Related papers: A functional equation whose unknown is P([0,1]) va…

We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given…

We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this…

The problem is considered as to whether a monotone function defined on a subset P of a Euclidean space can be strictly monotonically extended to the whole space. It is proved that this is the case if and only if the function is {\em…

There are several methods for proving the existence of the solution to the elliptic boundary problem $Lu=f \text{\,\, in\,\,} D,\quad u|_S=0,\quad (*)$. Here $L$ is an elliptic operator of second order, $f$ is a given function, and…

Ultrafunctions are a particular class of functions defined on a non-Archimedean field. They provide generalized solutions to functional equations which do not have any solutions among the real functions or the distributions. In this paper…

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

We consider certain subfamilies, of the family of univalent functions in the open unit disk, defined by means of sufficient coefficient conditions for univalency. This article is devoted to studying the problem of the well-known conjecture…

We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies.…

One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its…

We describe dynamical properties of a map $\mathfrak{F}$ defined on the space of rational functions. The fixed points of $\mathfrak{F}$ are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials.

Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…

In this paper, we investigate the existence of $C^n$, $n\in \mathbb{N}^+$, solutions for a class of second-order iterative functional equations involving iterates of the unknown function and a nonlinear term. Applying the Fiber Contraction…

We show that a well known uncertainty principle for functions on the circle can be derived from an uncertainty principle for the Euclidean motion group.

This paper is devoted to finding the general solutions of the functional equation $\sumin \sumjm h(p_iq_j)=\sumin h(p_i)+\sumjm k_j(q_j)+\lambda\sumin h(p_i)\sumjm k_j(q_j)$ valid for all complete probability distributions…

We give a series of very general sufficient conditions in order to ensure the uniqueness of large solutions for --$\Delta$u + f (x, u) = 0 in a bounded domain $\Omega$ where f : $\Omega$ x R $\rightarrow$ R + is a continuous function, such…

We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…

A problem based on the Extended Euclidean Algorithm applied to a class of polynomials with many factors is presented and believed to be hard. If so, it is a one-way function well suited for applications in digital signicatures.

We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…

This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…