Results 71 to 80 of about 292 (180)

Nevanlinna Theory via Stochastic Calculus

Journal of Functional Analysis, 1995
The author constructs a probabilistic version of Nevanlinna theory in general cases, improving the stochastic method by estimates of increasing processes for Brownian motions (Br.m.) and martingales (mart.) on manifolds. In Section 1 he establishes counterparts of the 1. and 2.
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On a question of Gundersen-Yang concerning entire solutions of binomial differential equations

Demonstratio Mathematica
The explicit forms of entire solutions of the binomial differential equationsa(z)f′f″−b(z)(f)2=c(z)e2d(z),a(z)ff′−b(z)(f″)2=c(z)e2d(z), $$a\left(z\right){f}^{\prime }{f}^{{\prime\prime}}-b\left(z\right){\left(f\right)}^{2}=c\left(z\right){e}^{2d\left(z ...
Long Jianren, Xia Mengting, Xiang Xuxu
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On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order

Annales Mathematicae Silesianae
In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one.
Banerjee Abhijit, Sarkar Jhuma
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Solutions of several general quadratic partial differential-difference equations in ℂ2

Demonstratio Mathematica
In this article, we have introduced general transformation to solving the general quadratic equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations.
Ahamed Molla Basir, Mandal Sanju
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A problem on spaces of holomorphic maps and the geometry of image domains

Concrete Operators
We present an old problem in Geometric Function Theory: characterizing the domains Ω⊂C ${\Omega}\subset \mathbb{C}$ for which every holomorphic map from the unit disk into Ω must belong to a specific function space X.
Cruz-Zamorano Francisco J.
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Nevanlinna theory on complete Kähler manifolds

, 2020
We study Nevanlinna theory on complete Kähler manifolds. As a consequence of the main result, we prove a defect relation of holomorphic mappings from complete Kähler manifolds of non-positive sectional curvature into complex projective manifolds under certain growth condition.
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Delocalization Transition for Critical Erdős-Rényi Graphs. [PDF]

Commun Math Phys, 2021
Alt J, Ducatez R, Knowles A.
europepmc   +1 more source

Holomorphic curves into projective spaces with some special hypersurfaces

Demonstratio Mathematica
In this article, we establish some truncated second main theorems for holomorphic curves into projective spaces with some special hypersurfaces and give some applications.
Cao Hongzhe, Wang Yuting, Xu Qingyong
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A Climatology of Long-Duration High 2-MeV Electron Flux Periods in the Outer Radiation Belt. [PDF]

J Geophys Res Space Phys, 2022
Mourenas D, Agapitov OV, Artemyev AV, Zhang XJ.   +3 more
europepmc   +1 more source

Entire solutions for a nonlinear differential equation

Electronic Journal of Differential Equations, 2011
In this article, we study the existence of solutions to the differential equation $$ f^n(z)+P(f)= P_1e^{h_1}+ P_2e^{h_2}, $$ where $ngeq 2$ is an positive integer, f is a transcendental entire function, $P(f)$ is a differential polynomial in f of ...
Jianming Qi, Jie Ding, Taiying Zhu
doaj