关键词： 逻辑函数   对称式   对偶规则   反演规则   对偶式   逻辑变量   开关函数   开关变量   布尔逻辑   运算法则   基本定理   数学  

摘要： 本文在布尔逻辑数学传统的“逻辑加、乘、否定”三种基本运算法则的基础上,作者根据较长时期的工程实践和理论研究,总结出两种新的运算规律即“逻辑减、除”运算法则,从而导出一系列新的基本定理和转换公式,提出了“逻辑函数图”和“对称性”等逻辑函数的图示方法和基本性质。

关键词： Algorithmic Problem   Algebraic Equivalent  

关键词： 待测元素   增量法   数学计算   黑度   分析线对  

摘要： 本文提出了增量法的一种数学计算方案。在原样中分别加入待测元素的不同增量Z1、Z2(假定Z1

关键词： 工程数学   学科:高等学校   学科:教材   算法语言   计算方法  

ISBN: (纸本)704001260X

摘要： 本书分两篇，这两篇是有机地联系在一起的。第一篇“算法语言”着重体现算法语言是算法的描述工具，为学习第二篇“计算方法”作准备。第二篇介绍电子计算机上的常用算法时，则尽量落实到框图或程序。

关键词： 列向量   列矢量   编译系统   矩阵相乘   算法   定理   机器语言   乘法运算   原根   下界   定义   杂凑函数   计算机科学   数学  

摘要： 近几年来,在计算机科学的研究领域中出现了称之为算法复杂性(Algorithms Comple-xity)的研究,此类工作吸引了许多科学家、学者的注意,也获得了不少成果.为了在短短的文字中谈及它和它与数学的关系,主要还是举例.

关键词： Mathematical Method   Bessel Function   Difference Equation   Mathematical Analysis   Homogeneous System  

摘要： The backward recurrence algorithm of J. C. P. Miller is generalized for homogeneous systems of linear difference equations. Necessary and sufficient conditions for both convergence and stability are given, and the results are demonstrated for scalar equations of arbitrary order. It is shown that the algorithm need not converge to a minimal solution. An application to the calculation of Incomplete Bessel functions is presented. © 1977 Springer-Verlag.

关键词： Feasible Solution   Mathematical Method   Programming Problem   Computational Result   Mathematical Programming  

摘要： Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and related structures which may be exploited by algorithms designed to solve them *** steps of an algorithm which by repeated application reduces the rows, columns, and bounds in a problem matrix and leads to the freeing of some variables are first presented. The ‘unbounded solution’ and ‘no feasible solution’ conditions may also be detected by this. Computational results of applying this algorithm are presented and *** algorithm to detect structure is then described. This algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized. Comparisons of computational results of applying different heuristics in this algorithm are presented and discussed.

关键词： Number Theory   Algebraic Geometry   Topological Group   Number Field   Algebraic Number  

关键词： Integers   Algorithms   Optimal solutions   Algebra   Integer programming   Inequality constraints   Lexicography   Simplex method   Prior knowledge  

摘要： This paper develops an algorithm for pure integer programming problems. It first transforms the integer programming problem to an algebraically equivalent Hermite canonical problem, and then employs the Fourier-Motzkin elimination. These algebraic operations transform the problem into a form that leads to an efficient implicit enumeration scheme to calculate an optimal solution. The algorithm constructs, in a finite number of operations, an optimal solution to an integer program with n variables and n or n + 1 inequality constraints. If the original problem has more than n + 1 constraints, then the integer program with only the constraints that are binding at an optimal linear programming solution is solved in place of the original problem. Computational results are presented.

关键词： Algorithms   Mathematical vectors   Trial de novo   Objective functions   Linearization   Approximation   Directional derivatives   Lagrange multipliers   Optimal solutions  

摘要： Part I of this paper presented a method for primal decomposition of large convex separable programs into a sequence of smaller subproblems. In this part, additional theory and development of a parametric subproblem-solution and step-size-determination technique completes the algorithm. A previously unsolved problem in the operations-research literature, the generalized modular design problem of Evans [Opns. Res. 18, 562–4 (1970)] is solved by the algorithm and numerical results provided.