关系代数中除法运算的表示

本文主要讨论了用基本运算表示除法运算的关系代数表达式.用图形法作为分析工具,给出了关系代数中除法运算的查询原理,解决了以往用抽象定义进行除法运算的难度,结合实例提出了讲授这些知识点的一些新思路和新方法,取得了较好的教学效果.     

数据库中关系代数除法运算的教学研究

关系代数中的除法运算是数据库课程中的难点问题。文章从关系代数除法运算的定义出发,以实例为牵引,通过类比整数的除法运算,阐明关系代数除法运算的本质,给出除法运算的基本运算表达方法并用SQL语句实现,突破除法运算的难点,以期取得较好的教学效果。     

关系代数中除法运算的教学探讨

从关系代数中除法运算的定义出发,以实例分析和图表表示为工具,通过类比整数的除法运算阐明关系除法运算的本质含义,并给出关系代数中除法运算的基本运算表达式。解决以往除法运算的抽象定义难以被学生理解的不足,促进学生对知识点的透彻理解,取得较好的教学效果。     

关系代数中“除法”运算与SQL中带有exists子查询的对比教学

采用关系代数除法运算与SQL中带有exists子查询的对比教学法。使学生通过实例理解除法运算。加深了对SQL中带有exists子查询的用法,并掌握了两者之间的联系,取得了较好的教学效果。     

基于关系代数运算的数据统计与分析——以场景教学系统数据库为例

关系代数语言是用传统的集合运算和专门的关系运算来表达查询的抽象语言,提供了一系列的关系代数操作,通过这种数学运行来指导数据库在关系操作上的程序实现。场景教学系统中每一个场景对应一个实际应用,场景中设置了问题,本文以系统数据库为例,给出了基于关系代数运算的数据统计分析过程,采用抽取样本法计算期望学习时长和学习时长标准差,并设计了一个测算学习者投入度的公式,对评价场景教学具有指导意义。     

实时数据库系统的时态关系代数

在《实时数据库系统的关系数据模型》一文中建立了实时数据库系统（ＲＴＤＢＳ）的实时关系数据模型（ＲＴＲＤＭ）。本文在ＲＴＲＤＭ模型基础上,详细讨论了ＲＴＤＢＳ的各种时态关系代数运算,而且这些时态关系代数运算是传统数据库系统中各种关系代数运算在ＲＴＲＤＭ上的推广,即当ＲＴＲＤＭ上关系的生命周期为「Ｎｏｗ,Ｎｏｗ」时,ＲＴＲＤＭ上的各种时态关系代数运算将退化为传统数据库下的各种关系代数运算。     

OO代数——一个面向对象的数据库的基本查询模型

本文提出了一个面向对象的数据库系统的基本查询模型－ＯＯ代数，它具有关系代数相似的形式，具有封闭性和远比关系代数强得多的表达能力。文中首先给出了面向对象的数据库系统的数据结构的一种形式化描述－ＯＳＧ，然后ＯＯ代数的五种基本运算：并、差、类间连接、类内选择及广义投影被一一定义，并说明了用关系代数实现这五种运算的方法。     

基于BCDM的含有变量的双时态关系代数研究*

在BCDM(双时态概念数据模型)中,时间变元Now和UC的存在解决了时态记录的频繁更新问题;但是时态变元的存在又给数据库的操作带来某种不确定性甚至是错误,同时引起关系代数运算的歧义。基于BCDM,通过绑定时间变元,用时态映射的集合定义时态关系,由此建立了一种含有时间变元的双时态关系代数体系。该关系代数体系在双时态运算下是封闭的。     

定点DSP中高精度除法的实现方法

各种集成化单片数字信号处理器（DSP）以其功能强、集成度高、应用灵活、性价比高等优点,在信号处理和系统控制中的主导性地位日益明显。许多信号处理和控制需要运用除法运算。一般的数字信号处理器中没有现成的除法指令。十多年前诞生的浮点DSP,由于其用硬件完成浮点数的运算,在数据处理和运算能力上大大超出定点DSP,处理除法运算也比定点DSP更为简单。     

SQL Server环境下交与差运算的设计与实现

针对关系代数中的交与差运算,重点分析了在SQL Server的环境下,如何设计一个通用的SQL查询语句,同时给出了两种运算的实现方法。通过实例验证了所设计的查询语句的有效性,并为更好地理解关系代数运算与SQL语句之间的关系奠定了基础。     

High-performance secure multi-party computation for data mining applications

Secure multi-party computation (MPC) is a technique well suited for privacy-preserving data mining. Even with the recent progress in two-party computation techniques such as fully homomorphic encryption, general MPC remains relevant as it has shown promising performance metrics in real-world benchmarks. Sharemind is a secure multi-party computation framework designed with real-life efficiency in mind. It has been applied in several practical scenarios, and from these experiments, new requirements have been identified. Firstly, large datasets require more efficient protocols for standard operations such as multiplication and comparison. Secondly, the confidential processing of financial data requires the use of more complex primitives, including a secure division operation. This paper describes new protocols in the Sharemind model for secure multiplication, share conversion, equality, bit shift, bit extraction, and division. All the protocols are implemented and benchmarked, showing that the current approach provides remarkable speed improvements over the previous work. This is verified using real-world benchmarks for both operations and algorithms.     

