关于一个超越性定理及其应用

本文对文［1］中一个超越性定理给出另外两个不同的简单证明,并用来证明某些通过在数域上定义的无穷乘积表示的函数在代数点上的值的超越性,从而构造了一些新的超越数.     

On interpolation of a class of functions by a number-theoretic method

In the present paper approximating functions for certain periodic functions in several variables with bounded mixed derivatives are constructed by making use of their values at the knots of some number-theoretic nets. The errors are estimated in theL _q-norm where 1≤q≤∞. This work is supported in part by the Alexander von Humbold Foundation and the National Natural Science Foundation of China     

An arithmetic property of Mahler's series

In the present note the algebraic independence of values of several Mahler series with certain particular and different parameters at algebraic points is established by means of a typical approximation method handling the Liouville type series. This work is supported by the National Natural Science Foundation of China     

用逼近方法建立代数无关性

应用逼近方法建立了一个关于复数代数无关性的一般性判别法则，并用来研究某些缺项级数在代数点和超越点上值的代数无关性．     

On the convergence of sequential number-theoretic method for optimization

1. IntroductionIn the papers [l] and [2] H. Niederreiter and K. McCurley gave a quasi-Monte Carlolnethod for the approxiInate computation of the extreme values of a mu1tivariab1e function.In l989 K.T. Fa11g and Y. Wang["'l proposed a sequential algorithm fOr optinlization bya number-theoretic method (abbr. SNTO), which is nlore effective than the Niederreiter'smethod in some cases, but it lacks a complete convergence result concerlling the a1gorithm.In the present note we will approach…     

从提包挂环说能量法

从提包挂环的形状以及在使用过程中位置的变化出发,说明了任何物体系统都有向能量最低状态转变的趋势. 借助旁证阐述了能量状态转换的条件,引出了物体的变形能和势能的概念,进一步引出了最小势能原理和能量法,介绍了在这方面有贡献的中外科学家. 最后讨论了几种提包挂环的形式.