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*-normal Functions on the Plane 认领 引用 被引量：1
1
作者 常建明 《Chinese Quarterly Journal of Mathematics》 2001年第4期55-60,共6页
We introduce a new class of meromorphic functions on the plane, *_ normal functions say, their properties are very similarly as the normal functions in the unit disk and give three necessary conditions in judging it. ... We introduce a new class of meromorphic functions on the plane, *_ normal functions say, their properties are very similarly as the normal functions in the unit disk and give three necessary conditions in judging it. Further we prove that each Julia exceptional function is *_normal and that there exists a *_normal function which has Julia aline. 展开更多
关键词 meromorphic function normal function *_normal function
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Normal Functions Concerning Shared Values 认领 引用
2
作者 WANG XIAO-JING 《Communications in Mathematical Research》 2009年第5期472-478,共7页
In this paper we discuss normal functions concerning shared values. We obtain the follow result. Let F be a family of meromorphic functions in the unit disc A, and a be a nonzero finite complex number. If for any f ∈... In this paper we discuss normal functions concerning shared values. We obtain the follow result. Let F be a family of meromorphic functions in the unit disc A, and a be a nonzero finite complex number. If for any f ∈F, the zeros of f are of multiplicity, f and f′ share a, then there exists a positive number M such that for any f∈F1（1-｜z｜^2） ｜f′（z）｜/1＋｜f（z）｜^2≤M. 展开更多
关键词 snared value normal family normal function
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A computational method for equivalent area distribution characterized by the normal contact behavior of two rough surfaces 认领 引用
3
作者 Linqiang ZHOU Shijie SONG +1 位作者 Hao QU Ji QIAN 《ENGINEERING Structure and Civil Engineering》 SCIE EI CAS CSCD 2026年第3期645-656,共12页
The contact state of surfaces significantly influences the dynamic properties of assemblies,where the contact area is the key parameter to describe the contact state of assemblies.To address the computational challeng... The contact state of surfaces significantly influences the dynamic properties of assemblies,where the contact area is the key parameter to describe the contact state of assemblies.To address the computational challenges associated with contact area distribution,an improved nominal contact area distribution model is proposed for accurately characterizing the contact state of surfaces.Based on the distribution pattern of contact area,a cumulative quantity function for nominal contact area in logarithmic form is established.And its superiority is proved by comparing with two traditional functions.Based on this,a fractal dimension conversion formula was derived to equate the contact of two rough surfaces to the contact of single rough surface,thereby the optimized expression for the nominal contact area distribution function is obtained.The proposed model is verified through actual contact analysis of the anchorage system(anchor plate and anchor base plate).The results show that the proposed cumulative quantity function for nominal contact area and equivalent fractal dimension function exhibit excellent fitting accuracy and feasibility.In the contact between two rough surfaces,the surface with the smaller fractal dimension dominates the contact behavior.The effectiveness and applicability of the proposed model in complex contact problems are verified through case studies.This research provides new theoretical tools for multiscale mechanical analysis of complex contact surfaces,which has important application value in these fields such as precision manufacturing and tribological optimization. 展开更多
关键词 fractal theory rough surface pressure grade equivalent fractal dimension normal contact area distribution function
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Normal Functions and α-Normal Functions 认领 引用 被引量：2
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作者 Yan Xu Department of Mathematics,Nanjing Normal University,Nanjing 210097 P.R.China 《Acta Mathematica Sinica,English Series》 SCIE 2000年第3期399-404,共6页
This paper has studied two open questions about normal functions due to Lappan,and obtained two corresponding results for α-normal functions.
关键词 Spherical derivative Normal function α-Normal function
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ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS 认领 引用 被引量：1
5
作者 RAUNOAULASKARI HEYUZAN ZHAORUHAN 《Chinese Annals of Mathematics,Series B》 SCIE 1996年第2期139-148,共10页
New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.
