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Nevanlinna's second main theorem is a far-reaching generalisation of Picard's Theorem concerning the value distribution of an arbitrary meromorphic function f. The theorem takes the form of an inequality containing a ramification term in…
In this paper, we compute universal inequalities of eigenvalues of a large class of second-order elliptic differential operators in divergence form, that includes, e.g., the Laplace and Cheng-Yau operators, on a bounded domain in a complete…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
This paper investigates the value distribution and growth properties of linear total differential polynomials $\mathcal{L}_k[D]f$ for meromorphic functions in several complex variables $\mathbb{C}^n$. By extending the classical Milloux…
In this work, we construct commutative rings of two variable matrix differential operators that are isomorphic to a ring of meromorphic functions on a rational manifold obtained from the $CP^1\times CP^1$ by identification of two lines with…
We consider elliptic differential operators on either the entire Euclidean space $\mathbb{R}^d$ or on subsets consisting of a cube $\Lambda_L$ of integer length $L$. For eigenfunctions of the operator, and more general solutions of elliptic…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not…
The purpose of this paper has twofold. The first is to establish a second main theorem for meromorphic functions on annuli and meromorphic function targets (may not be small functions) with truncated counting functions (truncation level 1)…
In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…
We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
It is shown that if three distinct values of a meromorphic function f:C^n -> P^1 of hyper-order strictly less than 2/3 have forward invariant pre-images with respect to a translation t:C^n -> C^n, t(z)=z+c, then f is a periodic function…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of $\mathbb{F}_q$ to construct minimal linear codes. By properties of…
We give explicit $q$-difference operators acting diagonally on wreath Macdonald $P$-polynomials in finitely many variables.
We study here class of 1D spectral-meromorphic (s-meromorphic) OD operators $L=\partial_x^n+\sum_{n-2\geq i\geq 0}a_{n-2-i}\partial_x^i$ with meromorphic coefficients $a_j$ near $x\in R$ such that all eigenfunctions $L\psi=\alpha\psi$ are…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
We define a nonlinear $q$-difference system $mathcal{P}_{N,(M_-,M_+)}$ as monodromy preserving deformations of a certain linear equation. We study its relation to a series $mathcal{F}_{N,M}$ defined as a certain generalization of…
Two meromorphic functions $f(z)$ and $g(z)$ sharing a small function $\alpha(z)$ usually is defined in terms of vanishing of the functions $f-\alpha$ and $g-\alpha$. We argue that it would be better to modify this definition at the points…