In this article we consider relative iteration of entire functions and studycomparative growth of the maximum term of iterated entire functions withthat of the maximum term of the related functions.

Classical methods to study and solve systems of polynomial equations are based on numerous avatars of Gröbner (standard) basis algorithms or Riquier-Janet type methods (Ritt-Wu’s algorithm). All these methods use implicitly but deeply the dense or sparse representation of multivariate polynomials, which is the computer science counterpart of the expansion of these mathematical objects on the mo...

We study the following questions: (1) What are all solutions to f ◦ f̂ = g ◦ ĝ in complex rational functions f, g ∈ C(X) and meromorphic functions f̂ , ĝ on the complex plane? (2) For which rational functions f(X) and g(X) with coefficients in an algebraic number field K does the equation f(a) = g(b) have infinitely many solutions with a, b ∈ K? We utilize various algebraic, geometric and analyti...

Relative spacings are relative differences between order statistics. In this context, we extend previous results concerning the increasing convex of two distributions from case consecutive to general spacings. The sufficient conditions given in terms expected proportional shortfall order. As an application, compare deprivation within some parametric families income distributions.