On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

Ａｓｉｓｋｎｏｗｎ ,ｉｔｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｔｏａｐｐｒｏｘｉｍａｔｅｕｎｂｏｕｎｄｅｄｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓ,ｅｓｐｅｃｉａｌｌｙｔｈｏｓｅｄｅｆｉｎｅｄｏｎａｌａｒｇｅｒａｎｇｅ .Ａｎｅｆｆｅｃｔｉｖｅｍｅｔｈｏｄｃａｌｌｅｄｔｈｅｍｅｔｈｏｄｏｆｍｕｌｔｉｐｌｉｅｒ ｅｎｌａｒｇｅｍｅｎｔｈａｓｂｅｅｎｐｕｔｆｏｒｗａｒｄｂｙＬ .Ｃ .ＨｓｕａｎｄＲ .Ｈ .Ｗａｎｇ[1— 3].Ｔｈｉｓｍｅｔｈｏｄｗａｓｇｒｅａｔｌｙｄｅｖｅｌｏｐｅｄｉｎ [4,5] .Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅ…     

Uniformly Most Powerful Invariant Test and Its Application

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＣｏｎｓｉｄｅｒｔｈｅｍｕｌｔｉｎｏｒｍａｌｄｉｓｔｒｉｂｕｔｉｏｎＮ(μ ,Σ) .Ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔ,ｕｎｄｅｒｔｈｅｌｏｓｓｆｕｎｃｔｉｏｎＬ(ｄ ,μ) =(ｄ -μ) (ｄ -μ)′,ｔｈｅｅｓｔｉｍａｔｏｒｓｏｆμｏｆｔｈｅｆｏｒｍａ1 Ｘ ,ｗｈｅｒｅａ1∈ (0 ,1 ) , Ｘｉｓａｓａｍｐｌｅｍｅａｎ ,ａｒｅｂｅｔｔｅｒｔｈａｎｔｈｅｌｉｋｅｌｉｈｏｏｄｅｓｔｉｍａｔｏｒ Ｘｉｆａｎｄｏｎｌｙｉｆｎμ′Σ- 1μ≤Ｃ1(1 )ｗｈｅｒｅＣ1=1 +ａ11 -ａ1ａｎｄｎｉｓｔｈｅｎｕｍ…     

Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＩｎｔｈｉｓｐａｐｅｒｗｅｕｓｅｔｈｅｓｔａｎｄａｒｄｎｏｔａｔｉｏｎｓｏｆｔｈｅＮｅｖａｎｌｉｎｎａｔｈｅｏｒｙｏｆｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓｏｒａｌｇｅｂｒｏｉｄｆｕｎｃｔｉｏｎｓ.Ｆｏｒｒｅｆｅｒｅｎｃｅｓｅｅｅ.ｇ.[1 ] .　Ｃｏｎｓｉｄｅｒｔｈｅｇｅｎｅｒａｌｉｚｅｄｈｉｇｈｅｒ ｏｒｄｅｒａｌｇｅｂｒａｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎΩ1(ｚ,ｗ)Ω2 (ｚ,ｗ) =Ｐ(ｚ,ｗ)Ｑ(ｚ,ｗ) , ( 1 )ｗｈｅｒｅΩ1(ｚ,ｗ) =∑…     

ON A CLASS OF NONLINEAR UNIFORM APPROXIMATION PROBLEMS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＸｂｅａｃｏｍｐａｃｔＨａｕｓｄｏｒｆｆｓｐａｃｅ ,ｗｉｔｈＣ(Ｘ)ｔｈｅｓｐａｃｅｏｆｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓｄｅｆｉｎｅｄｏｎＸ ,ａｎｄｌｅｔＭ Ｃ(Ｘ)ｂｅｎｏｎｅｍｐｔｙ.ＬｅｔＦ(ｘ ,ｙ) :Ｘ×Ｒ →Ｒｂｅａｎｏｎ ｎｅｇａｔｉｖｅｆｕｎｃｔｉｏｎ ,ａｎｄｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｍｉｎｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｆｉｎｄｙ∈Ｍｔｏｍｉｎｉｍｉｚｅ‖Ｆ(.,ｙ )‖ ,(1)ｗｈｅｒｅ‖Ｆ (.,ｙ )‖ =ｓｕｐｘ∈ＸＦ(ｘ ,ｙ(ｘ) ) .Ｔｈｅｍ…     

Zero-free Regions for Dirichlet L-functions and the Exceptional Set of Goldbach Numbers

Ｚｅｒｏ－ｆｒｅｅＲｅｇｉｏｎｓｆｏｒＤｉｒｉｃｈｌｅｔＬ－ｆｕｎｃｔｉｏｎｓａｎｄｔｈｅＥｘｃｅｐｔｉｏｎａｌＳｅｔｏｆＧｏｌｄｂａｃｈＮｕｍｂｅｒｓＬｉＨｏｎｇｚｅ（李红泽）ＭＲ（１９９１）ＳｕｂｊｅｃｔＣｌａｓｉｆｉｃａｔｉｏｎ：１１Ｎ１３，１...     

NORMAL FORMS OF INTEGRABLE SYSTEMS AT A RESONANT SADDLE

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄｔｈｅＲｅｓｕｌｔＣｏｎｓｉｄｅｒａｐｌａｎａｒａｎａｌｙｔｉｃｓｙｓｔｅｍｏｆｔｈｅｆｏｒｍｘ＝Ｐ（ｘ，ｙ），ｙ＝Ｑ（ｘ，ｙ），（１．１）ｗｈｅｒｅＰａｎｄＱａｒｅａｎａｌｙｔｉｃｆｕｎｃｔｉｏｎｓｉｎ（ｘ，ｙ）ｉｎ...     

ON THE STRUCTURES OF RANDOM MEASURE AND POINT PROCESS CONVOLUTION SEMIGROUPS

§0.ＩｎｔｒｏｄｕｃｔｉｏｎＫｅｎｄａｌｌ[1]ｆｏｕｎｄｅｄｔｈｅＤｅｌｐｈｉｃｓｅｍｉｇｒｏｕｐｔｈｅｏｒｙａｎｄｕｓｅｄｔｈｉｓｔｈｅｏｒｙｔｏｓｔｕｄｙｔｈｅｓｔｒｕｃｔｕｒｅｓｏｆｔｈｅｒｅｎｅｗａｌｓｅｑｕｅｎｃｅｓｅｍｉｇｒｏｕｐａｎｄｔｈｅｓｔａｎｄａｒｄｐ-ｆｕｎｃｔｉｏｎｓｅｍｉｇｒｏｕｐ.Ｄａｖｉｄｓｏｎ[2,3],ＲｕｚｓａａｎｄＳｚ啨ｋｅｌｙ[4]ａｎｄＨｅ[5,6]ｇｅｎｅｒａｌｉｚｅｄｔｈｅＤｅｌｐｈｉｃｓｅｍｉｇｒｏｕｐｔｈｅｏｒｙａｎｄｕｓｅｄｔｈｅｉｒｒｅｓｕｌｔｓｔｏｓｔｕｄ…     

Inverse Limit of Spaces of Upper Semicontinuous Functions

ＳｕｐｐｏｓｅｔｈａｔＸｉｓａｃｏｍｐａｃｔＨａｕｓｄｏｒｆｆｓｐａｃｅ,ａｎｄＵ(Ｘ)ｄｅｎｏｔｅｓｔｈｅｓｅｔｏｆａｌｌｔｈｅｕｐｐｅｒｓｅｍｉｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓｆｒｏｍＸｔｏ [0 ,1 ] .ＴｈｅｎＵ(Ｘ)ｉｓａｃｏｍｐｌｅｔｅｌａｔｔｉｃｅｕｎｄｅｒｔｈｅｐｏｉｎｔｗｉｓｅｏｒｄｅｒｉｎｇ ,ａｎｄｉｔｓｏｐｐｏｓｉｔｅｌａｔｔｉｃｅＵ(Ｘ) ｏｐｉｓａｃｏｎｔｉｎｕｏｕｓｌａｔｔｉｃｅ .ＴｈｕｓＵ(Ｘ)ｅｎｄｏｗｅｄｗｉｔｈｔｈｅｌｉｍ ｉｎｆｔｏｐｏｌｏｇｙｏｎＵ(Ｘ) ｏｐ,ｗｈｉｃ…     

伪辛群的Carter子群

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｉｎ 1 961Ｃａｒｔｅｒ[1]ｐｒｏｖｅｄｔｈａｔｉｎａｎｙｆｉｎｉｔｅｓｏｌｖａｂｌｅｇｒｏｕｐＧｔｈｅｒｅｅｘｉｓｔｓｓｅｌｆ ｎｏｒｍａｌｉｚｉｎｇｎｉｌｐｏｔｅｎｔｓｕｂｇｒｏｕｐｓ (Ｃａｒｔｅｒｓｕｂｇｒｏｕｐｓ) .ＴｈｅｃｏｎｃｅｐｔｏｆＣａｒｔｅｒｓｕｂｇｒｏｕｐｓｃｏｍｅｓｆｒｏｍｔｈｅｃｏｎｃｅｐｔｏｆＣａｒｔａｎｓｕｂａｌｇｅｂｒａｉｎＬｉｅａｌｇｅｂｒａ ,ｓｏｔｈｅｓｔｕｄｙｏｆＣａｒｔｅｒｓｕｂｇｒｏｕｐｓｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｉｎｇｒｏｕ…     

