Let A be a zero-sum free subset of Zn with |A| = k. We compute for k ≤ 7 the least possible size of the set of all subset-sums of A.

0≤n<x:n≡l( mod m) (−1)g In the case q = 2 we write Sm,l,2 = Sm,l, σ2(n) = σ(n). We call (2) a generalized Newman sum. In [7] we gave a quite another proof of the Coquet’s estimates for S3,0(x) and a fast algorithm for its calculation. Professor J.-P.Allouche kindly informed me about a misprint in Coquet’s theorem: for odd x η = η(x) = (−1) (but (−1) as in [2]; sf. [1], pp.98-99) An important ro...

Let σ n be the sum of all divisors id="M2"> and let id="M3"> open="[" close="]" t integral part id="M4"> . In this paper, we shall prove that id="M5"> ∑ ≤ x</m...

We study the problem of finding zero-sum blocks in bounded-sum sequences, which was introduced by Caro, Hansberg, and Montejano. Caro et al. determine minimum $\{-1,1\}$-sequence length for when there exist $k$ consecutive terms that sum to zero. corresponding sequence set $\{-1,1\}$ is replaced $\{-r,s\}$ arbitrary positive integers $r$ $s.$ This confirms a conjecture theirs. also construct $\...

The dynamics of the Reynolds stress tensor is given by an evolution equation coupling geometrical effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected. In this case, the Reynolds stress tensor is expressed as the sum of three tensor products of vector fields only associated with the mean flow. The vector fields are governed b...

We define a class of multi–hop erasure networks that approximates a wireless multi–hop network. The network carries unicast flows for multiple users, and each information packet within a flow is required to be decoded at the flow destination within a specified delay deadline. The allocation of coding rates amongst flows/users is constrained by network capacity. We propose a proportional fair tr...