We proved： Let F be a family of meromorphic functions in a domain D anda α ≠0, b ∈C. If f1（z） - α（f（z））^2 ≠ b, f≠ 0 and the poles of f（z） are of multiplicity ≥ 3 foreach f（z） ∈F, then F is normal in D.
In this paper, we generalize an, inequality of meromorphic mappings to quasimeromorphic ones. Applying the results here, we can establish a normal criterion of quasimeromorphic mappings.
In this paper, Bloch’s principle is discussed and a normal criterion is asserted. If Fis a family of meromorphic functions in domain D, for every function f∈F then F is normal in D.
In this paper, the Bloch principle is discussed and a normal criterion is asserted. Let (?) be a family of meromorphic functions on a domain D, a≠0,∞; b≠∞, n≥4. If for any f ∈(?) there existsf’ - afn≠b, then (...In this paper, the Bloch principle is discussed and a normal criterion is asserted. Let (?) be a family of meromorphic functions on a domain D, a≠0,∞; b≠∞, n≥4. If for any f ∈(?) there existsf’ - afn≠b, then (?) is normal in D.展开更多
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.
In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive intege...In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive integers. For every f ∈ F, all of whose zeros have multiplicity at least (nk+2)/(n-1). If f(f(k))nand g(g(k))nshare z in D for each pair of functions f and g, then F is normal.展开更多
In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers s...In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers satisfying m ≥ n ＋ 2 and d≥k＋1/m-n-1 and a（≠ 0）, b be two finite constants. Suppose that every f∈F has all its zeros and poles of multiplicity at least k and d, respectively. If （fn）（k）-afm and （gn）（k） -agm share the value b for every pair of functions （f, g） of ~, then is normal in D. Our results improve the related theorems of Schwick （Schwick W. Normality criteria for families of meromorphic function. J. Anal. Math., 1989, 52： 241-289）, Li and Gu （Li Y T, Gu Y X. On normal families of meromorphic functions. J. Math. Anal. Appl., 2009, 354： 421-425）.展开更多
In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this ...In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this paper improve some previous results.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
The MohroCoulomb criterion has been widely used to explain formation of fractures. However, it fails to explain large strain deformation that widely occurs in nature. There is presently a new theory, the MEMC, which i...The MohroCoulomb criterion has been widely used to explain formation of fractures. However, it fails to explain large strain deformation that widely occurs in nature. There is presently a new theory, the MEMC, which is mathematically expressed as Meff = （（σ1-σ3） L.sin 2α sin α）/2, where σ1-σ3 represents the yield strength of the related rock, L is a unit length and a is the angle between σ1 and deformation bands. This criterion demonstrates that the maximum value appears at angles of ±54.7° to σ1 and there is a slight difference in the moment in the range of 55°±10°. The range covers the whole observations available from nature and experiments. Its major implications include： （1） it can be used to determine the stress state when the related deformation features formed; （2） it provides a new approach to determine the Wk of the related ductile shear zone if only the ratio of the vorticity and strain rate remains fixed; （3） It can be used to explain （a） the obtuse angle in the contraction direction of conjugate kink-bands and extensional crenulation cleavages, （b） formation of low-angle normal faults and high-angle reverse faults, （c） lozenge ductile shear zones in basement terranes, （d） some crocodile structures in seismic profiles and （e） detachment folds in foreland basins.展开更多
文摘We proved： Let F be a family of meromorphic functions in a domain D anda α ≠0, b ∈C. If f1（z） - α（f（z））^2 ≠ b, f≠ 0 and the poles of f（z） are of multiplicity ≥ 3 foreach f（z） ∈F, then F is normal in D.
基金the National Natural Science Foundation of China (No.198710 64 )
文摘In this paper, we generalize an, inequality of meromorphic mappings to quasimeromorphic ones. Applying the results here, we can establish a normal criterion of quasimeromorphic mappings.
文摘In this paper, Bloch’s principle is discussed and a normal criterion is asserted. If Fis a family of meromorphic functions in domain D, for every function f∈F then F is normal in D.
文摘In this paper, the Bloch principle is discussed and a normal criterion is asserted. Let (?) be a family of meromorphic functions on a domain D, a≠0,∞; b≠∞, n≥4. If for any f ∈(?) there existsf’ - afn≠b, then (?) is normal in D.
文摘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.
文摘In this paper, we study the normality criteria of meromorphic functions concerning shared fixed-points, we obtain: Let F be a family of meromorphic functions defined in a domain D. Let n, k ≥ 2 be two positive integers. For every f ∈ F, all of whose zeros have multiplicity at least (nk+2)/(n-1). If f(f(k))nand g(g(k))nshare z in D for each pair of functions f and g, then F is normal.
文摘In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
文摘In this paper, we consider normality criteria for a family of meromorphic functions concerning shared values. Let F be a family of meromorphic functions defined in a domain D, m, n, k and d be four positive integers satisfying m ≥ n ＋ 2 and d≥k＋1/m-n-1 and a（≠ 0）, b be two finite constants. Suppose that every f∈F has all its zeros and poles of multiplicity at least k and d, respectively. If （fn）（k）-afm and （gn）（k） -agm share the value b for every pair of functions （f, g） of ~, then is normal in D. Our results improve the related theorems of Schwick （Schwick W. Normality criteria for families of meromorphic function. J. Anal. Math., 1989, 52： 241-289）, Li and Gu （Li Y T, Gu Y X. On normal families of meromorphic functions. J. Math. Anal. Appl., 2009, 354： 421-425）.
基金The NSF(11271090) of Chinathe NSF(S2012010010121) of Guangdong Provincethe Graduate Research and Innovation Projects(XJGRI2013131) of Xinjiang Province
文摘In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this paper improve some previous results.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
文摘We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
基金This work is financed by the grants of the National Natural Science Foundation of China （Grant No 40272084, 40472101 and 40572123）.
文摘The MohroCoulomb criterion has been widely used to explain formation of fractures. However, it fails to explain large strain deformation that widely occurs in nature. There is presently a new theory, the MEMC, which is mathematically expressed as Meff = （（σ1-σ3） L.sin 2α sin α）/2, where σ1-σ3 represents the yield strength of the related rock, L is a unit length and a is the angle between σ1 and deformation bands. This criterion demonstrates that the maximum value appears at angles of ±54.7° to σ1 and there is a slight difference in the moment in the range of 55°±10°. The range covers the whole observations available from nature and experiments. Its major implications include： （1） it can be used to determine the stress state when the related deformation features formed; （2） it provides a new approach to determine the Wk of the related ductile shear zone if only the ratio of the vorticity and strain rate remains fixed; （3） It can be used to explain （a） the obtuse angle in the contraction direction of conjugate kink-bands and extensional crenulation cleavages, （b） formation of low-angle normal faults and high-angle reverse faults, （c） lozenge ductile shear zones in basement terranes, （d） some crocodile structures in seismic profiles and （e） detachment folds in foreland basins.