On Theorem of the “Mountain Impasse” Type

ＬｅｔＦ（ｕ），Ｇ（ｕ）ｂｅＣ１－ｆｕｎｃｔｉｏｎａｌｓｏｎａＨｉｌｂｅｒｔｓｐａｃｅＨａｎｄｓｕｐｕ∈ＨＦ（ｕ）＝∞．ＬｅｔＫｂｅａｃｏｍｐａｃｔｍｅｔｒｉｃｓｐａｃｅａｎｄｌｅｔＫｂｅａｎｏｎ－ｅｍｐｔｙｃｌｏｓｅｄｓｕｂｓｅｔ≠Ｋ，ｐ∈Ｃ（Ｋ；Ｈ）．ＤｅｎｏｔｅＦＲ＝｛ｕ∈Ｈ｜Ｆ（ｕ）Ｒ｝；　　　　　　ΦＲ＝｛ｐ∈Ｃ（Ｋ；ＦＲ）｜ｐ＝ｐｏｎＫ｝；ｃ（Ｒ）＝ｉｎｆｐ∈ΦＲｍａｘξ∈ＫＧ（ｐ（ξ））；ｃ０＝ｍａｘξ∈ＫＧ（ｐ（ξ））；Φ∞＝｛ｐ∈Ｃ（Ｋ；Ｈ）｜ｐ＝ｐｏｎＫ｝；…     

Picard values and the growth of meromorphic functions

The purpose of this paper is to investigate the growth of meromorphic functions concern- ing Picard values with a radially distributed value. This generalizes a classic result due to Hayman [Hayman, W. K.： Picard values of meromorphic functions and their derivatives. Ann. of Math., 70, 9-42 （1959）].     

涉及Picard例外值的亚纯函数正规族

本文研究了徐炎等人在文(Xu Y,Wu F Q,Liao L W.Picard values and normal families of meromorphic functions,Proc.R.Soc.Edinburgh,2009,139:1091-1099.)中提出的一个有关亚纯函数正规族猜想,得到了两个正规定则...     

关于具有四个分担值的亚纯函数的唯一性

对具有四个分担值的亚纯函数的唯一性进行了研究,得到：如果两个非常数的亚纯函数具有四个判别的IM分担值,那么要么这两个函数CM分担这四个值,要么这两个函数的这些值的密指量（计数函数）满足不一等式。     

Borel's directions and shared values

In this article, we study the problems of Borel's directions of meromorphic functions concerning shared values and prove that if two meromorphic functions of infinite order share three distinct values, their Borel's directions are same.     

角域内亚纯函数的唯一性定理

该文研究了复平面上的亚纯函数在角域内分担两个集合的唯一性,将仪洪勋和林伟川最近得到的复平面上的亚纯函数在全平面上分担两个集合的唯一性定理中的在全平面上分担两个集合的条件改成在角域内分担两个集合,得到了几个唯一性定理.     

Small functions and weighted sharing three values

This article studies the problem of the uniqueness of meromorphic functions that weighted sharing three values which improve some results given by Yi [Theorem 4, Yi, H.X., 1995, Unicity theorems for meromorphic functions that share three values. Kodai Mathematical Journal, 18, 300-314] and Ueda [Ueda, H., 1983, Unicity theorems for meromorphic or entire functions II. Kodai Mathematical Journal, 6, 26-36] and other authors. An application of these new results, if f and g are two distinct nonconstant meromorphic functions sharing 0, 1 and CM, and a is a nonconstant rational function, then N2)(r,1/(g-a))= [image omitted] An example shows that the latter result is not true for some transcendental small functions of f and g.     

与其导数具有分担值的亚纯函数唯一性

为进一步丰富亚纯函数唯一性理论,寻求更佳的唯一性条件,利用亚纯函数Nevanlinna理论更精确地估计亚纯函数的n重值点的计数函数,得到两个亚纯函数与其导数具有某些分担值时的唯一性定理,推广和改进了相关文献的相关结果.     

Normality of meromorphic functions with multiple zeros and shared values

In this paper, we study the normality of a family of meromorphic functions and general criteria for normality of families of meromorphic functions with multiple zeros concerning shared values are obtained.     

On differential polynomials, fixpoints and critical values of meromorphic functions

We prove some results concerning functions ? meromorphic of finite lower order in the plane, such that ??″?α(?′)² has few zeros, where α is a constant, using in part new estimates for the multipliers at fixpoints of certain functions. We go on to consider zeros of derivatives and the minimal lower growth of meromorphic functions with finitely many critical values.     

分担函数集的正规定则

本文将亚纯函数正规性与分担函数集相结合,探讨了亚纯函数族F正规与F中任意两个函数f与g分担函数的个数,f与其导数f'分担函数的个数及函数f的重值的个数三者之间的关系,给出了一个综合判定亚纯函数族正规的充分条件.