Related papers: What lies between polynomial and exponential growt…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under…

We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.

Exponential growth occurs when the growth rate of a given quantity is proportional to the quantity's current value. Surprisingly, when exponential growth data is plotted as a simple histogram disregarding the time dimension, a remarkable…

This paper presents an algebraic-geometric construction of the derivative developed initially within the class of polynomial functions without introducing limits at the initial stage. Tangency is characterized by an algebraic condition: the…

This paper is devoted to present new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved…

For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial…

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

The $T$-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the $C$-function of the…

We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…

We present a global version of the {\L}ojasiewicz inequality on comparing the rate of growth of two polynomial functions in the case the mapping defined by these functions is (Newton) non-degenerate at infinity. In addition, we show that…

We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.

We prove that polycyclic groups are of polynomial growth or of uniform exponential growth.

We compute the rate of exponential growth of the free inverse monoid of rank $r$ (and hence an upper bound on the corresponding rate for all $r$-generated inverse monoids and semigroups). This turns out to be an algebraic number strictly…

This paper determines the rate of growth to infinity of a scalar autonomous nonlinear functional differential equation with finite delay, where the right hand side is a positive continuous linear functional of $f(x)$. We assume $f$ grows…

Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were…

This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely…

The avalanche polynomial on a graph captures the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this…