3,809 research outputs found
Existence, uniqueness and stability for a class of third order dissipative problems depending on time
We prove new results regarding the existence, uniqueness, (eventual)
boundedness, (total) 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 Liapunov functional V depending on two
parameters, which we adapt to the characteristics of the problem.Comment: Latex file, 20 pages, 7 figures. To appear in "Nonlinear Analysis:
Theory, Methods & Applications
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 and a
semigroup ideal , produces a new numerical semigroup, denoted by
S\Join^b\E (where is any odd integer belonging to ), such that
S=(S\Join^b\E)/2. In particular, we characterize the ideals such that
is almost symmetric and we determine its type.Comment: 17 pages. Accepted for publication on: Semigroup Foru
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
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
Properties of chains of prime ideals in an amalgamated algebra along an ideal
Let be a ring homomorphism and let be an ideal of . In
this paper, we study the amalgamation of with along with respect to
(denoted by ), 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 , the and the 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
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