Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring of prime characteristic . Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to ; this theory is then applied in the later sections of the paper to the top local cohomology module of and used to show that, if is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.

     

Monte Carlo模拟中的分立子群近似

本文给出了一种寻找SU(2)群的非阿贝尔分立子群的方法,并讨论了推广到SU(n)群的可能性。     

Harn数字签名方案的改进

Harn数字签名方案中 ,签名者不需计算任何逆 ,验证者只需计算 2个模指数 ,因此相对于其它基于离散对数数字签名方案计算量大大减少。但该方案 ,不能抵抗同态攻击 ,并且随机密钥 k不能重复使用。文章针对该方案的不足 ,提出一种改进方案 ,新方案不但保留了 Harn数字签名计算速度快及容易实现密钥共享等优点 ,而且能够有效抵抗同态攻击 ,并且在随机密钥 k重复使用时能够确保方案的安全性     

关于G逆半群的构造

本文讨论一类重要的半群即Ｇ逆半群,文中给出Ｇ逆半群的主要的几例子,并详尽地讨论了Ｇ逆半群的构造。     

Categories of Projective Geometries with Morphisms and Homomorphisms

Projective geometries studied as Pasch geometries possess morphisms and homomorphisms. A homomorphic image of a projective geometry is shown to be projective. A projective geometry is shown to be Desarguesian iff it is a homomorphic image of a higher dimensional one, which in a sense is dual to the classical imbedding theorem. Semi-linear maps induce morphisms which are homomorphisms iff the associated homomorphisms of skewfields are isomorphisms. Projective geometries form categories with morphisms as well as homomorphisms and Desarguesian ones form a subcategory with Desarguesian homomorphisms.     

关于τ-coneat同态

引入τ－ｃｏｎｅａｔ同态的概念,研究τ－ｃｏｎｅａｔ同态与τ－投射模之间的关系。证明了在一定条件下,Ｍ是τ－投射模当且仅当零同态０→Ｍ是τ－ｏｎｅａｔ。     

中心二面体群与二面体群之间的同态个数

基于群理论中中心二面体群与二面体群的群结构以及元素的性质,利用代数学及数论的相关理论, 计算中心二面体群与二面体群之间的同态个数。作为应用,验证了 T.Asai & T.Yoshida 猜想对此类群成立。     

一类非交换群与二面体群之间的同态个数

计算了一类非交换群与二面体群之间的同态个数。作为应用,验证了这2个群之间的同态个数满足T. Asai和T. Yoshida的猜想。     

余Frame中余Frame同余关系及其应用

在余Frame中或余Frame之间引入了余Frame同余关系和余Frame同态的概念,并对相关性质及应用进行了研究.得到主要结论:余Frame关于余Frame同余关系的商集仍是余Frame; 余Frame同余关系关于余Frame同态的逆仍是余Frame同余关系; 余Frame同态的相关性质.     

On colorings of graph powers

In this paper, some results concerning the colorings of graph powers are presented. The notion of helical graphs is introduced. We show that such graphs are hom-universal with respect to high odd-girth graphs whose (2t+1)th power is bounded by a Kneser graph according to the homomorphism order. Also, we consider the problem of existence of homomorphism to odd cycles. We prove that such homomorphism to a (2k+1)-cycle exists if and only if the chromatic number of the (2k+1)th power of is less than or equal to 3, where is the 3-subdivision of G. We also consider Nešet?il’s Pentagon problem. This problem is about the existence of high girth cubic graphs which are not homomorphic to the cycle of size five. Several problems which are closely related to Nešet?il’s problem are introduced and their relations are presented.