一个Lie代数的子代数及其相关的两类Loop代数

本文构造了Lie代数A2的一个子代数A2,通过选取恰当的基元阶数得到相应的一个loop代数A2,由此设计一个等谱问题,利用屠格式得到了一个新的Liouville可积的Hamilton方程族.作为其约化情形,得到了一个非线性有理分式型演化方程.再由一个矩阵变换,得到了换位运算与A2等价的Lie代数A1的一个子代数A1,将A1再扩展成一个新的高维loop代数G,利用G获得了所得方程族的一类扩展可积系统.     

亚正定矩阵的Kronecker积

研究亚正定矩阵kronecker积的亚正定性,得到了一个充要条件,同时得到Hadamard积亚正定性的一个充要条件.     

半群上条件正定函数的扩张

讨论半群上条件正定函数的扩张问题.得到一个扩张定理.作为应用,得到有界扩张定理和Pontryagin空间上量子力学的一个基本定理.     

E~3中闭曲面上的一个积分公式及其应用

利用Minkowski公式,得到了等距浸入在E3中的闭曲面上的一个有趣积分公式,应用此公式得到了闭曲面的一个特征.     

估计量的优化

全国性的抽样调查若以各省级单位为子总体进行抽样设计,则可得到各省级单位的估计量.若各省级单位再次进行抽样,则可得到另一个估计量.利用这两个估计量构造了一个新的估计量,该估计量的精度优于这两个估计量中的任何一个.     

均匀分布的一个特征

本文先得到一个有关均匀分布的不等式，再进一步证明只有均匀分布具有这一性质，从而得到均匀分布的一个特征．     

R~N拟线性椭圆型方程两个非负解的存在性

该文运用变分方法研究R~N上一类拟线性椭圆型方程,得到一定条件下这类问题的两个非负解的存在性.其中一个解是通过局部极小得到的,另一个是运用山路引理得到的.     

Hardy-Hilbert重级数定理的一个改进

利用Gram矩阵的正定性和Bernoulli不等式得到Holder不等式的一个加强的结果.由此建立了Hardy-Hilbert重级数定理的一个改进.特别,当p=2时,得到了经典的Hilbert重级数定理的一个很强的结果.     

关于一个改进的Hardy-Hilbert不等式

通过建立权系数并利用改进了的Hlder不等式,得到了一个新的改进的Hardy-Hilbert不等式.当p=2时,便得到了经典的Hilbert不等式的一个改进.     

Toda-Smith谱同伦群的具有第六滤子的新非平凡元素族

当p≥7,n≥3时,本文找到一个永久循环 ,它在Adams谱序列中收敛到 的一个非零元素,由Adams分解得到 ,使得 ,进而得到 并且它具有第六滤子．     

An algebraic certificate for Budan’s theorem

The existing algorithms to construct the real closure of an ordered field involve very high complexities. These algorithms are based on Sturm’s theorem which we suspect to be one reason for the complexities since all known proofs of Sturm’s theorem use Rolle’s theorem which is problematic in a constructive context.Therefore we propose to replace the use of Sturm’s theorem by Budan’s theorem. In this paper we present as a first step in this direction an algebraic certificate for Budan’s theorem. An algebraic certificate is a certain kind of proof of a statement. In particular, it is an algorithm which produces, from an arbitrary data in the premise of the statement, explicit (in)equalities which express the conclusion.     

关于图的导出森林独立系统

本文研究图的导出森林独立系统.在这个独立系统中,独立集是指导出子图不含圈的点子集.文中证明了图G的导出森林独立系统是拟阵当且仅当G是块森林.文中同时给出了在强弦图上求最大导出森林的多项式算法.     

Approximation of the eigenvalues of a fourth order differential equation with non-smooth coefficients

The eigenvalues of a fourth order, generalized eigenvalue problem in one dimension, with non-smooth coefficients are approximated by a finite element method, introduced in an earlier work by the author and A. Lutoborski, in the context of a similar source problem with non-smooth coefficients. Error estimates for the approximate eigenvalues and eigenvectors are obtained, showing a better performance of this method, when applied to eigenvalue approximation, compared to a standard finite element method with arbitrary mesh.     

Performance bounds on multiprocessor scheduling strategies for statically allocated programs

In multiprocessors with static allocation of processes to processors, scheduling can be done locally for each processor. The scheduling strategy may have dramatic effect on the execution time of a parallel program. It is an NP-hard problem to find an optimal schedule, and very little is known of how close the heuristic solutions get.The major result here is a theorem stating that if certain program parameters, which can be obtained from an execution of the program on a single-processor, are known, the execution time of the optimal schedule can be calculated within a factor equal to the largest number of border processes on one processor. Border processes are processes which communicate with other processors. The program parameters are obtained using a previously developed tool.Due to the generality of this theorem, the proof is rather complex because it has to cover a large range of situations. The theorem itself, however, is easy to apply, making it possible to compare the performance of different scheduling strategies with the optimal case. The proof also gives important hints on how to design efficient scheduling algorithms for statically allocated programs.     

关于Fuzzy度量点式刻画的一点注记

本文中重新定义由一个点式Ｆｕｚｚｙｐ．ｑ．度量ｄ所诱导的Ｆｕｚｚｙｐ．ｑ．度量｛Ｄｒ｜ｒ＞０｝（代替［１］中的相关重域映射族）．在新的定义下，点式Ｆｕｚｚｙｐ．ｑ．（ｐ．）度量与Ｆｕｚｚｙｐ．ｐ．（ｐ．）度量之间有令人满意的──对应关系．     

Thinking and Turing's test

The questions raised by A. M. Turing in his paper on thought and machines are discussed. Human thought is considered in turn as a concept of normal language usage, as a basic concept of psychology, and as the basis of intellectual activity. It is concluded that neither of these notions of thought identifies something specific that a human being can or cannot do. The imitation game proposed by Turing for deciding whether a machine can think is found to result from an arbitrary empoverishment of the channel of communication between the interrogator and the item under investigation. Turing's notions of thinking are shown to lead to logical difficulties. An alternative view of consciousness, that would place it beyond the reach of any finite test, is finally discussed.     

AHP在师范院校毕业生质量评价中的应用

陶凤梅，杨启昌．ＡＨＰ在师范院校毕业生质量评价中的应用．数理统计与管理，１９９８，１７（４），４～９．本文介绍了运用带概率条件的层次分析法确定师范院校毕业生质量综合评价中各评价指标重要度的方法，建立了师范院校毕业生质量综合评价层次结构     

A Geometrical Proof of Shiota's Theorem on a Conjecture of S. P. Novikov

We give a new proof of Shiota's theorem on Novikov's consecture, which states that the K.P. equation characters Jacobians among all indecomposable principally polarized abelian varieties.     

Cogroups in algebras over an operad are free algebras

Let be an operad defined over a field of characteristic zero. Let R be a cogroup in the category of complete -algebras. In this article, we show that R is necessarily the completion of a free -algebra. We also handle the case of cogroups in connected graded algebras over an operad, and the case of groups in connected graded coalgebras over an operad. Received: August 26, 1996 and final version, February 4, 1998