18 research outputs found
Observation and inverse problems in coupled cell networks
A coupled cell network is a model for many situations such as food webs in
ecosystems, cellular metabolism, economical networks... It consists in a
directed graph , each node (or cell) representing an agent of the network
and each directed arrow representing which agent acts on which one. It yields a
system of differential equations , where the component
of depends only on the cells for which the arrow
exists in . In this paper, we investigate the observation problems in
coupled cell networks: can one deduce the behaviour of the whole network
(oscillations, stabilisation etc.) by observing only one of the cells? We show
that the natural observation properties holds for almost all the interactions
Multiplicative Functionals on Algebras of Differentiable Functions
For a class of Banach spaces E including separable spaces and realcompact superreflexive spaces, it is shown in this note that every nonzero scalar homomorphism on the algebra Cm() of all Cm- functions defined on an open subset of E is given by evaluation at some point of
Weak-polynomial convergence on spaces lp and Lp
This paper is concerned with the study of the set P-1 (0), when P varies over all orthogonally additive polynomials on l(p) and L (p) spaces. We apply our results to obtain characterizations of the weak-polynomial topologies associated to this class of polynomials
Estimates of disjoint sequences in Banach lattices and R.I. function spaces
We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions