Abstract We show that some classical identities about multiplicative functions, and the Riemann zeta-function, may conveniently be interpreted in terms of the addition of ±1 to some alphabets. Résumé Nous montrons que des identités classiques concernant des fonctions multiplicatives de la théorie des nombres, et la fonction zeta de Riemann, s’interprètent commodément en terme de l’opération : “...

In this paper we investigate threshold based networks performing 2 1 addition using redundant binary operand representations. In particular we concern with establishing the networks with the smallest network depth assuming small weight and fan-in values. First we propose a depth-4 implementation and we show that the 2 1 addition can be computed by a threshold network with the size in the order ...

We study the Minkowski length L(P ) of a lattice polytope P , which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P . The Minkowski length represents the largest possible number of factors in a factorization of polynomials with exponent vectors in P , and shows up in lower bounds for the minimum distance of toric codes. In this paper we give a...

A total of 78 orthodontic patients participated in a study of the degree of decalcification inhibition induced by daily treatment with 0.4% SnF2 gel. Control patients (n = 39) were managed exactly as were the test patients (n = 39) except that the latter were instructed to brush at bedtime each day with the gel. In the nongel users, 24 (64.1%) developed decalcification after 18-24 months bandin...