针对信息安全专业《近世代数》课程改革的探讨

针对信息安全专业的《近世代数》教学,分析信息安全专业学生与数学专业学生在《近世代数》学习上存在的差异性,并因此提出如何调整《近世代数》的教学内容使其更适合信息安全专业学生的学习,探讨针对信息安全专业《近世代数》学习的教学方法改革,从而提高信息安全专业学生学习《近世代数》的积极性和效果。     

基于申威1621处理器的BLAS一级函数优化

BLAS (Basic Linear Algebra Subprograms)是一个基本线性代数操作的数学函数标准, 该库函数分为三个级别, 每个级别提供了向量与向量(1级)、向量与矩阵(2级)、向量与向量(三级)之间的基本运算. 本文研究了在申威1621处理器上BLAS一级函数的优化方案, 以函数AXPY为例, 充分利用平台的架构特点对其进行性能调优,设计了自动的线程分配方案. 实验结果显示优化过后的BLAS一级函数AXPY相对于GotoBLAS参考实现版本的单核和多核加速比分别高达4.36和9.50, 对于每种优化方式均得到了一定的性能提升.     

研究生“抽象代数”开放课程的建设

分析了抽象代数课程建设中存在的一些问题,介绍了教育信息化背景下抽象代数开放课程的建设,阐述了如何将信息技术渗透到抽象代数课程的建设中。     

Connecting the 3D DGS Calques3D with the CAS Maple

Many (2D) Dynamic Geometry Systems (DGSs) are able to export numeric coordinates and equations with numeric coefficients to Computer Algebra Systems (CASs). Moreover, different approaches and systems that link (2D) DGSs with CASs, so that symbolic coordinates and equations with symbolic coefficients can be exported from the DGS to the CAS, already exist. Although the 3D DGS Calques3D can export numeric coordinates and equations with numeric coefficients to Maple and Mathematica, it cannot export symbolic coordinates and equations with symbolic coefficients. A connection between the 3D DGS Calques3D and the CAS Maple, that can handle symbolic coordinates and equations with symbolic coefficients, is presented here. Its main interest is to provide a convenient time-saving way to explore problems and directly obtain both algebraic and numeric data when dealing with a 3D extension of “ruler and compass geometry”. This link has not only educational purposes but mathematical ones, like mechanical theorem proving in geometry, geometric discovery (hypotheses completion), geometric loci finding… As far as we know, there is no comparable “symbolic” link in the 3D case, except the prototype 3D-LD (restricted to determining algebraic surfaces as geometric loci).     

On the ambiguation of Polish notation

In this paper we study an alternative way of treating Polish notation. Instead of proving unique reading for a well-behaved set of terms, we interpret any string of the alphabet in a monoid that extends, in a specifiable sense, the given algebra of functions.     

事件的持续时间的表示与推理

现实世界中事件的持续时间是难以精确测量的,其起始时刻及结束时刻经常是模糊的。本文用事件的持续函数的概念来表示事件的持续时间,并用有限的近似区间的概念来描述无限的持续函数,应用Heisenberg测不准原理,将Allen的区间代数网络的13种基本时态关系压缩为7种基本时态关系,并构造了新的基本时态关系的复合运算表。     

一种将需求模型转换为软件体系结构模型的方法

需求模型到软件体系结构(SA)模型的转换是软件工程领域的一个研究热点。针对DERM所建立的ACP风格的需求模型,以扩展Petri网风格的SA模型为模型转换的目标,以行为映射为模型转换的依据,提出了一种将需求模型转换为SA模型的方法。首先,讨论了模型转换的整体思路;其次,将行为特征模型中的各个结点转换为SA模型中的构件和连接件,并提出了相应的转换规则;再次,讨论了属性特征模型中主动属性特征的转换,并提出了子系统划分的策略;最后,通过案例研究展示了该方法在从需求模型到SA模型的转换中的有效性。     

Converting SQL queries into relational algebra

We present an algorithm for converting a semantically meaningful SQL query into an equivalent algebraic expression. The relational algebra we employ consists of the following operators: union, intersection, difference, Cartesian product, selection, and projection. The SQL queries we consider can have an arbitrary level of nesting but are restricted in three ways. We assume that they do not contain an ORDER BY or a GROUP BY clause, all SELECTs are in fact SELECT DISTINCTs, and that no aggregate functions are used. The first two assumptions are made in order to remain faithful to the definition of a relation as a set of rows. The last assumption is needed since there is no standard for incorporating aggregate functions into a relational algebra. The research results in this paper will be useful in implementing an SQL user interface for database management systems that internally employ relational algebra. They can also be used in optimizing the evaluation of SQL queries.     

在基于模型诊断中计算最小碰集算法

介绍了基于模型诊断中的计算碰集的算法 ,并分析比较了各算法的效率和计算结果。其中的逻辑型数组算法、递归算法、BHS 树算法、布尔代数算法、GA算法均是笔者近年来研究的结果。     

基于Mining-SEC方法的电路等价性验证

针对时序电路的等价性验证难题,提出基于Mining-SEC的定界等价性验证方法。将待验证时序电路按时间帧展开为多项式符号代数表示的电路集合,利用时间序列数据挖掘方法挖掘其中的不变量和相应的全局约束,不变量可以是任意多项式。此外还可挖掘电路中的不合法约束和复杂的多项式关系,通过以上方法可以明显降低求解空间。使用基于SMT的验证引擎检验电路等价性。实验结果表明,该方法可以快速地实现验证收敛,得到平均1~2个量级的验证加速,并且可以有效消除虚假验证。