Abstract. Let G be a finite abelian group, and let η(G) be the smallest integer d such that every sequence over G of length at least d contains a zero-sum subsequence T with length |T | ∈ [1, exp(G)]. In this paper, we investigate the question whether all non-cyclic finite abelian groups G share with the following property: There exists at least one integer t ∈ [exp(G)+1, η(G)− 1] such that eve...

(2) Show that we can convert an instance of that problem to an instance with a gap: that is, given a set of polynomials, create a new set of polynomials where at most a small fraction can simultaneously be made zero. Or, in other words, if there is no common zero, then most of the polynomials will be non-zero at any given point. This gap comes at the price of worse arity. The new polynomials we...

The zero modes and the zero resonances of the Dirac operator H = α · D + Q(x) are discussed, where α = (α1, α2, α3) is the triple of 4× 4 Dirac matrices, D = 1 i ∇x, and Q(x) = ` qjk(x) ́ is a 4× 4 Hermitian matrix-valued function with |qjk(x)| ≤ C〈x〉, ρ > 1. We shall show that every zero mode f(x) is continuous on R and decays at infinity with the decay rate |x| if 1 < ρ < 3, |x| log |x| if ρ =...

Abstract We explore the response of Earth’s coupled climate and carbon system to an idealized sequential addition removal CO 2 atmosphere, following a symmetric continuous emissions pathway, in contrast discontinuous pathways that have largely informed our understanding net zero negative date. find, using both Earth model ensemble simple realizations, warming during reduction phases is defined ...

We present an example of a zero-dimensional F-space that is not strongly zero-dimensional.

let $g=(v,e)$ be a simple graph. a set $ssubseteq v$ isindependent set of $g$,  if no two vertices of $s$ are adjacent.the  independence number $alpha(g)$ is the size of a maximumindependent set in the graph. in this paper we study and characterize the independent sets ofthe zero-divisor graph $gamma(r)$ and ideal-based zero-divisor graph $gamma_i(r)$of a commutative ring $r$.

zero tillage practices have a direct effect on soil microbial communities modifying soil productivity and sustainability. the crop sequences used can change the aforementioned properties, too. in this study, we evaluated the effect of crop sequences under zero tillage management on soil biological and chemical properties including vertical distribution of soil organic carbon, soil basal respira...