in this paper, we introduce the idea of relative order and type of entire functions represented by banach valued dirichlet series of two complex variables to generalize some earlier results.proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by dirichlet series is the same as that of it...

The standard measure for the quality of online algorithms is competitive ratio. This generally applicable, and some problems it works well, but others fails to distinguish between that have very different performance. Thus, ever since its introduction, researchers worked on improving measure, defining variants, or measures based other concepts improve situation. Relative worst-order analysis (R...

We show that the naive mean-field approximation correctly predicts leading term of logarithmic lower tail probabilities for number copies a given subgraph in G(n,p) and arithmetic progressions length random subsets integers entire range densities where is viable. Our main technical result provides sufficient conditions on maximum degrees uniform hypergraph H guarantee edges, induced by binomial...

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.

For any polynomial ideal I, let the minimal triangular set contained in the reduced Buchberger-Gröbner basis of I with respect to the purely lexicographical term order be called the W-characteristic set of I. In this paper, we establish a strong connection between Ritt’s characteristic sets and Buchberger’s Gröbner bases of polynomial ideals by showing that the W-characteristic set C of I is a ...

Abstract Elimination of unknowns in systems equations, starting with Gaussian elimination, is a problem general interest. The finding an priori upper bound for the number differentiations elimination system differential-algebraic equations (DAEs) important challenge, going back to Ritt (1932). first characterization this via asymptotic analysis due Grigoriev’s result (1989) on quantifier differ...