Interval Arithmetic with Containment Sets

The idea of containment sets (csets) is due to Walster and Hansen, and the theory is mainly due to the first author. Now that floating point computation with infinities is widely accepted, it is necessary to achieve the same for interval computation. The cset of a function over a set in its domain space is the set of all limits of normal function values over that set. Csets form a sound basis for defining a number of practical models for interval arithmetic that handle division by zero and related operations in an intuitive and consistent manner. Cset-based systems offer new opportunities for compiler optimization by rearranging interval expressions, achieving tighter bounds by reducing dependencies within the expression. This paper presents basic theory. It discusses division by zero, the case for a global flag to support ``loose' evaluation, performance, and semantics. It presents numerical examples using a trial Matlab implementation.     

装备战时基地级维修作业分工优化

为快速完成装备修理任务,根据装备战时基地级维修的特点,提出了战时基地级装备维修作业分工的数学模型,在多工种多任务维修作业分工问题的基础上给出了带时间窗口的维修作业分工问题求解方案。根据该作业分工模型,利用遗传算法的特性,将问题背景与算法相融合,运用实例进行试验及分析。试验结果表明,本文提出的方法能有效地解决装备战时基地级维修作业分工优化问题。     

Sparse polynomial division using a heap

In 1974, Johnson showed how to multiply and divide sparse polynomials using a binary heap. This paper introduces a new algorithm that uses a heap to divide with the same complexity as multiplication. It is a fraction-free method that also reduces the number of integer operations for divisions of polynomials with integer coefficients over the rationals. Heap-based algorithms use very little memory and do not generate garbage. They can run in the CPU cache and achieve high performance. We compare our C implementation of sparse polynomial multiplication and division with integer coefficients to the routines of the Magma, Maple, Pari, Singular and Trip computer algebra systems.     

Some modified results of the subtraction and division operations on interval neutrosophic sets

An interval neutrosophic set (INS), characterised by the truth, indeterminacy and falsity membership functions, is a powerful structure for handling the uncertain, imprecise and incomplete information existing in the real world in a better way. Under this environment, an attempt is made to define the subtraction and division operations, by imposing some new constrained conditions, after removing the shortcomings of existing operations. The deficiencies of the existing operations are validated through some counterexamples. Further, various desirable properties related to these operations are investigated in detail. Finally, some numerical examples are provided to validate it.     

基于SD数据表示的大数除法VLSI高速实现

在诸如信息安全应用领域中，除法运算特别是大数（多个机器字长整数）除法运算速度是制约公钥密码算法运算速度提高的瓶颈。针对公钥密码算法VLSI实现需要，本文在介绍SD数据表示的基础提出了一种新的大数除法算法，并给出了其VLSI实现逻辑结构。实验结果表明，这种除法器的VLSI实现具有很好的性价比。     

一种新型2-D模板卷积结构的FPGA实现

在实时图像处理过程中,2-D模板卷积是一种重要的操作,FPGA以其特有的全并行处理机制使得这种操作在硬件设计中得以较好的实现。本文提出了一种基于FPGA的模板卷积运算的新方案,相比传统方案,这种方案在结构上能以较少的硬件资源达到相同的流水深度。为了满足系统对实时性的要求,针对某些特定类型的模板,给出了一种简化的卷积器结构,同时,介绍了一种模板归一化除法运算的硬件实现方法。     

On the primitivity of the division of fuzzy relations

 Allowing for flexible queries enables database users to express preferences inside elementary conditions and priorities between conditions. The division is one of the algebraic operators defined in order to query regular databases. This operation aims at the selection of A-elements which are connected with (at least) a given subset of B-elements, e.g., the stores which ordered all the items supplied by a given manufacturer. It is mainly used in the framework of the relational model of data, although it makes sense in object-oriented databases as well. In the relational context, the division is a non-primitive operation which may be expressed in terms of other operations, namely projection, Cartesian product and set difference. When fuzzy predicates appear, this operator needs to be extended to fuzzy relations and this requires the replacement of the usual implication by a fuzzy one. This paper proposes two types of meaning of the extended division and it investigates the issue of the primitivity of the extended operation (i.e., if the division of fuzzy relations is expressible in terms of other operations). The final objective is to decide whether this operator is necessary or not for the purpose of flexible querying and to help the design of a query language supporting flexible queries, among which those conveying a division of fuzzy relations.     

高性能浮点除法和开方的设计与实现

在基于现场可编程门阵列（FPGA）的设计中,低延时、高吞吐量、小面积是3个主要考虑因素。针对以上因素,提出不同基数SRT浮点除法和开方算法,设计基于Virtex—IIproFPGA的可变位宽浮点除法和开方的3种实现方案,包括小面积的迭代实现、低延时的阵列实现和高吞吐量的流水实现。实验结果表明,对于浮点除法和开方算法的流水实现,在综合面积符合要求的基础上,实现频率最高分别可达到180MHz和200MHz以上,证明了该实现方案的有效I陛。     

基于FPGA的快速除法算法设计与实现

介绍了一种新的除法算法,该算法是利用Taylor展开公式的近似,采用两次乘法操作和一张较小的查找表.整个算法采用verilog语言描叙,设计灵活、实现简单.仿真结果表明该算法具备较高的精度与较快的运算速度.