for any reduced commutative $f$-ring with identity and bounded inversion, we show that a condition which is obviously necessary for the socle of the ring to coincide with the socle of its bounded part, is actually also sufficient. the condition is that every minimal ideal of the ring consist entirely of bounded elements. it is not too stringent, and is satisfied, for instance, by rings of conti...

Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Gröbner bases depending on the values of the parameters. An improvement using a discriminant ideal to rewrite the tree was described by Manubens and the author in 2005. In this paper we describe how to iterate the use ...

in this paper we study some results on noetherian semigroups. we  show that if  $s_s$ is an  strongly  faithful $s$-act and $s$ is a duo weakly noetherian, then we have the following.

We analyze the security of the SHA-3 finalist BLAKE. The BLAKE hash function follows the HAIFA design methodology, and as such it achieves optimal preimage, second preimage and collision resistance, and is indifferentiable from a random oracle up to approximately 2 assuming the underlying compression function is ideal. In our work we show, however, that the compression function employed by BLAK...

Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Gröbner bases depending on the values of the parameters. An improvement using a discriminant ideal to rewrite the tree was described by Manubens and the author in 2005. In this paper we describe how to iterate the use ...

Memristors have pinched hysteresis loops in the V − I plane. Ideal memristors are everywhere non-linear, cross at zero and are rotationally symmetric. In this paper we extend memristor theory to produce different types of non-ideality and find that: including a background current (such as an ionic current) moves the crossing point away from zero; including a degradation resistance (that increas...