Related papers: Entire Functions Sharing Small Functions With Thei…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set…
We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal…
In this paper, we give a simple proof and strengthening of a uniqueness theorem of meromorphic functions which partially share 0, $\infty$ CM and 1 IM with their difference operators. Meanwhile, we partial solve a conjecture given by…
A brief survey of the zeta function regularization and multiplicative anomaly issues when the associated zeta function of fluctuation operator is the regular at the origin (regular case) as well as when it is singular at the origin…
In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.
We consider uniqueness results for meromorphic functions $f:{\mathbb C} \to \widehat{\mathbb C}$ such that for certain values $a\in {\mathbb C}$ the implication $f(z)=a \Rightarrow f'(z)=a$ holds, i.e. that $f$ and $f'$ share values {\it…
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…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
As a motivation, we first recall the possible connection of electric-magnetic duality to finiteness in N=1 super-Yang-Mills theories (SYM). Then, we present the criterion for all-order finiteness (i.e., vanishing of the beta-functions at…
In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
Let f_1,f_2,..., be functions chosen independently and uniformly from the set of all functions from a set of cardinality n into itself. Let g_t be the composition of the first t functions, and let T be the smallest t for which g_t is…
In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…
All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…
In this paper we use the Bezoutiant method to describe the conditions under which two entire functions have not common roots. We apply the general results to concrete examples. In particular we consider the Bessel functions.
In this brief note we critically examine the process of partial and of total differentiation, showing some of the problems that arise when we relate both concepts. A way to solve all the problems is proposed.