关键词 Entire function Bloch function Normal function
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Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems 认领 引用 被引量：5
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作者 Bin Zhou Guang-Ren Duan Yun-Li Wu 《International Journal of Automation and computing》 2008年第2期125-131,共7页
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize... In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements. 展开更多
关键词 Second-order descriptor linear systems normal Luenberger functions observer Sylvester matrix equation parametricsolutions
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THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS 认领 引用 被引量：5
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作者 柴富杰 高宗升 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期121-132,共12页
In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent... In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary. 展开更多
关键词 algebroid multifunctions normal families coefficient functions Hausdorff distance
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SOME NORMALITY CRITERIA OF MEROMORPHIC FUNCTIONS 认领 引用 被引量：8
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作者 雷春林 方明亮 曾翠萍 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1667-1674,共8页
Let F be a family of functions meromorphic in a domain D, let n ≥ 2 be a positive integer, and let a ≠ 0, b be two finite complex numbers. If, for each f ∈ F, all of whose zeros have multiplicity at least k ＋ 1, a... Let F be a family of functions meromorphic in a domain D, let n ≥ 2 be a positive integer, and let a ≠ 0, b be two finite complex numbers. If, for each f ∈ F, all of whose zeros have multiplicity at least k ＋ 1, and f ＋ a（f^（k））^n≠b in D, then F is normal in D. 展开更多
关键词 meromorphic function value distribution normal families
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NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS SHARING A HOLOMORPHIC FUNCTION AND THE CONVERSE OF THE BLOCH PRINCIPLE 认领 引用 被引量：7
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作者 姜云波 高宗升 《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1503-1512,共10页
In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based o... In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems. 展开更多
关键词 meromorphic function holomorphic function shared function normal family Bloch principle
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NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS WITH SHARED VALUES 认领 引用 被引量：6
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作者 陈玮 田宏根 扈培础 《Acta Mathematica Scientia》 SCIE CSCD 2016年第1期87-93,共7页
We obtain some normality criteria of families of meromorphic functions sharing values related to Hayman conjecture, which improves some earlier related results.
关键词 meromorphic function shared value normal family
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NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS 认领 引用 被引量：3
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作者 孙道椿 《Acta Mathematica Scientia》 SCIE 2010年第1期166-172,共7页
By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.
关键词 Hausdorff distance meromorphic algebroid functions normality criteria
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Normal Families of Holomorphic Functions Concerning Zero Numbers 认领 引用 被引量：1
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作者 Yang Qi 《Communications in Mathematical Research》 CSCD 2018年第2期97-105,共9页
In this paper, we study the normal families related with a Hayman conjecture of higher derivative concerning zero numbers, and get one normal criteria.Our result improve some earlier related result.
关键词 holomorphic function shared value normal criterion
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Some Normality Criteria for Families of Meromorphic Functions 认领 引用
13
作者 Chen Jun-fan Cai Xiao-hua 《Communications in Mathematical Research》 CSCD 2018年第2期125-132,共8页
Let κ be a positive integer and F be a family of meromorphic functions in a domain D such that for each f ∈ F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least κ + 1. L... Let κ be a positive integer and F be a family of meromorphic functions in a domain D such that for each f ∈ F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least κ + 1. Let α and b be two distinct finite complex numbers. If for each f ∈ F, all zeros of f;-α are of multiplicity at least 2,and for each pair of functions f, g ∈ F, f;and g;share b in D, then F is normal in D. 展开更多
关键词 meromorphic function normal family multiple value shared value
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Normal Families of Zero-free Meromorphic Functions II 认领 引用 被引量：2
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作者 DENG Bing-mao LIU Dan +1 位作者 WANG Xue-qin YA NG De-gui 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第3期438-446,共9页
Let k, m be two positive integers with m ≤ k and let F be a family of zero-free meromorphic functions in a domain D, let h(z) ≡ 0 be a meromorphic function in D with all poles of h has multiplicity at most m. If, fo... Let k, m be two positive integers with m ≤ k and let F be a family of zero-free meromorphic functions in a domain D, let h(z) ≡ 0 be a meromorphic function in D with all poles of h has multiplicity at most m. If, for each f ∈ F, f(k)(z) = h(z) has at most k- m distinct roots(ignoring multiplicity) in D, then F is normal in D. This extends the results due to Chang[1], Gu[3], Yang[11]and Deng[1]etc. 展开更多
