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
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, 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
In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
Liquid core reduction(LCR)technology,originally developed for continuous thin-slab casting,allows space for a submerged entry nozzle in a mold while improving production efficiency.Recent experimental attempts explore...Liquid core reduction(LCR)technology,originally developed for continuous thin-slab casting,allows space for a submerged entry nozzle in a mold while improving production efficiency.Recent experimental attempts explore the implementation of LCR in regular slab casting processes.However,regular slabs(2–3 times thicker than thin slabs)face critical challenges in terms of excessive deformation and stress concentration under external forces,which induce intermediate cracks and thus hinder successful LCR adoption in regular slab production.This study evaluates the feasibility of LCR for producing regular slabs and identifies optimal reduction parameters to prevent crack initiation.A three-dimensional thermal–mechanical coupled model is proposed using the finite element method(FEM),integrated with the equivalent replacement liquid steel(ERLS)method and the normalized Cockcroft–Latham damage model,to achieve quantitative prediction of intermediate crack risk during the LCR process.The ERLS model simulates the extrusion flow and expulsion behavior of the liquid core,and its accuracy is validated against actual production measurements.To identify the critical damage value leading to intermediate crack initiation,this study conducts a consistency analysis between high-temperature tensile tests and FEM-based simulations using damage models.Based on this value,crack prediction is performed for Q355 slabs with cross-sectional dimensions of 170 mm×1450 mm.Using the prediction results,an optimal reduction scheme is determined,wherein the second segment accounts for 50%of the total reduction,the third segment for 32.5%,and the fourth segment for 17.5%,with the theoretical value of maximum reduction being 34 mm.These results provide actionable guidelines for the potential implementation of LCR in regular slab-casting systems.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 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
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, 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In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
基金financially supported by the Na-tional Natural Science Foundation of China (No.52474355)the Fundamental Research Funds for the Central Uni-versities,China (No.N25DCG006).
文摘Liquid core reduction(LCR)technology,originally developed for continuous thin-slab casting,allows space for a submerged entry nozzle in a mold while improving production efficiency.Recent experimental attempts explore the implementation of LCR in regular slab casting processes.However,regular slabs(2–3 times thicker than thin slabs)face critical challenges in terms of excessive deformation and stress concentration under external forces,which induce intermediate cracks and thus hinder successful LCR adoption in regular slab production.This study evaluates the feasibility of LCR for producing regular slabs and identifies optimal reduction parameters to prevent crack initiation.A three-dimensional thermal–mechanical coupled model is proposed using the finite element method(FEM),integrated with the equivalent replacement liquid steel(ERLS)method and the normalized Cockcroft–Latham damage model,to achieve quantitative prediction of intermediate crack risk during the LCR process.The ERLS model simulates the extrusion flow and expulsion behavior of the liquid core,and its accuracy is validated against actual production measurements.To identify the critical damage value leading to intermediate crack initiation,this study conducts a consistency analysis between high-temperature tensile tests and FEM-based simulations using damage models.Based on this value,crack prediction is performed for Q355 slabs with cross-sectional dimensions of 170 mm×1450 mm.Using the prediction results,an optimal reduction scheme is determined,wherein the second segment accounts for 50%of the total reduction,the third segment for 32.5%,and the fourth segment for 17.5%,with the theoretical value of maximum reduction being 34 mm.These results provide actionable guidelines for the potential implementation of LCR in regular slab-casting systems.
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1 .Introduetion Afteritiaing the ooncept of normal family of meromorphio funoions,P·Monteleotablsshod aniport criterion for norality.Let F be a family
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.
