Related papers: Tropical Nevanlinna theory and ultra-discrete equa…
The two-dimensional Helmholtz equation separates in elliptic coordinates based on two distinct foci, a limit case of which includes polar coordinate systems when the two foci coalesce. This equation is invariant under the Euclidean group of…
We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…
In this paper, we discuss meromorphic solutions of functional equations over non-Archimedean fields, and prove analogues of the Clunie lemma, Malmquist-type theorem and Mokhon'ko theorem.
It is shown that if w(z) is a finite-order meromorphic solution of the equation H(z,w) P(z,w) = Q(z,w), where P(z,w) = P(z,w(z),w(z+c_1),...,w(z+c_n)) is a homogeneous difference polynomial with meromorphic coefficients, and H(z,w) =…
In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…
In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
Generalizing supertropical algebras, we present a "layered" structure, "sorted" by a semiring which permits varying ghost layers, and indicate how it is more amenable than the "standard" supertropical construction in factorizations of…
This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary,…
We show that for a vanishing period difference operator of a meromorphic function \( f \), there exist the following estimates regarding proximity functions, \[ \lim_{\eta \to 0} m_\eta\left(r, \frac{\Delta_\eta f - a\eta}{f' - a} \right) =…
This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix…
In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…
This paper establishes the version of Nevanlinna theory based on Hahn difference operator $\mathcal{D}_{q,c}(g)=\frac{g(qz+c)-g(z)}{(q-1)z+c}$ for meromorphic function of zero order in the complex plane $\mathbb{C}$. We first establish the…
This thesis delves into the geometry of abstract tropical curves, exploring their complete linear system and associated tropical submodules. We establish a lower bound on the dimension of tropical submodules in terms of the Baker-Norine…
We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
In this paper, we investigate meromorphic solutions in $\mathbb{C}^m$ of the nonlinear differential equation \[\displaystyle f^n\partial_u(f)g^n\partial_u(g)=1,\] where $\partial_u(f)=\sum_{j=1}^mu_j\partial_j(f)$ and $\sum_{j=1}^m u_j\neq…
This is the first part of the review article which focuses on theory and applications of Herglotz-Nevanlinna functions in material sciences. It starts with the definition of scalar valued Herglotz-Nevanlinna functions and explains in detail…
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
This note finds a new characterization of complete Nevanlinna-Pick kernels on the Euclidean unit ball. The classical theory of Sz.-Nagy and Foias about the characteristic function is extended in this note to a commuting tuple $\bfT$ of…