ON THE GENERALIZED GLAISHER－HONG‘S CONGRUENCES

51. Notations and IntroductionListed below are some general notations which wi1l be used thIoughout this note:pea prime number greater than 3,cl l, mt r, s E N,(:) = n!/(kl(n -- k)!)--the binomial coefficient,Bk--the kth Bernoulli number in the "even suthe" notation, e.g., Bo = 1, B1 =--1/2, B2 = 1/6, B3 = 0,',B.(x) = Z (:)Bkx"--*--the Bernoulli polynomial.k=0As is known, the Bernoulli numbers are defined by the symbolic recurrence relationB.+l = (B + 1)"+', n = 1, 2,', Bo = l, whic…     

Lusternik-Schnirelmann 定理的推广

本文根据Brouwer映射度的理论和微分拓扑的基本方法推广了Lusternik_Schnirelmann定理     

中国科学院新增选学部委员简介

<正> 1933年1月生,国家地震局地质研究所研究员,任国家地震局地质研究所所长,中国力学学会地球动力学直属专业组成员.1978年被授予全国劳动模范称号,1986年被国家科委批准为国家级有突出贡献的中青年科技专家,1989年获得首届李四光地质科学奖,博士生导师.     

一类格序半群的同余

本文讨论了一类可换格序半群的同余性质。给出了这类格序半群同余的表示和同态分解定理。这个结论一般化了［１］和［２］中的结果。     

同核RELAY相干传递技术在复杂天然有机化合物1H谱解析中的应用

用同核化学位移相关谱和同核RELAY谱等二维NMR方法完全归属了复杂天然有机化合物人参皂甙Rb₁的¹H NMR谱线,并用积算符方法证实一级和二级RELAY实验中观察到的意外交叉峰是通过远程偶合传递的RELAY信号。     

关于二次规划问题分段线性同伦算法的改进

本文利用Ｃｈｏｌｅｓｋｙ分解，Ｇａｕｓｓ消去等技术和定义适当的同伦映射，将关于二次规划问题的分段线性同伦算法加以改进，改进后的算法，对于严格凸二次规划来说，计算效率与Ｇｏｌｄｆａｒｂ－Ｉｄｎａｎｉ的对偶法相当。     

Order Environments of Topological Spaces

In this paper it is proved that a space may be realized as the set of the maximal elements in a continuous poset if and only if it is Tychonoff.     

NOTES ON GLAISHER＇S CONGRUENCES

Let p be an odd prime and let n≥1,k≥0 and r be integers,denote by Bk the kth Bernoulli number,It is proved that(i) If r≥1 is odd and suppose 1≥r+4,then ∑j=1^p-1 1/(np+j)^r=-(2n+1)r(r+1)/2(r+2)Bp-r-2p^2(mod p^3).(ii)If r≥2 is even and suppose p≥r+3, then p-1∑j=1 1/(np+j)^r=r/r+1Bv-r-1p(mod P^2).(iii) p-1∑j=1 1/(np+j)p-2=-(2n+1)p(mod P^2).This result generalizes the Glaisher‘s congruence. As a corollary, a generalization of the Wolsten-holme‘s theorem is obtained.