Guowei Zhang (2017)
Open Mathematics
Similarity:
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
Similarity:
Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
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
Similarity:
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
Similarity:
Armen Edigarian (2004)
Annales Polonici Mathematici
Similarity:
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
Similarity:
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
Similarity:
We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
Ahmed Ayache, Hanen Monceur (2011)
Colloquium Mathematicae
Similarity:
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.
Mokeeva, N.V. (2005)
Zapiski Nauchnykh Seminarov POMI
Similarity:
Edgar Lee Stout (2009)
Annales Polonici Mathematici
Similarity:
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
Similarity:
Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)
Open Mathematics
Similarity:
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
Similarity:
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
Similarity:
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
Similarity:
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
Similarity:
Abhijit Banerjee, Molla Basir Ahamed (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
We prove the uniqueness of meromorphic functions sharing some three sets with finite weights.
Jun-Fan Chen (2017)
Open Mathematics
Similarity:
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
Similarity:
Karol Borsuk (1972)
Colloquium Mathematicae
Similarity:
Wei-Ran Lü, Hong-Xun Yi (2003)
Annales Polonici Mathematici
Similarity:
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.
Yuxian Chen, Zhaojun Wu (2012)
Annales Polonici Mathematici
Similarity:
This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.
Xiao-Min Li, Hong-Xun Yi (2009)
Annales Polonici Mathematici
Similarity:
We deal with a uniqueness theorem of two meromorphic functions that share three values with weights and also share a set consisting of two small meromorphic functions. Our results improve those by G. Brosch, I. Lahiri & P. Sahoo, T. C. Alzahary & H. X. Yi, P. Li & C. C. Yang, and others.
Peter Pflug, Włodzimierz Zwonek (1998)
Annales Polonici Mathematici
Similarity:
We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Xiao-Min Li, Hong-Xun Yi (2010)
Annales Polonici Mathematici
Similarity:
We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.
Brian D. Sleeman, Chen Hua (2000)
Revista Matemática Iberoamericana
Similarity:
A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries...
Rodolfo Salvi (2005)
Banach Center Publications
Similarity:
In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover,...