Stability and attractivity for a class of dissipative phenomena

We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations arising in Superconductor Theory, Quantum Mechanics and in the Theory of Viscoelastic Materials.Comment: Latex2e file, 12 pages. To appear in Rend Ma

Stability properties for some non-autonomous dissipative phenomena proved by families of Liapunov functionals

We prove some new results regarding the boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may contain time-dependent coefficients. The class includes equations arising in Superconductor Theory, and in the Theory of Viscoelastic Materials. In the proof we use a family of Liapunov functionals W depending on two parameters, which we adapt to the `error', i.e. to the size of the chosen neighbourhood of the null solution.Comment: Latex file, 12 page

The numerical duplication of a numerical semigroup

In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup $S$ and a semigroup ideal $E\subseteq S$, produces a new numerical semigroup, denoted by S\Join^b\E (where $b$ is any odd integer belonging to $S$), such that S=(S\Join^b\E)/2. In particular, we characterize the ideals $E$ such that $S\Join^bE$ is almost symmetric and we determine its type.Comment: 17 pages. Accepted for publication on: Semigroup Foru

A family of quotients of the Rees algebra

A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring. It is shown that several properties of the rings of this family do not depend on the particular member.Comment: 17 pages. To appear on "Communications in Algebra

On the associated graded ring of a semigroup ring

Let (R;m) be a numerical semigroup ring. In this paper we study the properties of its associated graded ring G(m). In particular, we describe the H^0_M for G(m) (where M is the homogeneous maximal ideal of G(m)) and we characterize when G(m) is Buchsbaum. Furthermore, we find the length of H^0_M as a G(m)-module, when G(m) is Buchsbaum. In the 3-generated numerical semigroup case, we describe the H^0_M in term of the Apery set of the numerical semigroup associated to R. Finally, we improve two characterizations of the Cohen-Macaulayness and Gorensteinness of G(m) given in [2] and [3], respectively.Comment: 20 page

Properties of chains of prime ideals in an amalgamated algebra along an ideal

Let $f:A \to B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by ${A\Join^fJ}$), a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D'Anna and Fontana in 2007, and other classical constructions (such as the $A+ XB[X]$, the $A+ XB[[X]]$ and the $D+M$ constructions). In particular, we completely describe the prime spectrum of the amalgamated duplication and we give bounds for its Krull dimension.Comment: J. Pure Appl. Algebra (to appear