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NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS SHARING A HOLOMORPHIC FUNCTION AND THE CONVERSE OF THE BLOCH PRINCIPLE 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 FAMILY OF MEROMORPHIC FUNCTIONS SHARING HOLOMORPHIC FUNCTIONS AND THE CONVERSE OF THE BLOCH PRINCIPLE 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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Normality Criteria of Meromorphic Functions Concerning Shared Analytic Function 被引量:1
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作者 YANG QI 《Communications in Mathematical Research》 CSCD 2016年第1期47-56,共10页
In this paper, we use Pang-Zalcman lemma to investigate the normal family of meromorphic functions concerning shared analytic function, which improves some earlier related results.
关键词 meromorphic function entire function shared function normal family
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Torque Sharing Function Control of Switched Reluctance Machines with Reduced Current Sensors 被引量:1
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作者 Wei Peng Johan Gyselinck +1 位作者 Jin-Woo Ahn Dong-Hee Lee 《CES Transactions on Electrical Machines and Systems》 2018年第4期355-362,共8页
This paper presents a Torque Sharing Function(TSF)control of Switched Reluctance Machines(SRMs)with different current sensor placements to reconstruct the phase currents.TSF requires precise phase current information ... This paper presents a Torque Sharing Function(TSF)control of Switched Reluctance Machines(SRMs)with different current sensor placements to reconstruct the phase currents.TSF requires precise phase current information to ensure accurate torque control.Two proposed methods with different chopping transistors or a new PWM implementation require four or two current sensors to replace the current sensors on each phase regardless of the phase number.For both approaches,the actual phase current can be easily extracted during the single phase conducting region.However,how to separate the incoming and outgoing phase current values during the commutation region is the difficult issue to deal with.In order to derive these two adjacent currents,the explanations and comparisons of two proposed methods are described.Their effectiveness is verified by experimental results on a four-phase 8/6 SRM.Finally,the approach with a new PWM implementation is selected,which requires only two current sensors for reducing the number of sensors.The control system can be more compact and cheaper. 展开更多
关键词 Current sensor placement pulse width modulation(PWM) switched reluctance machines torque sharing function
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Normal Families and Shared Functions
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作者 WANG Xue-qin LEI Chun-lin 《Chinese Quarterly Journal of Mathematics》 2015年第2期267-273,共7页
Let k be a positive integer,let h be a holomorphic function in a domain D,h■0and let F be a family of nonvanishing meromorphic functions in D.If each pair of functions f and q in F,f^((k)) and g^((k)) share h in D,th... Let k be a positive integer,let h be a holomorphic function in a domain D,h■0and let F be a family of nonvanishing meromorphic functions in D.If each pair of functions f and q in F,f^((k)) and g^((k)) share h in D,then F is normal in D. 展开更多
关键词 normal families meromorphic functions shared functions
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The Normal Family of Meromorphic Functions Concerning Shared Analytic Function
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作者 YANG Qi YUAN Wen-jun TIAN Hong-gen 《Chinese Quarterly Journal of Mathematics》 2022年第1期26-36,共11页
In this paper,we study the normal criterion of meromorphic functions concerning shared analytic function.We get some theorems concerning shared analytic function,which improves some earlier related results.
关键词 Meromorphic function Shared function Normal family
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Uniqueness of meromorphic functions concerning differential polynomials
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作者 QIAO Lei 《Journal of Chongqing University》 CAS 2007年第2期146-150,共5页
Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials sh... Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem. 展开更多
关键词 meromorphic function sharing value differential polynomia
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DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE
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作者 张继龙 杨连中 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1865-1874,共10页
In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k + 12. If f^n+ af^(k)and ... In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k + 12. If f^n+ af^(k)and g^n+ ag^(k)share b CM and the b-points of f^n+ af^(k)are not the zeros of f and g, then f and g are either equal or closely related. 展开更多
关键词 meromorphic function differential polynomial share value
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Normality Family and Shared Functions by Meromorphic Functions and Its Differential Polynomials
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作者 LU Qian LI Jin Dong 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期541-548,共8页
In this paper, we obtain the following normal criterion: Let F be a family of mero-morphic functions in domain D belong to C, all of whose zeros have multiplicity k + 1 at least. If there exist holomorphic functio... In this paper, we obtain the following normal criterion: Let F be a family of mero-morphic functions in domain D belong to C, all of whose zeros have multiplicity k + 1 at least. If there exist holomorphic functions α(z) not vanishing on D, such that for every function f(z) ∈F, f(z) shares α(z) IM with L(f) on D, then F is normal on D, where L(f) is linear differential polynomials of f(z) with holomorphic coefficients, and k is some positive numbers. We also proved coressponding results on normal functions. 展开更多
关键词 meromorphic functions differential polynomials normal criterion shared functions.
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