解析几何教学中的思维训练——从构造性解法谈起

介绍在解析几何教学中如何运用构造性解法与非构造性解法培养学生的思维能力,以及如何在解题过程中对学生进行思维能力训练.由于构造性解法与非构造性解法所体现出来的思维水平与思维特征均有较大差距,因此,主要研究如何由问题的构造性解法过渡为非构造性解法,有计划地、分阶段地完成解析几何教学所承担的思维训练的任务.     

交比在初等几何中的应用

本文首先给出交比的定义、性质,然后分析交比在初等几何中的应用范围、基本方法、应用技巧,最后通过典型例题加以论证。     

Desargues对偶定理的推广及应用

Desargues对偶定理主要用于证明仿射平面上的共点线,为使Desargues对偶定理能在初等几何中有所应用,将无穷远点还原为直线的平行,并运用其解决欧氏平面上的线共点问题。     

Similarity-based denoising of point-sampled surface

A non-local denoising (NLD) algorithm for point-sampled surfaces (PSSs) is presented based on similarities, including geometry intensity and features of sample points. By using the trilateral filtering operator, the differential signal of each sample point is determined and called "geometry intensity". Based on covariance analysis, a regular grid of geometry intensity of a sample point is constructed, and the geometry-intensity similarity of two points is measured according to their grids. Based on mean shift clustering, the PSSs are clustered in terms of the local geometry-features similarity. The smoothed geometry intensity, i.e., offset distance, of the sample point is estimated according to the two similarities. Using the resulting intensity, the noise component from PSSs is finally removed by adjusting the position of each sample point along its own normal direction. Experimental results demonstrate that the algorithm is robust and can produce a more accurate denoising result while having better feature preservation.     

线性变换下正态分布随机变量列的分布

多维正态分布N（μ,∑）在正交变换下,有相互独立的η1,η2…,ηn且ηk-N（0,σk^2）,使对服从正态分布N（μ,∑）的ξ=（ξ1,ξ2…,ξn）的讨论,转化为相互独立的η1,η2…,ηn．     

《高等代数与解析几何》课程一体化教学内容与方法的优化研究

本文以东北财经大学为例,探讨了将高等代数与解析几何两门课程根据财经类院校的特点进行整合优化的必要性,以理论研究为基础,以充分调研为依据,以学生为主体,以经济管理中问题背景为载体,对这门课程的基本内涵和框架进行有益探索,以处理好代数与几何的知识更新、提高与学生的可接受性之间的矛盾,解决具体内容选取的广泛性与深入性的矛盾。     

关于PerKai多项式

通过对相关Legendre多项式的PerKai多项式的性质的探讨 ,导出了相关Legendre多项式的正交多项式序列的一般形式     

水飞蓟宾提取方法的研究

用超声波法对水飞蓟中水飞蓟宾进行了提取,对提取条件采用正交回归方法进行了设计,将给出的最佳条件用于超声波提取法与热回流提取法进行了对照实验,得出超声波提取法优于热回流提取法的结论。     

佩兰中黄酮类化合物提取工艺的研究

采用超声波法从佩兰中提取黄酮类化合物,通过正交实验研究了最佳提取条件,并建立了佩兰中总黄酮的光谱分析方法.本法的回收率为93.56%-101.50%,相对标准偏差小于0.20%.方法的准确度和精密度均令人满意,而且操作简便易行.     

Vascular architecture:is it a helpful histopathological biomarker for hepatocellular carcinoma?

Hepatocellular carcinoma(HCC) remains one of the major public health problems throughout the world.Although originally associated with tumorigenic processes,liver angiogenesis has also been observed in the context of different liver in-flammatory,fibrotic,and ischemic conditions.Here we investigate the fractal dimension as a quantitator of non-Euclidean two-dimensional vascular geometry in a series of paired specimens of primary HCC and surrounding non-tumoral tissue,and discuss why this parameter might provide additional information regarding cancer behavior.The application of fractal geometry to the measurement of liver vascularity and the availability of a computer-aided quantitative method can eliminate errors in visual interpretation,and make it possible to obtain closer-to-reality numerals that are compulsory for any measurement process.