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We describe bounded, holomorphic functions on the complex 2-disc, that admit meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski…

Complex Variables · Mathematics 2022-06-24 János Kollár

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…

Complex Variables · Mathematics 2015-04-01 Virender Singh , Kuldeep Singh Charak

This article aims at finding sufficient conditions for a family of meromorphic functions to be normal by involving partial sharing of sets with differential polynomials. Moreover, corresponding results for normal meromorphic functions are…

Complex Variables · Mathematics 2025-10-24 Kuldeep Singh Charak , Nikhil Bharti , Anil Singh

This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…

History and Overview · Mathematics 2026-01-05 Teo Banica

In this article we have studied complex linear homogeneous difference equations where the coefficients are meromorphic functions, having finite iterated p-phi order. We have made some estimations on the growth of its nontrivial solutions.…

Complex Variables · Mathematics 2022-06-23 Anirban Bandyopadhyay , Chinmay Ghosh , Sanjib Kumar Datta

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.

Complex Variables · Mathematics 2022-06-08 Zhiguo Ding , Michael E. Zieve

In this paper, we survey and study definitions and properties of tropical polynomials, tropical rational functions and in general, tropical meromorphic functions, emphasizing practical techniques that can really carry out computations. For…

Algebraic Geometry · Mathematics 2011-01-17 Yen-lung Tsai

The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has…

Complex Variables · Mathematics 2018-02-05 J. K. Langley

In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.

Algebraic Geometry · Mathematics 2017-08-10 Yu. I. Manin

This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic ordinary differential equations of any…

Exactly Solvable and Integrable Systems · Physics 2018-06-11 Robert Conte , Tuen Wai Ng , Chengfa Wu

In this paper, we characterize meromorphic solutions $f(z_1,z_2),g(z_1,z_2)$ to the generalized Fermat Diophantine functional equations $h(z_1,z_2)f^m+k(z_1,z_2)g^n=1$ in $\mathbf{C}^2$ for integers $m,n\geq2$ and nonzero meromorphic…

Complex Variables · Mathematics 2021-06-04 Wei Chen , Qi Han , Qiong Wang

This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of…

Dynamical Systems · Mathematics 2018-01-08 Walter Bergweiler

The purpose of the paper is to rectify a series of errors occurred in [2], [17], [20] for a particular situation. To get a fruitful solution and to overcome the issue, we introduce a new form of set sharing namely restricted set sharing,…

Complex Variables · Mathematics 2021-03-02 Abhijit Banerjee , Arpita Kundu

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

Classical Analysis and ODEs · Mathematics 2007-05-23 Stephen Semmes

The main purpose of this paper is to derive some subordination and superordination results involving certain of integral operator for meromorphic univalent functions in the punctured open unit disk. Several sandwich-type results are also…

Complex Variables · Mathematics 2016-12-23 Khudair Hussain

The main result of this paper shows a totally new necessary and sufficient condition to determine both real and complex zeros of derivative of all entire and meromorphic functions of one complex variable in the extended complex plane. By…

Complex Variables · Mathematics 2022-04-01 ZhaoKun Ma , Lande Ma

The purpose of this is the study of certain coherent sheaves of meromorphic forms on reduced complex space and particularly their behavior with respect to pull back and higher direct image.

Algebraic Geometry · Mathematics 2025-01-20 Mohamed Kaddar

The purpose of this paper is to investigate the non-constant entire as well as meromorphic solutions of the Fermat-type partial differential-difference equation: \[\left(\sum_{j=1}^m\frac{\partial f(z_1, z_2, \ldots, z_m)}{\partial…

Complex Variables · Mathematics 2025-12-03 Sujoy Majumder , Debabrata Pramanik

This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…

Combinatorics · Mathematics 2007-05-23 Volker Kaibel , Marc E. Pfetsch

We give an alternative and simpler method for getting pointwise estimate of meromorphic solutions of homogeneous linear differential equations with coefficients meromorphic in a finite disk or in the open plane originally obtained by Hayman…

Complex Variables · Mathematics 2013-12-24 Yik-Man Chiang