In this paper,we obtain a normality criterion for families of meromorphic functions concerning‘wandering’shared functions,which generalizes and improves Montel’s criterion and the related results due to Schwick,Xu-...In this paper,we obtain a normality criterion for families of meromorphic functions concerning‘wandering’shared functions,which generalizes and improves Montel’s criterion and the related results due to Schwick,Xu-Fang,Xu-Qiu,and Grahl-Nevo.Also,a normality relationship between two families is given.展开更多
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
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.
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.
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
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
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
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
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
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
Function secret sharing(FSS)is a secret sharing technique for functions in a specific function class,mainly including distributed point function(DPF)and distributed comparison function(DCF).As an important basis for f...Function secret sharing(FSS)is a secret sharing technique for functions in a specific function class,mainly including distributed point function(DPF)and distributed comparison function(DCF).As an important basis for function secret sharing,DPF and DCF are the foundation for the extension of this technique to other more general and complex function classes.However,the function classes corresponding to the current DPF and DCF schemes are almost all unary function classes,and there is no efficient construction for multivariate function classes.The applications of FSS can be extended with the development of a multivariate scheme,e.g.,a multi-keyword private information retrieval scheme can be constructed.To solve this problem,this paper presents a binary DCF scheme based on the“two-layer binary tree”structure.In a binary tree structure,each node computes the seed of its child nodes based on its own seed.The key technique is to realize the transition transfer of seeds by using oblivious transfer,to connect two unary structures.Theoretical analysis and experimental results show that our binary scheme changes from single-round communication in the original definition to multiround communication,and has great advantages in communication cost and computation efficiency.For the security parameterλand input length n,the key size is reduced from to O(λn^(2))to O(λn)In addition,we explore the extensions and applications of the above method.In the batch computation,this paper uses oblivious transfer(OT)extension to realize the one-time transmission of multiple pairs of seeds and optimize its communication efficiency.By extending the structure from“two-layer”to“multi-layer”,a secret sharing scheme of multivariate mixed basic function is proposed based on the serial thought.Furthermore,by employing the parallel thought,a general 2-layer FSS structure from OT for multivariate mixed basic functions is explored to enhance the efficiency,where the first layer is composed of d parallel binary trees with d representing the input dimension,and the second layer is one binary tree of depth d.And the applications of our schemes in multi-keyword private information retrieval are presented.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11471163)。
文摘In this paper,we obtain a normality criterion for families of meromorphic functions concerning‘wandering’shared functions,which generalizes and improves Montel’s criterion and the related results due to Schwick,Xu-Fang,Xu-Qiu,and Grahl-Nevo.Also,a normality relationship between two families is given.
基金Supported by the National Natural Science Foundation of China（l1371149, 11301076, 11201219）
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant No.11961068).
文摘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.
文摘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.
基金the"11.5"Research & Study Programe of SWUST(No.06zx2116)
文摘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.
文摘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.
基金funded by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under grant number 101.04-2014.41the Vietnam Institute for Advanced Study in Mathematics for financial support
文摘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.
基金The test bench was supported by The Future Planning(NRF-2016H1D5A1910536)“Human Resources Program in Energy Technology”of the Korea Institute of Energy Technology Evaluation and Planning(KETEP),granted financial resource from the Ministry of Trade,Industry&Energy,Republic of Korea.(No.20164010200940)The authors would like to thank FONDS DAVID ET ALICE VAN BUUREN and FONDATION JAUMOTTE-DEMOULIN for the funding“Prix Van Buuren-Jaumotte-Demoulin”.
文摘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.
文摘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.
基金supported by the NNSF(11201014,11171013,11126036,11371225)the YWF-14-SXXY-008,YWF-ZY-302854 of Beihang Universitysupported by the youth talent program of Beijing(29201443)
文摘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.
基金supported by National Key R&D Program of China(No.2022ZD0161901)the National Natural Science Foundation of China(Grant No.62072023)+3 种基金Beijing Natural Science Foundation(No.4242024)the Open Project Fund of the State Key Laboratory of Cryptology,China(No.MMKFKT202120)the Exploratory Optional Project Fund of the State Key Laboratory of Complex&Critical Software Environment(No.SKLCCSE-2025ZX-XX)the Fundamental Research Funds of Beihang University,China(Nos.YWF-21-BJ-J-1041 and YWF-23-L-1033).
文摘Function secret sharing(FSS)is a secret sharing technique for functions in a specific function class,mainly including distributed point function(DPF)and distributed comparison function(DCF).As an important basis for function secret sharing,DPF and DCF are the foundation for the extension of this technique to other more general and complex function classes.However,the function classes corresponding to the current DPF and DCF schemes are almost all unary function classes,and there is no efficient construction for multivariate function classes.The applications of FSS can be extended with the development of a multivariate scheme,e.g.,a multi-keyword private information retrieval scheme can be constructed.To solve this problem,this paper presents a binary DCF scheme based on the“two-layer binary tree”structure.In a binary tree structure,each node computes the seed of its child nodes based on its own seed.The key technique is to realize the transition transfer of seeds by using oblivious transfer,to connect two unary structures.Theoretical analysis and experimental results show that our binary scheme changes from single-round communication in the original definition to multiround communication,and has great advantages in communication cost and computation efficiency.For the security parameterλand input length n,the key size is reduced from to O(λn^(2))to O(λn)In addition,we explore the extensions and applications of the above method.In the batch computation,this paper uses oblivious transfer(OT)extension to realize the one-time transmission of multiple pairs of seeds and optimize its communication efficiency.By extending the structure from“two-layer”to“multi-layer”,a secret sharing scheme of multivariate mixed basic function is proposed based on the serial thought.Furthermore,by employing the parallel thought,a general 2-layer FSS structure from OT for multivariate mixed basic functions is explored to enhance the efficiency,where the first layer is composed of d parallel binary trees with d representing the input dimension,and the second layer is one binary tree of depth d.And the applications of our schemes in multi-keyword private information retrieval are presented.
