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...

In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

This paper addresses the problem of learning a Nash equilibrium in γ-discounted multiplayer general-sum Markov Games (MGs) in a batch setting. As the number of players increases in MG, the agents may either collaborate or team apart to increase their final rewards. One solution to address this problem is to look for a Nash equilibrium. Although, several techniques were found for the subcase of ...