关键词 meromorphic function normality shared value
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A Note on Normal Families of Meromorphic Functions and Sharing Set 认领 引用 被引量：1
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作者 XIAO Bing WU Qi-feng YUAN Wen-jun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期360-365,共6页
In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplic... In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D. 展开更多
关键词 entire function normal family meromorphic function share value set
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Normal Families of Holomorphic Functions Concerning Shared a Polynomial 认领 引用 被引量：1
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作者 LIU Zhi-hong LI Ying-chun HUANG Bin 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期394-399,共6页
In this paper,we study normal families of holomorphic function concerning shared a polynomial.Let F be a family of holomorphic functions in a domain D,k(2)be a positive integer,K be a positive number andα(z)be a poly... In this paper,we study normal families of holomorphic function concerning shared a polynomial.Let F be a family of holomorphic functions in a domain D,k(2)be a positive integer,K be a positive number andα(z)be a polynomial of degree p(p 1).For each f∈F and z∈D,if f and f sharedα(z)CM and|f(k)(z)|K whenever f(z)-α(z)=0 in D, then F is normal in D. 展开更多
关键词 holomorphic functions normal family shared values polynomial
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Normality Criteria of Meromorphic Functions Sharing a Meromorphic Function 认领 引用 被引量：1
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作者 Pai YANG Xue WANG Xuecheng PANG 《Journal of Mathematical Research with Applications》 CSCD 2014年第5期543-548,共6页
Let F be a family of meromorphic functions in D, and let ψ（≠ 0） be a meromorphic function in D all of whose poles are simple. Suppose that, for each f ∈ F, f ≠0 in D. If for each pair of functions {f, g} ∩ F, f... Let F be a family of meromorphic functions in D, and let ψ（≠ 0） be a meromorphic function in D all of whose poles are simple. Suppose that, for each f ∈ F, f ≠0 in D. If for each pair of functions {f, g} ∩ F, f′ and g′ share ψ in D, then F is normal in D. 展开更多
关键词 meromorphic function shared values normality criteria.
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NORMAL FAMILY OF MEROMORPHIC FUNCTIONS SHARING HOLOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BLOCH PRINCIPLE 认领 引用 被引量：1
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作者 Nguyen Van THIN 《Acta Mathematica Scientia》 SCIE CSCD 2017年第3期623-656,共34页
In 1996, C. C. Yang and P. C. Hu [8] showed that： Let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n 〉 2, n1,… , nk are nonnegative integers such... In 1996, C. C. Yang and P. C. Hu [8] showed that： Let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n 〉 2, n1,… , nk are nonnegative integers such that n1＋… ＋ nk ≥1; thus fn（f′）n1…（f（k））nk-a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥2. Namely, we prove that fn（f′）n1…（f（k））nk-a（z） has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k≥ 2, and a（z） 0 is a small function of f and n ≥ 2, n1,… ,nk are nonnegative integers satisfying n1＋ …＋ nk ≥1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by d. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y. Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloeh＇s principle. 展开更多
关键词 Normal family Nevanlinna theory meromorphic function sharing function differential pOlynomial
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Some Results on Unicity of Entire Functions Related to Normal Families 认领 引用
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作者 章文华 《Journal of Shanghai Jiaotong university(Science)》 EI 2006年第1期113-115,共3页
This paper studied the connection between normal family and unicity, and proved some results on unicity of entire functions. Mostly, it was proved： Let f be a nonconstant entire function, and let a, c be two nonzero ... This paper studied the connection between normal family and unicity, and proved some results on unicity of entire functions. Mostly, it was proved： Let f be a nonconstant entire function, and let a, c be two nonzero complex numbers. If E（a,f）=E（a,f＇ ）, and f＂（z）=c whenever f＇ （z）=a, then f（z）=Ae^（cz）/u ＋（ac-a^2）/c.The proof uses the theory of normal families in an essential way. 展开更多
关键词 holomorphie function unieity normal family derivative
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Normal Families of Meromorphic Functions and Shared Set 认领 引用
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作者 TIAN Hong-gent CHEN Weit YUAN Wen-jun 《Chinese Quarterly Journal of Mathematics》 2015年第2期159-165,共7页
In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f h... In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m > 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results 展开更多
关键词 meromorphic function shared set normal family
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