On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

图形屏幕上的三维度量

本文利用轴测投影原理和性质，阐述了在计算机图形屏幕上如何建立常见的轴测坐标系，给出了在二维的图形屏幕 上进行三维坐标的度量方法以及三维点坐标与二维屏幕默认坐标之间的换算公式，并以一个实例说明这种方法在绘制曲面图形 时的简便与简洁。     

分布交互仿真环境研究

分布交互仿真是一种新兴的仿真技术，分布交互仿真环境的研究具有重人的理论意义和实用价值。本文分析了分布交互仿真环境的功能需求，指出了它的设计原则。     

茴香酸乙酯的合成

从茴香油生产茴香醛的废渣、废液中提取副产品茴香酸，合成茴香酸乙酯。对合成条件进行了研究，取得了满意的结果。     

树与色树

给出了色树的两种性质；（１）色树相关联的两个顶点对应的串是色分划的不同色组对应的串；（２）色树顶点的对应串所含链的上等。并应用构造方法证明了任意树都是以树，从而解决了遗留问题。     

线图求根

给定线图G,如何求得根图H,使G=L(H)?本文就无向图和有向图作出解答.     

有穷长半模偏序集上的一个定理

本文是对参考文献[1]第二章定理14证明的补充和改进。该定理乃指: 定理14.在任何上(或下)半模的有穷长的偏序集内,Jordan-Dedekind链条件成立。 文献[1]中,考虑上半模情形,谈到已知一个连接链:γ∶a=x_0相似文献   

用焓法有限元解相变问题的离散化方法

为了消除应用焓法进行含有相变的有限元传热计算结果呈台阶形的现象,本文作者提出“焓计算单元”和“固相分数”的概念,并将几种一维有限元实施方案的计算结果与精确解对比,说明采用所提出的概念,可以使有限元计算得出更为合理的结果。