In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.
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
In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in un...In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.展开更多
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.
Using Ahlfors’ theory of covering surface and a type-function,we confirm the existence theorem of a Borel radius and a T-radius for the algebroidal function dealing with multiple values in the unit disc,which briefly...Using Ahlfors’ theory of covering surface and a type-function,we confirm the existence theorem of a Borel radius and a T-radius for the algebroidal function dealing with multiple values in the unit disc,which briefly extend some results for the algebroidal functions in the complex plane展开更多
In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality（see[1,4]）of meromorphic functions to algebroid functions.
In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk ...In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.展开更多
In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and ...In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.展开更多
Guided by Lo.Yang＇s method, we concern the question that how algebroid func- tions are determined by their multiple values and deficient values and we prove an at most 3v-valued theorem for algebroid functions. The r...Guided by Lo.Yang＇s method, we concern the question that how algebroid func- tions are determined by their multiple values and deficient values and we prove an at most 3v-valued theorem for algebroid functions. The results are complemented by an example for completeness.展开更多
In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-...In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.展开更多
In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function el...In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.展开更多
In this paper, we prove that for an algebroid function w（z）, the singular direction argz = φ0, satisfying that for arbitrary ε（0 〈 ε 〈 2/π） and any given α ∈ C^^,limr→＋∞ log τ/n（τ,φ0-ε,φ0＋ε,w=a...In this paper, we prove that for an algebroid function w（z）, the singular direction argz = φ0, satisfying that for arbitrary ε（0 〈 ε 〈 2/π） and any given α ∈ C^^,limr→＋∞ log τ/n（τ,φ0-ε,φ0＋ε,w=a）=＋∞ holds with at most; 2v possible exceptional values of a, is the Ncvanlinna direction of w（z）.展开更多
In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we gene...In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping＇s.展开更多
In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theor...In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.展开更多
In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which includ...In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.展开更多
In this paper,we construct k-valued random analytic algebroid functions for the first time.By combining the properties of random series,we study the growth and Bor el points of random analytic algebroid functions in t...In this paper,we construct k-valued random analytic algebroid functions for the first time.By combining the properties of random series,we study the growth and Bor el points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.展开更多
This paper discusses some basic properties of algebroid functions in a subdomain of the complex plane and some similar results (to those in the whole complex plane) and a new situation are showed.
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain...Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金supported by NSFC (10871076,10771011)SRFDP (20050574002)NKBRP (2005CB321902)
文摘In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.
文摘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.
基金supported by NNSF of China(10471048)SRFDP(20050574002)
文摘In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.
基金Sponsored by the NSFC (10871076)the RFDP (20050574002)
文摘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.
基金supported by the National Natural Science Foundation of China (11101096)
文摘Using Ahlfors’ theory of covering surface and a type-function,we confirm the existence theorem of a Borel radius and a T-radius for the algebroidal function dealing with multiple values in the unit disc,which briefly extend some results for the algebroidal functions in the complex plane
基金supported by National Natural Science Foundation of China(1047104810771011)the Fundamental Research Funds for the Central Universities
文摘In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality（see[1,4]）of meromorphic functions to algebroid functions.
文摘In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.
基金supported by NSF of China (11209119511171119+1 种基金11101096)the STP of Education Department of Jiangxi Province,China (GJJ12179)
文摘In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.
基金partially supported by Natural Science Foundation of China(11271227)PCSIRT(IRT1264)
文摘Guided by Lo.Yang＇s method, we concern the question that how algebroid func- tions are determined by their multiple values and deficient values and we prove an at most 3v-valued theorem for algebroid functions. The results are complemented by an example for completeness.
基金The NSF (10471048) of Chinathe Research Fund (20050574002) for the DoctoralProgram of Higher Education
文摘In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.
基金supported by the National Natural Science Foundation of China(11501127)Guangdong Natural Science Foundation(2015A030313628)+1 种基金the Training Plan for Outstanding Young Teachers in Higher Education of Guangdong(Yqgdufe1405)the Open Fund of the National Higher Education Quality Monitoring Data Center(Guangzhou)(G1613)
文摘In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the defi- nition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.
基金supported by NSFC (10471048)NSF of Henan Province in China (112300410300)
文摘In this paper, we prove that for an algebroid function w（z）, the singular direction argz = φ0, satisfying that for arbitrary ε（0 〈 ε 〈 2/π） and any given α ∈ C^^,limr→＋∞ log τ/n（τ,φ0-ε,φ0＋ε,w=a）=＋∞ holds with at most; 2v possible exceptional values of a, is the Ncvanlinna direction of w（z）.
基金supported by the National Natural Science Foundation of China(11201083 and 11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)
文摘In this paper, the authors introduce a kind of reducible algebroid functions, that is general algebroid functions and obtain two fundamental theorems of general algebroid functions. At last, as an application, we generalized a theorem of Li Guoping＇s.
基金Supported by the NNSF of China(10471048)Supported by the Doctoral Foundation of the Education Committee of China(20050574002)
文摘In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.
基金supported by the Natural Science Foundation of China(11871108)Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhai+2 种基金Guangdong Natural Science Foundation(2018A030313954)Guangdong Universities(Basic Research and Applied Research)Major Project(2017KZDXM038)Guangdong Provincical Anti-monopoly Law Enforcement and Big Data Analysis Research Center Project(2019D04)。
文摘In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.
基金The second author was supported by the National Natural Science Foundation of China(11501127)Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(2014KQNCX068)The third author was supported by the Foundation of Guangzhou Civil Aviation College(18X0428).
文摘In this paper,we construct k-valued random analytic algebroid functions for the first time.By combining the properties of random series,we study the growth and Bor el points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.
文摘This paper discusses some basic properties of algebroid functions in a subdomain of the complex plane and some similar results (to those in the whole complex plane) and a new situation are showed.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
