Babbage’s guidelines for the design of mathematical notations

The design of good notation is a cause that was dear to Charles Babbage’s heart throughout his career. He was convinced of the “immense power of signs” (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage’s writings, for the first time in a systematic way. Babbage’s desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed.     

GDD-P在进位计数制中的应用

以“进位计数制”为测验内容,运用基于多级评分的广义距离法（简记为GDD-P）进行认知诊断,得到被试的属性掌握模式,这不仅验证了可以对多级评分测验进行认知诊断,且提供了一种多级评分认知诊断的应用范例。     

RNA二级结构点括号图与CT文件表示法的相互转换算法研究

由于RNA二级结构表示方法对其功能和相似性的研究具有关键性作用,通过对现有RNA二级结构的各种表示方法进行讨论,重点介绍了点括号图表示法和二级结构平面图文本（CT文件）表示法,给出二者之间的相互转换算法,并通过实例验证了该转换算法准确、有效,可为研究RNA二级结构的相似性提供有效的数据支持.     

Gauss’ quadratic reciprocity theorem and mathematical fruitfulness

This paper presents an account of the fruitfulness of new mathematical calculi in terms of their relationship to existing mathematical methods which is suggested by Carl Friedrich Gauss. This is done by considering some remarks that Gauss made explaining the fruitfulness of new calculi. These can be clarified in the context of his own (very fruitful) theory of congruences, which is considered as a case study for this alternative account. Such an account has the benefit of not being dependent on a particular metaphysical view in the philosophy of mathematics.     

What is a Definition?

According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further examples that suggest many definitions are much more than mere convenient abbreviations. This revised version was published online in July 2006 with corrections to the Cover Date.     

有机化学结构信息的计算机高效表达：化合物骨架的处理与编码

描述了一种能简便而准确地表达有机结构信息的线民生标记处理方法，在高效处理官能团的表达与识别的基础上，进一步研究了化合物骨架的编码与表达，并给出数十种基本骨架的编码。该编码系统具有便于输出输入操作、环境紧凑明Ｌｉａｏ、存贮空间节省，代码直观易辨且完全只取决于结构信息的拓扑性质。     

论音乐记谱法的演进与发展

据历史文献记载,中国最早的谱式是记载在汉代成书的《礼记·投壶》篇中的鼓谱;最具中国传统音乐特点的记谱方式,是集记录音响过程和演奏技法为一体的古琴专用的文字谱和减字谱。在欧洲地区,随着圣咏的传播而发展创立了一套五线谱记谱体系,从而成为当今记录音乐的通用谱式。从音乐记谱法发展史来看,不管是中国还是西方,都经历了较为复杂的发展过程。20世纪音乐数字化的实现,使记谱法呈现出多样化发展的方向,并将在现代科学技术的推动下取得全面而创新的发展。     

灰度积分投影和圆形标记法结合的人眼定位

讨论对于自然光下摄像头采集的人脸照片的眼睛定位算法,该算法是基于灰度积分投影和圆形标记法实现。分为以下三个步骤:首先,在RGB空间下对图像进行肤色检测,得到可能的人脸图像,通过形态学处理排除噪声等干扰;然后,根据亮度分量对人脸区域进行分割,得到五官图,并通过灰度投影对人眼进行粗定位;最后,通过圆形标记法,把区域内的白色空洞转化成面积相等且质心为圆心的圆形,经过几何特征筛选排除干扰圆得到双眼的两个圆形。该算法在Matlab平台上进行仿真实验,结果表明,此算法对于复杂背景下特别是存在类肤色干扰情况时人眼定位效果好、精度高。     

计算机辅助气动系统逻辑设计的研究

对计算机辅助气动系统逻辑设计进行了深入研究，选择逻辑综合的方法作为计算机辅助气动系统逻辑设计的基础理论基本方法，采用立方符号表述逻辑函数，把逻辑运算表示为立方的相交、相容及锐积运算，提出用判断最小项来完成对给定程序的判和校正，进而实现了计算机辅助逻辑综合，得到了的逻辑设计结果。     

基于事件相关电位绝对时间标记法的汽车造型语义评价方法

借助Muse脑电设备,采用绝对时间标记法,探索事件相关电位（ERP）实验的造型评价方法,从而缩短造型设计评估周期,提高企业内部造型设计决策效率。首先通过句尾歧义经典实验范式,验证Muse脑电设备可用于ERP的N400经典实验范式研究,其次进行多模态语义加工研究的复合刺激范式实验,验证Muse脑电设备测试结果。结果表明,Muse脑电设备在对汽车造型语义与文字语义进行测量时,能够准确采集N400成分并进行比较。N400成分可以在特定刺激下反映用户的真实想法,提高汽车造型决策效率,降低造型设计成本。