关键词： Nonlinear algebraic equations   conjugate direction methods   optimization   projection algorithms  

摘要： In this paper, it is shown that, when two subclasses of algorithms in the ABSg family are applied to a set of nonlinear algebraic equations, then the convergence is superlinear. The conditions for the theorem to be true are essentially the same as those that apply to the Newton method.

摘要： The powerful concept of Gr?bner bases and an extension of the Buchberger algorithm for their computation have been generalised to enveloping algebras of Lie algebras. Algorithms for the computation of syzygies by use of Gr?bner bases are given. This is the first method which allows the transformation of right fractions into left fractions in the Lie field of any finite dimensional Lie algebra. That enables CAS calculations in Lie fields. An AMP program LIEFIELD has been written for this purpose. Another AMP program SYZYGY produces a generating set of the syzygy module of any finite subset of an enveloping algebra. Examples for both programs are presented for the Weyl algebra and the so(3).

摘要： In this paper we define the binary tree algebraic computation (BTAC) problem and develop an efficient parallel algorithm for solving this problem. A variety of graph problems (minimum covering set, minimum r-dominating set, maximum matching set, etc.) for trees and two terminal series parallel (TTSP) graphs can be converted to instances of the BTAC problem. Thus efficient parallel algorithms for these problems are obtained systematically by using the BTAC algorithm. The parallel computation model is an exclusive read exclusive write PRAM. The algorithms for tree problems run in O(log n) time with O(n) processors. The algorithms for TTSP graph problems run in O(log m) time with O(m) processors where n (m) is the number of vertices (edges) in the input graph. These algorithms are within an O(log n) factor of optimal.

关键词： 光谱分析   数学计算法   掺入杂质法   三标准试样法  

摘要： 本文对“光谱分析中增量法的一种数学计算法”实际应用方面提出两点改进的建议:(一)事先对试样元素含量X作大致准确的估计,再用Z=x,Z=5X作为确定两个增量的大小。(二)用扣除背景并以背景为内标线进行分析。从而使该法得到更为切实的应用。通过在同样操作条件下的比较,得出该法的准确度虽比“三标准试样法”稍低,但比“掺入杂质法”高得多。

关键词： 反正切函数   主值   圆心   arctanz   复变函数   算法   数学基础   数理哲学  

摘要： 这是复变反三角函数研究过程中所写的几篇文章之三。本文为复变反正切函数Arc tan z的主值arc tan z建立了表达式(10)、(11),为Arc tan z建立了新的表达式(12)、(13),然后详尽地研究了函数arc tan z的映射性质。公式(10)、(11)更正了[1]、[2]中有关arc tan z定义方面的错误,并且(10)或(6)、(9)已成了我们构造arc tan z有效算法的数学基础。

关键词： 图算法   对线   取值   图象   对数值   建筑  

摘要： 图象取值实质上是一种图算法,它能够表达两个变量之间的关系,作为最简单的图算形式,在建筑工程中固然具有相当的应用范围,但是它的功能是较低的。例如对于某种建筑材料,确定它的容重值γ,要依据重量W和体积V两个指标,应用以下公式计算:

关键词： 供热系统   供热设备   热力系统   供热方式   热源点   热负荷   双抽机组   供热能力   热力站   凝汽机组   数学模型   试验模型  

摘要： 本文将一般供热系统供热方式优化问题概括为有容量约束的多地点、多设备、多产品的工厂布置问题,构造出相应的混合0-1整数规划模型。对优化模型中涉及的热源费用和供热管网费用的计算方法作了说明。扼要介绍了求解优化模型的反向跟踪分支限界算法。