Guowei Zhang (2017)
Open Mathematics
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In this paper we study the iterated order and oscillations of the solutions to some complex linear differential equations in angular domains. Our theorems improve some recent results.
Stefan Bergman (1977)
Annales Polonici Mathematici
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Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Väisälä, Jussi (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Armen Edigarian (2004)
Annales Polonici Mathematici
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We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.
Cai-Feng Yi, Yu Wang, Hong-Yan Xu (2010)
Annales Polonici Mathematici
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We investigate the properties of meromorphic functions on an angular domain, and obtain a form of Yang's inequality on an angular domain by reducing the coefficients of Hayman's inequality. Moreover, we also study Hayman's inequality in different forms, and obtain accurate estimates of sums of deficiencies.
Nikolai Nikolov (2006)
Annales Polonici Mathematici
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We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
Sayantan Maity, Abhijit Banerjee (2023)
Mathematica Bohemica
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We study unique range sets of meromorphic functions over an angular domain in the light of weighted sharing. One of our main results generalizes and improves a result of Xu et al. (2014). Most importantly, we have pointed out a gap in the proofs of some main results of Rathod (2021) and subsequently rectifying the gap we have conveniently improved the results.
Ahmed Ayache, Hanen Monceur (2011)
Colloquium Mathematicae
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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.
Sanjay Mallick, Abhijit Banerjee (2021)
Mathematica Bohemica
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The purpose of the paper is to represent the two shared set problems in an elaborative and convenient manner. In the main result of the paper, we have exhaustively treated the two shared set problem on the open complex plane. As a consequence of the main result, we have investigated the same problem in a different perspective, which has yet not been studied. Further, two examples have been exhibited in the paper to show the sharpness of some of these results.
Mokeeva, N.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Edgar Lee Stout (2009)
Annales Polonici Mathematici
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We construct some envelopes of holomorphy that are not equivalent to domains in ℂⁿ.
McCarthy, John, Papadopoulos, Athanase (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)
Open Mathematics
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In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
Hong Yan Xu, San Yang Liu (2017)
Open Mathematics
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The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).
Indrajit Lahiri, Arindam Sarkar (2005)
Annales Polonici Mathematici
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We prove a result on the uniqueness of meromorphic functions sharing three values with weights and as a consequence of this result we improve a recent result of W. R. Lü and H. X. Yi.
Xiu-Qing Lin, Wei-Chuan Lin (2011)
Annales Polonici Mathematici
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This paper is devoted to the study of uniqueness of meromorphic functions sharing only one value or fixed points. We improve some related results due to J. L. Zhang [Comput. Math. Appl. 56 (2008), 3079-3087] and M. L. Fang [Comput. Math. Appl. 44 (2002), 823-831], and we supplement some results given by M. L. Fang and X. H. Hua [J. Nanjing Univ. Math. Biquart. 13 (1996), 44-48] and by C. C. Yang and X. H. Hua [Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406].
Meerschaert, M.M., Scheffler, H.-P. (1996)
Journal of Applied Analysis
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Abhijit Banerjee, Molla Basir Ahamed (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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We prove the uniqueness of meromorphic functions sharing some three sets with finite weights.
Jun-Fan Chen (2017)
Open Mathematics
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We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.
V. Barucci, D.E. Dobbs, M. Fontana (1986)
Manuscripta mathematica
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Karol Borsuk (1972)
Colloquium Mathematicae
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Wei-Ran Lü, Hong-Xun Yi (2003)
Annales Polonici Mathematici
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We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.