《画法几何》教学内容的精选

按照“大平台，多方向”教学模式的要求，非机械类专业《工程制图》课程教学应以培养学生具有正确分析形体的形状与位置和一定的图解能力为目标，精选画法几何教学内容，为工程制图打下良好的理论基础。     

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.     

在聋校几何教学中应重视“动”

聋校的几何教学历来是数学教学中的难点,聋生的听力缺陷所导致的抽象思维低下在这类教学中体现得最为明显。在教学中,应通过鼓励学生动手做、动脑想、动口说、动笔画,提高几何教学的效果。     

Quality of geometry instruction and its short-term impact on students' understanding of the Pythagorean Theorem

This article presents findings from a German–Swiss video-based classroom study. The research examines how three basic dimensions of instructional quality impact the development of students' understanding of the Pythagorean Theorem. The study sample comprised 19 German and 19 Swiss mathematics classes. A three-lesson introductory unit on the Pythagorean Theorem was videotaped in all classes. Multilevel analyses revealed both classroom management and cognitive activation to have positive effects on mathematics achievement. The results also provide empirical evidence that cognitive activation and a supportive climate moderate the relationship between mathematics-related interest and mathematics achievement.     

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。     

On numerical calculation in symplectic approach for elasticity problems

The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues, The latter group can be further divided into α- and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed.     

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.     

《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。