Related papers: A uniqueness problem concerning entire functions a…
In the paper, concerning a question of Yi [23], we study general criterion for the uniqueness of an L-function and a general meromorphic function. Our results improve and extend all the existing results in this direction [23, 18, 17, 4] to…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
A new problem is studied, the concept of exactness of a second order nonlinear ordinary differential equations is established. A method is constructed to reduce this class into a first order equations. If the second order equation is not…
We consider the entire characteristic functions of order 2 and we prove some decomposition theorems in a multidimensional case. We show that the lack of zeros of the density function is a necessary but not a sufficient (as in the…
In this article we prove existence, uniqueness and regularity for the singular equation \begin{eqnarray*} \begin{cases} |\nabla u|^{\alpha}(F(D^{2}u)+h(x)\cdot\nabla u)+c(x)|u|^{\alpha}u+p(x)u^{-\gamma}=0 \ \mbox{ in } \ \Omega\\ u>0 \…
In this paper we prove some normality criteria for a family of meromorphic functions, which involves the zeros of certain differential polynomials generated by the members of the family.
We deal with consistency results for the existence of universal models in natural classes of models (more exactly--a somewhat weaker version). We apply a result on quite general family to T_feq and to the class of triangle-free graphs.
We consider the Neumann problem in $C^2$ bounded domains for fully nonlinear second order operators which are elliptic, homogenous with lower order terms. Inspired by \cite{bnv}, we define the concept of principal eigenvalue and we…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath\'eodory--Fej\'er--Tur\'an problem. The first variation imposes the additional requirement that the function is…
The Riemann problem is studied in the case when the unknown function has nonisolated singularities, concentrated on the real axis. The problem is used for the factorization of functions, holomorphic outside of the unit circle and the real…
It is shown that with appropriate boundary conditions, a real function satisfying the differential equation $f'(x) = f(x+a)$ has all known properties of the sine function. A number of elementary derivations are presented including proofs…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
We consider a continuous family $(f_s)$, $s\in[0,1]$ of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant (or…
In this article we propose a new class of the even entire function connected with the product and series with the real coefficients. We address a sufficient condition for all real zeros for it. As a typical example, we give an answer to the…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
For every countable ordinal number $\alpha$ we construct an entire function $f=f_\alpha$ such that the family $\left\{f(nz):n\in\mathbb{N}\right\}$ is exactly $Q_\alpha$-normal in the unit disk.
Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full operator algebra is normal. We also characterize those…