background: liver cancer mortality is high in thailand but utility of related vital statistics is limited due to national vital registration (vr) data being under reported for specific causes of deaths. accurate methodologies and reliable supplementary data are needed to provide worthy national vital statistics. this study aimed to model liver cancer deaths based on verbal autopsy (va) study in...

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 $\...

Let Fq be the finite field of q elements. Let H ⊆ Fq be a multiplicative subgroup. For a positive integer k and element b ∈ Fq, we give a sharp estimate for the number of k-element subsets of H which sum to b.