共查询到20条相似文献,搜索用时 31 毫秒
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Guo Ping Zhan 《数学学报(英文版)》2013,29(4):703-716
In this paper, we consider the dynamics of the map z→exp(z)/z on the punctured plane C*=C\{0}. We show that for almost every point z ∈ C*, the ω-limit set of z is equal to {0, ∞}. In particular, the map is not recurrent. 相似文献
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We compute the Fourier coefficients of the weight one modular form \(\eta (z)\eta (2z)\eta (3z)/\eta (6z)\) in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates of the modular form \(\eta (z)^4/\eta (2z)^2\). In the last section we use our main result to give an elementary proof of an identity by Victor Kac. 相似文献
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E. G. Goluzina 《Journal of Mathematical Sciences》2004,122(6):3608-3615
Let T be the class of functions f(z) = z + a
2
z
2 + . . . that are regular in the unit disk and satisfy the condition Im f(z) Im z > 0 for Im z 0, and let z
1 and z
2 be any distinct fixed points in the disk |z| < 1. For the systems of functionals mentioned in the title, the regions of values on T are studied. As a corollary, the regions of values of f'(z
2) and f'(z
1) on the subclasses of functions in T with fixed values f (z
1), f (z
2) and f (z
1), f'(z
1), respectively, are found. Bibliography: 7 titles. 相似文献
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We consider a Dirichlet problem driven by the anisotropic p-Laplacian, with a reaction having the competing effects of a singular term and a parametric superlinear perturbation. We prove a bifurcation-type theorem describing the changes of the set of positive solutions as the parameter varies. We also prove the existence of minimal positive solutions. 相似文献
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Prof. Joseph Cima 《Monatshefte für Mathematik》1976,81(2):89-93
We prove that forf a normalized schlicht function in the disk the boundary values of log |f(z)/z| satisfy a growth condition on subarcs of the unit circle . 相似文献
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We study the non-existence of finite order meromorphic solutions to the Fermat-type difference equation \({f^3(z)+f^3(z+c)=1}\) over the complex plane C. An application to the unique range set problem is discussed.
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It is proved that the rational maps in the family {z → z m +λ/z d : λ ∈ ?\{0}} for integers m, d ≥ 2 have no Herman rings. 相似文献
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Yu. V. Azarina 《Journal of Mathematical Sciences》1990,49(2):871-875
Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 48, pp. 26–32, 1987. 相似文献