Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

软起动器的数字控制技术

首先提出了全数字电子软起动器的优势和应用特点,接着描述了软起动器的硬件组成—主回路、检测回路、显示模块、数字控制器,并且简单的介绍了它们在电路中的功能和作用。重点介绍了软件设计中的关键部分—斜坡电压控制算法、限流起动算法和六个晶闸管的顺序触发算法在Intel80C196KC单片机的实现,其中限流起动是用传统的控制方法PID来实现。     

Applications of interval arithmetic in solving polynomial equations by Wu''''s elimination method

Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm.     

大学生口算能力的实验研究

为考察大学生的口算能力,我们随机选取30名大学生为被试进行口算的实验研究,主要结论如下:(1)大学生的口算速率在加、减、乘、除法之间存在差异,从快到慢依次为:除法,借位减法,不借位减法,不进位加法,进位加法,乘法;(2)口算的广度从大到小依次为:不进位的加法广度,进位加法广度,不借位减法广度,借位减法广度,除法广度,乘法广度;(3)大学生口算的速度和广度既无显著的专业差异,也无显著的性别差异.     

A Relationship Among Gentzen's Proof-Reduction,Kirby-Paris' Hydra Game and Buchholz's Hydra Game

We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φ_ω (0) (while that of PA or of Kirby-Paris' Game is φ₁ (0) = ?₀) in the Veblen hierarchy of ordinals.     

Theory and Application of Characteristic Finite Element Domain Decomposition Procedures for Coupled System of Dynamics of Fluids in Porous Media

For a coupled system of multiplayer dynamics of fluids in porous media,the characteristic finiteelement domain decomposition procedures applicable to parallel arithmetic are put forward.Techniques suchas calculus of variations,domain decomposition,characteristic method,negative norm estimate,energy methodand the theory of prior estimates are adopted.Optimal order estimates in L~2 norm are derived for the error inthe approximate solution.     

非线性理论在PID控制器中的应用

近年来，非线性理论在PID控制器中的应用十分迅速和广泛，如将模糊理论、神经网络理论、混沌理论、遗传算法、博实论等一系列非线性理论应用在PID控制器中，形成了模糊、神经网络、基因即遗传、混沌等PID控制器，并广泛应用于复杂的工业过程控制中。本文主要就几种PID控制器研究的现状与存在问题进行了分析。     

GnetFtp搜索引擎的算法设计与实现

剖析了搜索引擎中采用的中文检索与分词技术,提出了新算法GnetFtp,介绍了该算法的基本原理和程序实现工具,并将该算法与其它搜索引擎作了比较.在数据量、功能选项、速度等方面优于国内一般搜索引擎,但落后于百度等知名搜索引擎,仍有较大改进空间.     

一种SPC控制图的优化算法研究

统计过程控制SPC技术是保证预防原则、实现过程控制的科学管理方法,其应用已不再局限于工业领域.传统的单变量SPC控制图虽能反映整个过程的变化趋势,但只对较大的偏差敏感,对持续的、较小的偏差反应迟钝.提出了一种加权控制图的优化算法,这种算法能够反映较小偏差的变化,并以-X-R控制图为例加以比较.