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Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f…

Complex Variables · Mathematics 2021-04-02 Kuldeep Singh Charak , Manish Kumar , Rahul Kumar

In this paper, we prove two normality criteria for families of some functions concerning shared values, the results generalize those given by Hu and Meng. Some examples are given to show the sharpness of our results.

Complex Variables · Mathematics 2014-08-28 Xiaobin Zhang , Junfeng Xu

In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and…

Analysis of PDEs · Mathematics 2018-06-25 M. O. Mamchuev

In this paper we prove some normality criteria for a family of meromorphic functions concerning shared analytic functions, which extend or generalized some result obtained by Y. F. Wang, M. L. Fang~\cite{WF} and J. Qui, T. Zhu ~\cite{QZ}.

Complex Variables · Mathematics 2019-06-10 Sanjay Kumar , Poonam Rani

An example in the article shows that the first derivative of $f(z)=\frac{2}{1-e^{-2z}}$ sharing $0$ CM and $1,\infty$ IM with its shift $\pi i$ cannot obtain they are equal. In this paper, we study the uniqueness of meromorphic function…

Complex Variables · Mathematics 2022-05-09 XiaoHuang Huang

The purpose of this article is to deal with the multiple values and uniqueness problem of meromorphic mappings from $\mathbb{C}^{m}$ into the complex projective space $\mathbb{P}^{n}(\mathbb{C})$ sharing fixed and moving hypersurfaces. We…

Complex Variables · Mathematics 2017-02-24 Tingbin Cao , Hongzhe Cao

The objective of the paper is twofold. The first objective is to study the uniqueness problem of meromorphic function $f(z)$ when $f^{(1)}(z)$ shares two distinct finite values $a_1$, $a_2$ and $\infty$ CM with $\Delta_cf(z)$. In this…

Complex Variables · Mathematics 2025-10-28 Abhijit Banerjee , Sujoy Majumder , Nabadwip Sarkar

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

The aim of this paper is to consider the value distribution of a differential monomial generated by a transcendental meromorphic function.

Complex Variables · Mathematics 2018-12-06 Bikash Chakraborty

In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…

Complex Variables · Mathematics 2026-05-11 Sujoy Majumder , Debabrata Pramanik , Jhilik Banerjee

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

In 2023, Li, Du, Yi proved a uniqueness theorem for L functions in the extended Selberg class under the assumptions of positive degree, a shared functional equation, and the sharing of three complex values. This was later strengthened by…

Complex Variables · Mathematics 2026-04-02 Arpita Kundu , Abhijit Banerjee

The first objective of the paper is to estimate logarithmic partial derivative for meromorphic functions in several complex variables. Our estimations for logarithmic partial derivatives extend the results of Gundersen \cite{GG2} to the…

Complex Variables · Mathematics 2025-09-10 Junfeng Xu , Sujoy Majumder , Nabadwip Sarkar

In this paper, we discuss the joint value distribution of $L$-functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$-functions and some mean value theorems, which give evidence…

Number Theory · Mathematics 2021-02-26 Shōta Inoue , Junxian Li

We study the benefit of sharing representations among tasks to enable the effective use of deep neural networks in Multi-Task Reinforcement Learning. We leverage the assumption that learning from different tasks, sharing common properties,…

Machine Learning · Computer Science 2024-01-19 Carlo D'Eramo , Davide Tateo , Andrea Bonarini , Marcello Restelli , Jan Peters

An example in the article shows that the first derivative of $f(z)=\frac{2}{1-e^{-2z}}$ sharing $0$ CM and $1,\infty$ IM with its shift $\pi i$ cannot obtain they are equal. In this paper, we study the uniqueness of meromorphic function…

Complex Variables · Mathematics 2023-07-31 Xiao Huang

In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number,…

Complex Variables · Mathematics 2022-04-17 XiaoHuang Huang

In this paper, we consider the fractional sum of the divisor functions. We can improve previous results considered by Bordell\'{e}s \cite{Bo} and Liu-Wu-Yang \cite{LWY}.

Number Theory · Mathematics 2023-01-18 Wei Zhang

We consider transcendental meromorphic functions for which the zeros, 1-points and poles are distributed on three distinct rays. We show that such functions exist if and only if the rays are equally spaced. We also obtain a normal family…

Complex Variables · Mathematics 2022-03-08 Walter Bergweiler , Alexandre Eremenko

The purpose of this article is to study the uniqueness problem for meromorphic mappings from $\mathbb{C}^{n}$ into the complex projective space $\mathbb{P}^{N}(\mathbb{C}).$ By making using of the method of dealing with multiple values due…

Complex Variables · Mathematics 2015-03-27 Ting-Bin Cao , Hong-Xun Yi