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We discuss an extension of the $C$-theorem to chiral theories. We show that two monotonically decreasing $C$-functions can be introduced. However, their difference is a constant of the renormalization group flow. This constant reproduces…

High Energy Physics - Theory · Physics 2009-10-30 Fiorenzo Bastianelli , Ulf Lindstrom

We present some results on two meromorphic functions from S to the Riemann sphere sharing a number of values where S is a Riemann surface of one of the following types: compact, compact minus finitely many points, the unit disk, a torus,…

Complex Variables · Mathematics 2016-10-05 Andreas Schweizer

Let $q, n, m \in \mathbb{N}$ be such that $q$ is a prime power and $a, b \in \mathbb{F}$. In this article we establish a sufficient condition for the existence of a primitive normal pair $(\alpha, f(\alpha)) \in \mathbb{F}_{q^m}$ over…

Number Theory · Mathematics 2024-05-10 Arpan Chandra Mazumder , Dhiren Kumar Basnet

In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…

Complex Variables · Mathematics 2026-05-12 Sujoy Majumder , Debabrata Pramanik , Shantanu Panja

In 1992, Gundersen (Complex Var. Elliptic Equ.20 (1992), no. 1-4, 99-106.) proposed the following famous open question: if two non-constant meromorphic functions share three values IM and share a fourth value CM, then do the functions…

Complex Variables · Mathematics 2026-01-07 Xiao-Min Li , Qing-Fei Zhai , Hong-Xun Yi

Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on…

Complex Variables · Mathematics 2025-05-13 Vibhuti Arora , Vinayak M

We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…

Statistics Theory · Mathematics 2013-10-22 Cécile Amblard , Stephane Girard , Ludovic Menneteau

We show that the family ${\cal F}_k$ of all meromorphic functions $f$ in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f|}(z)\ge C \qquad \mbox{ for all } z\in D$$ (where $k$ is a natural number and $C>0$) is quasi-normal. The proof relies…

Complex Variables · Mathematics 2017-11-15 Jürgen Grahl , Shahar Nevo

In this paper we have mainly focused on the uniqueness of two meromorphic functions under the realm of two shared sets problem with certain restrictions which in turn improve the results of { P. Sahoo and H. Karmakar, Uniqueness theorems…

Complex Variables · Mathematics 2020-09-01 Abhijit Banerjee , Saikat Bhattacharyya

We consider an inference on the eigenvalues of the covariance matrix of a multivariate normal distribution. The family of multivariate normal distributions with a fixed mean is seen as a Riemannian manifold with Fisher information metric.…

Statistics Theory · Mathematics 2018-10-12 Yo Sheena

In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the…

Complex Variables · Mathematics 2013-09-03 H. Orhan , N. Magesh , V. K. Balaji

By introducing the notion of distributive constant for a family of closed subschemes, we establish a general form of the second main theorem for algebraic nondegenerate meromorphic mappings from a generalized $p$-Parabolic manifold into a…

Complex Variables · Mathematics 2026-02-17 Si Duc Quang

We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then…

Complex Variables · Mathematics 2017-02-01 Faruk Abi-Khuzam , Florian Bertrand , Giuseppe Della Sala

Let $\mathcal{A}$ denote the class of analytic functions $f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ normalized by $f(0)=0$, $f'(0)=1$. In the present article, we obtain the sharp estimates of the Schwarzian norm for…

Complex Variables · Mathematics 2022-12-14 Md Firoz Ali , Sanjit Pal

This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…

Complex Variables · Mathematics 2024-03-26 Si Duc Quang

A univalent meromorphic function defined on $\Delta:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $\Delta$ is bi-univalent meromorphic in $\Delta$. For certain subclasses of meromorphic bi-univalent functions,…

Complex Variables · Mathematics 2011-08-23 Suzeini Abd Halim , Samaneh G. Hamidi , V. Ravichandran

The connection between the commutativity of a family of $n\times n$ matrices and the generalized joint numerical ranges is studied. For instance, it is shown that ${\cal F}$ is a family of mutually commuting normal matrices if and only if…

Functional Analysis · Mathematics 2020-02-10 Chi-Kwong Li , Yiu-Tung Poon , Ya-Shu Wang

In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for…

Complex Variables · Mathematics 2015-04-14 Feng Lü , Weiran Lü

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…

Complex Variables · Mathematics 2020-08-24 Abhijit Banerjee , Saikat Bhattacharyya

In this paper, we investigate the value distribution for linear q-difference polynomials of transcendental meromorphic functions of zero order which improves the results of Xu, Liu and Cao (\cite{Xu & Liu & Cao & 2015}). We also investigate…

Complex Variables · Mathematics 2021-03-08 Goutam Haldar