The symmetry of the CS condition on one-sided ideals in a prime ring

Let R be a prime ring and e∈R be an idempotent. We show that eR_R is nonsingular, CS and if and only if is nonsingular, CS and .     

Generalization ofP-hypergroups

Si definiscono e si studiano larghe classi di ipergruppi derivanti da comuni semi-gruppi.     

Lawson-Hoffmann对偶定理的推广

本文讨论了Z－连续偏序集的一系列性质，主要证明了Z－连续偏序集范畴对偶等价于完全分配格范畴的一个满子范畴．     

辛甫生公式的推广

给出了具有3次代数精度的条件,对辛甫生求积公式进行了推广,利用待定系数方法推导出了一般性的公式,并从该推广的方法导出了三点高斯公式.     

广义分段Koszul代数

广义分段Koszul代数(简称为κ_p代数)一般是一类二次代数,其平凡模允许有非单纯的投射分解.利用Yoneda-Ext代数E(A)给出了分次代数A是κ_p代数的一个充分条件,同时讨论了κ_p代数的商代数是否继承κ_p性质.     

广义分段Koszul代数

广义分段Koszul代数(简称为K_p代数)一般是一类二次代数,其平凡模允许有非单纯的投射分解.利用Yoneda-Ext代数E(A)给出了分次代数A是K_p代数的一个充分条件,同时讨论了K_p代数的商代数是否继承K_p性质.     

Goodman公式的推广

1959年,Goodman发现了任一p阶图中k₃与k₃的个数之和,即f₃,仅是顶点的度d_i的函数之和（1≤i≤p）.人们总企图求得k₄的个数与k₄个数之和的公式f₄.首先,证明f₄并不仅是d_i的函数之和（1≤i≤p）;然后,求了f₄的公式,但它们还依赖一个自同构图c₁₁.     

Generalization of Chebyshev polynomials

Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 1, pp. 217–218, January–February, 1990.     

Generalization of hermite polynomials

A generalization of the Hermite polynomials is given. Some relations which let one construct orthogonal Hermite polynomials successively are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1524–1528, November, 1990.     

Generalization of Regular Modules

We study generalizations of regular modules by Ramamurthy and Mabuchi. These are also generalizations of fully right idempotent and fully left idempotent rings, respectively. We also define and study the properties of *-weakly regular modules, a generalization of fully idempotent rings.     

A Generalization of C—semigroup

§ 1.ＴｈｅＧｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐ　Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｌｅｔＸｂｅａＢａｎａｃｈｓｐａｃｅ,ａｎｄＢ(Ｘ)ｔｈｅｓｐａｃｅｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｉｎｔｏＸ .　Ｄｅｆｉｎｉｔｉｏｎ 1 .1　ＳｕｐｐｏｓｅＣｉｓａｂｏｕｎｄｅｄｉｎｊｅｃｔｉｖｅｏｐｅｒａｔｏｒｆｒｏｍＸｉｎｔｏＸ .Ｔｈｅｆａｍｉｌｙｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓ (Ｓ(ｔ) ) ｔ≥ 0 ｉｓａｇｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐｉｆｉｔｈａｓｔｈｅｆｏｌｌｏｗｉｎｇ…     

HX环的推广

在文[1,2]的基础上推广了HX环,提出了弱HX环的概念,并重新讨论了拟商环。证明了在正则条件下拟商环与弱HX环的统一性;同时也得到了一致弱HX环与普通商环的关系。     

辛普生公式的推广

推广了数值积分中著名的辛普生公式,讨论了中值点的渐近性.     

三角函数的推广

利用函数方程定义仿正切函数类,再用仿正切函数定义仿正、余弦函数类,并对这些函数类进行研究.所定义的函数类中的函数具有通常三角函数的性质及运算规律,故而可将其作为三角函数的某种推广.通过实例证实.了通常的正切函数其实是仿正切函数的一种解析延拓.     

Toeplitz定理的推广

本文将Ｔｏｅｐｌｉｔｚ定理推广到函数情形，为证明和计算一类函数极限提供了一种方法。     

Generalization of analytic functions

The concept of analyticity for complex functions on time scale complex plane was introduced by Bohner and Guseinov in 2005. They developed completely delta differentiability, delta analytic functions on products of two time scales, and Cauchy-Riemann equations for delta case.In this research paper we study on continuous, discrete and semi-discrete analytic functions and developed completely nabla differentiability, nabla analytic functions on products of two time scales, and Cauchy-Riemann equations for nabla case.     

Generalization of quasi-Koszul algebras

In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and K p algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of K p algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-K p algebra.