实系数高次函数性质研究

本文研究实系数三、四次函数的性质：零点、极值点、拐点的个数;奇偶性;对称中心坐标、对称轴方程,并将其拓广到一般实系数高次多项式函数。     

数学选择题的简捷解题方法探讨

利用轮换对称性的结论,对近几年全国硕士研究生入学统一考试数学试题中选择题的一题多解的分析．寻找具有轮换对称性条件的微积分题型的一种简便解法,从而提高数学选择题的解题速度。     

浅析对称性在数学解题中的应用

自然界中许多事物都呈现对称性,在数学学习和研究中更是如此。重视对称性的应用并且恰当地利用对称性,可以为我们提供解题思路, 帮助我们简化数学中的计算和证明。     

重积分计算中的对称性定理及应用

利用积分区域的对称性和被积函数的奇偶性可以简化二重积分和三重积分的计算,为此,给出基本的、常用的对称性定理,并赋予严格的证明和应用实例.再在此基础上将其推广,使得对称性定理更具有一般性,进而也扩大了它的适用范围.     

对称性与守恒律

本文从对称性入手，阐述了物理操作的对称性的实质即为守恒律，并从系统的机械能对坐标的平移、旋转及时间平移的对称性出发。推导出动量、角动量及机械能守恒律。同时进一步阐述了“对称性破缺”所包含的深远意义。     

Iris Localization Algorithm Based on Improved Generalized Symmetry Transform

Accuracy and fastness of iris localization are very important in automatic iris recognition. A new fast iris localization algorithm based on improved generalized symmetry transform (GST) was proposed by utilizing iris symmetry. GST was improved in three aspects: 1 ) A new distance weight function is defined. The new weight function, which is effective in iris localization, utilized the characteristic of irises that the iris is a circular object and it has one inner boundary and one outer boundary. 2) Each calculation of the symmetry measurement of a pair of symmetry points was performed by taking one point of a pair as the starting point of the transformation. This is the most important reason for fast iris localization, due to which, repetitious computation was largely excluded. 3) A new phase weight function was proposed to adjust GST to locate circle target much better because the inner part of iris is darker than the outer part. The edge map of iris image was acquired and GST was only implemented on the edge point, which decreased computation without loss of accuracy. The modification of distance weight function and phase weight function leads to the accuracy of localization, and other ideass peed up the localization. Experiments show that the average speed of new algorithm is about 7.0-8.5 times as high as traditional ones including integro-differential operator and Hough transform method.     

企业技术联盟的公平分配

企业技术联盟的公平分配是一个综合性概念，它指各联盟成员的个体分配以及成员间分配均处于对称状态。企业技术联盟的公平分配指数能较好地反映各成员的分配结果，故能作为测度分配是否公平的尺度。对于联盟中出现的各种分配失衡现象，成员企业应采取不同的态度与措施。     

对黄金分割及其教育意义的思考

黄金分割是毕达哥拉斯、欧多克斯、欧几里得、斐波那契等许多数学家经过不懈的努力,打造并留给我们的数学遗产.这份遗产,在其它学科也有重要应用.在美学上,它是一条普遍的最具和谐性的形式法则;在哲学上,它与中国两千多年前孔子的“中庸”和合思想遵循同一模式.从数学上看,则表达了对称、协调、再生的思想.数学、自然、美学、哲学、社会、教育之间原是天涯若比邻。     

Problem-Solving Preferences of Mathematics Teachers: Focusing on Symmetry

The aim of the study presented in this paper was to explore factors that influence teachers' problem-solving preferences in the process of (a) solving a problem, (b) explaining it to a peer, (c) liking it, and (d) teaching it. About 170 mathematics teachers took part in the different stages of the study. A special mathematical activity was designed to examine factors that influence teachers' problem-solving preferences and to develop teachers' preferences concerning whether to use symmetry when solving the problems. It was implemented and explored in an in-service program for professional development of high-school mathematics teachers. As a result, three interrelated factors that influence teachers' problem-solving preferences were identified: (i) Two patterns in teachers' problem-solving behavior, i.e., teachers' tendency to apply a stereotypical solution to a problem and teachers' tendency to act according to problem-solving beliefs, (ii) the way in which teachers characterize a problem-solving strategy, (iii) teachers' familiarity with a particular problem-solving strategy and a mathematical topic to which the problem belongs. Findings were related to teachers' developing thinking in solving problems and using them with their students. The activity examined in this paper may serve as a model for professional development of mathematic teachers and be useful for different professional development programs.     

The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry

Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four students in a sophomore-level inorganic chemistry class at a small private university were divided by pre-selected lab groups into two groups, lecture and computer, for introductory information about point group symmetry. Both groups had low prior knowledge of symmetry elements although the lecture group had significantly higher knowledge than the computer group. After initial instruction, the lecture group scored significantly higher than the computer group on a point group assessment, even when prior knowledge was controlled. A second assessment, given after both groups had follow-up information from computer courseware, showed no significant difference between the groups. The computer group significantly improved between the two assessments, the lecture group did not. At the end-of-the semester post-test showed no significant difference between the two groups, although only 50% of the students in each group achieved mastery. Factors affecting the significant improvement of the low prior knowledge, computer group were examined and recommendations for future research provided.