逻辑函数在布尔减-除-非代数系统中的标准DOS和SOD展开式

本文首先证明了布尔减、布尔除与非运算构成完备集,并根据布尔减、布尔除与非运算的运算规则和性质,从与或非代数系统中的最小项、最大项展开式出发,推导了任意逻辑函数在减除非代数系统中的标准DOS(减之除)和标准SOD(除之减)展开式。最后举例说明了二个代数系统中展开式之间的转换。本文的工作对进一步完善布尔代数的四则运算理论具有一定的意义。     

基于高斯回归预测的超声成像高分辨率重建

油水两相流过程的可视化检测对多相流研究与石油和化工等工业生产具有重要意义。超声层析成像技术具有非侵入、无辐射、安装方便等优点,在油水两相流检测中有很好的应用前景。针对超声层析成像实现低对比度声学特性的油、水两相介质分布重建问题,提出一种高分辨率图像重建方法。该方法通过构建基于阶段奇异值分解的降维同步代数重建算法,在保证重建精度的同时提高重建速度,并采用高斯回归模型将低分辨率的重建结果转化为高分辨率图像。仿真模拟测试结果表明,该算法重建图像误差小、分辨率较高,能满足实时成像要求。     

实代数数符号判定的一种新算法

根据多元多项式结式、笛卡尔符号法则、多项式实根隔离和实连续函数的性质等理论,给出对任意实代数数进行符号判定的一种新算法.测试实例表明,本文提出的算法还能有效地解决Maple系统中关于浮点数运算的一些缺陷.     

哥德巴赫猜想与素数

布朗提出并证明的命题(9、9)不是哥德巴赫猜想原题，只是一个近似猜想原题的设想，所证结果都是不肯定的。在上世纪七十年代，华罗庚等数学大师就判定筛法不可能证明到命题(1，1)。我们用综合代数法分析证明了哥德巴赫猜想原题，所得结果完全符合原题要求。     

同角三角函数平方关系的变形与应用

从同角三角函数的三个平方关系出发 ,分别从三个数成等差数列和等比数列联想到 6个关系式。然后举例说明这些关系式为我们提供了把某些三角问题转化为代数问题解答的途径 ,并且在解某些题时 ,显得简洁明快。     

关于代数微分方程的超越整解的增长性

研究了如下代数微分方程a(z)f′^2 (b2(z)／f^2 b1(z)f b0(z)f′=d3(z)f^3 d2(z)f^2 d1(z)f d0(z)(这里a(z),bi(z)(0≤i≤2)和dj(z)(0≤j≤3)是多项式)超越整函数解的增长性，这类方程与有名的代数微分方程C（z，w）w′^2 B(z,w)w′ A(z,w)=0(C(z,w)≠0,B(z,w)和A（z，w)是z和w的3个多项式)有紧密的关系．详细地给出了第1个方程的整函数解的增长性与它的3个多项式的次数之间的关系．     

Generalizing in the context of an early algebra intervention (La generalización en el contexto de una intervención algebraica temprana)

ABSTRACT

This study aims to understand the instructional interactions that foster students’ generalizing. By analysing video-recorded lessons from 13 different Grade 3 classrooms in which an early algebra intervention was implemented, activities related to generalizing and students’ generalizing activities were identified, and the nature of the relationships between these activities were explored. Namely, I consider the activities that potentially encourage students’ generalizing and the generalizing that students themselves do, and describe ways in which these activities interact. The findings have both practical and theoretical implications; in the former case, they provide insight into the design of instruction to foster generalizing, and in the latter case, they contribute to an ongoing conversation about students’ mathematics learning.     

Equivalence and relational thinking: preservice elementary teachers’ awareness of opportunities and misconceptions

This study examined awareness of equivalence and relational thinking exhibited by 30 preservice elementary teachers in order to assess their initial preparedness to engage students in these two important aspects of early algebraic reasoning. Findings indicated that preservice teachers collectively demonstrated an awareness of relational thinking both in identifying opportunities offered by tasks to engage students in this thinking and in identifying this thinking in samples of student work. However, in proposing difficulties students might have with selected tasks, few participants demonstrated the understanding that many elementary school students hold misconceptions about the meaning of the equal sign. Implications of these findings for preservice and inservice teacher education are discussed.     

行列式展开法则证明的局限性分析与新证法

在现行《线性代数》教材中,关于行列式按行(列)展开法则推论的证明,基本上采用同一种方法。该证法虽简捷,但却容易使人误认为此证法具有很大局限性,过于特殊,失去了一般性。用计算机程序可简捷明了地证明出此推论的正确性。     

建立概率模型解代数问题

通过建立概率模型，求解数列、排列组合等代数问题。