In this paper,we study normal families of meromorphic functions.By using the idea in[11],we obtain some normality criteria for families of meromorphic functions that concern the number of zeros of the differential pol...In this paper,we study normal families of meromorphic functions.By using the idea in[11],we obtain some normality criteria for families of meromorphic functions that concern the number of zeros of the differential polynomial,which extends the related result of Li,and Chen et al..An example is given to show that the hypothesis on the zeros of a(z)is necessary.展开更多
In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D , k be a positive integer and a(z) , a 1(z) , a 2(z) , ......In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D , k be a positive integer and a(z) , a 1(z) , a 2(z) , ... , a k(z) be analytic in D such that a(z)0 . If f(z)≠0 and the zeros of f (k) (z)+a 1(z)f (k-1) (z)+...+a k(z)f(z)-a(z) are of multiplicity at least 2 for each f∈F , then F is normal in D . This result improves Miranda s norm...展开更多
In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the nor...In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.展开更多
我们用初等方法证明了Chang等人在Journal of Algebra上发表的文章的主要结果:令p是一个素数,q是p的方幂,F_q是含q个元的有限域.若整数n≥2,则任一个n次首一非零迹的不可约多项式都是F_q上的正规多项式当且仅当n是p的方幂或n是一个不等...我们用初等方法证明了Chang等人在Journal of Algebra上发表的文章的主要结果:令p是一个素数,q是p的方幂,F_q是含q个元的有限域.若整数n≥2,则任一个n次首一非零迹的不可约多项式都是F_q上的正规多项式当且仅当n是p的方幂或n是一个不等于p的素数且q为n的一个原根.展开更多
It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powe...It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grbner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grbner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grbner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.展开更多
文摘In this paper,we study normal families of meromorphic functions.By using the idea in[11],we obtain some normality criteria for families of meromorphic functions that concern the number of zeros of the differential polynomial,which extends the related result of Li,and Chen et al..An example is given to show that the hypothesis on the zeros of a(z)is necessary.
文摘In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D , k be a positive integer and a(z) , a 1(z) , a 2(z) , ... , a k(z) be analytic in D such that a(z)0 . If f(z)≠0 and the zeros of f (k) (z)+a 1(z)f (k-1) (z)+...+a k(z)f(z)-a(z) are of multiplicity at least 2 for each f∈F , then F is normal in D . This result improves Miranda s norm...
文摘In this paper,generalized the ideas of theory of distributions,defined locally convex space depend on operator T,given a new method to change the study of a unbounded operator to a bounded operator, and proved the normal solvability of operator polynomial P (T) on FM space that depend on operator T.
基金supported by the National Natural Science Foundation of China under Grant No.11701370the Natural Science Foundation of Shanghai under Grant No.15ZR1401600
文摘It is one of the oldest research topics in computer algebra to determine the equivalence of Riemann tensor indexed polynomials. However, it remains to be a challenging problem since Grbner basis theory is not yet powerful enough to deal with ideals that cannot be finitely generated. This paper solves the problem by extending Grbner basis theory. First, the polynomials are described via an infinitely generated free commutative monoid ring. The authors then provide a decomposed form of the Grbner basis of the defining syzygy set in each restricted ring. The canonical form proves to be the normal form with respect to the Grbner basis in the fundamental restricted ring, which allows one to determine the equivalence of polynomials. Finally, in order to simplify the computation of canonical form, the authors find the minimal restricted ring.
