the case that the system becomes unbalanced due to external disturbances, the acceleration projection control （APC） loop, will be activated to keep the dynamic stability of the walking robot through modifying the input torques. The preliminary experimental results on a robot leg demonstrate that the proposed method can actually make the robot keep a stable motion under unknown external perturbations.     

小比例尺航片制作正射影像的方法研究

利用1：50000～1：60000航片制作1：10000正射影像的实验性方法正处于研究阶段．探讨了在实验中保证正射影像精度的实施方案,如DEM数据采集和影像镶嵌、匀色的关键技术的解决方法．对利用1：50000-1：60000航片制作1：10000正射影像的关键问题进行了分析。并提出了解决方案．