Let S (n), for n E N+ denote the Smarandache function, then S (n) is defined as the smallest m E N+, with nlm!. From the definition one can easily deduce that if n = prlp~2 .. . p~k is the canonical prime factorization of n, then Sen) = max{S(pfi)}, where the maximum is taken over the i's from 1 to k. This observation illustrates the importance of being able to calculate the Smarandache functio...

In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...

The purpose of this article is to study the convergence of a few series .... ith the Erdos function. The work is based on results concerning the convergence of some series with the Smarandache function.

In this paper we IS not a power of 2, then product sequence of the first prime 2. prove that if r> 1 and r the Smarandache r-power kind contains onlv one J

Let P and Q denote the Smarandache cubic product sequences of the first kind and the second kind respectively. In this paper we prove that P contains only one power 9 and Q does not contain any power.

In this paper we define S algebras and show that every finite group can be found in some S algebra.  We define and study the S degree of a finite group and determine the S degree of several classes of finite groups such as cyclic groups, elementary abelian $p$-groups, and dihedral groups $D_p$.

Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, U.S.A. [email protected] Jean Dezert ONERA 29 Av. de la Division Leclerc 92320 Châtillon, France. [email protected] Abstract – This paper introduces the notion of qualitative belief assignment to model beliefs of human experts expressed in natural language (with linguistic labels). We show how qualitativ...