The main obstruction to apply the field descent method when ω(N)>2 is the fact that primitivity of T⊆ZN does not imply (T−T)∩Z⋆N≠∅, as can be seen from the Remark immediately after Lemma 7.1. However, it needs to be emphasized that so far this metho…

This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings, kissing …

Let φ be a white noise RDS on a complete, d-dimensional smooth Riemannian manifold E with respect to an ergodic metric dynamical system (Ω,P,θ) and let (Pt) be the associated Markovian semigroup. Further assume that φt(ω,⋅)∈C1,δloc for some δ>0 and …

The next Lemma is a slight modification of [FV10b, Theorem A.13]. The proof follows the ideas of [FH12, Theorem 3.1].

In this paper, we have studied the minimum cost flow problem in a time-varying network to capture temporal features of many real-world problems. In this problem, arc and node costs, arc and node capacities, and supplies and demands can change over t…

We now introduce the important notion of regularity.

We compare HomotopyContinuation.jl against the established software packages Bertini and PHCpack. For this we pick a range of real-world polynomial systems of different type, presented in Table 1222The authors discovered the examples in the excellen…