The Australian Journal of Mathematical Analysis and Applications
In this paper, we introduce para-chaotic tuples of operators and we give some relations between para-chaoticity and Hypercyclicity Criterion for a tuple of operators.
Stability of mixed additive-quadratic Jensen type functional equation in various spaces
In this paper, we prove the generalized Hyers-Ulam stability of the following mixed additive-quadratic functional equation: 2f(x+y2)+f(x-y2)+f(y-x2)=f(x)+f(y) in various spaces.
Extensions of the poisson bracket to differential forms and multi-vector fields
Abstract The Poisson bracket defined originally on the smooth function algebra of a Poisson manifold is extended to the space of all co-exact forms of this manifold. For the extended bracket analogues of the basic constructions and formulae of the standard hamiltonian formalism are given. The Poisson bracket is extended also, in a dual way, to the space of all co-exact multi-vector fields. Finally, we define the graded Lie algebra homomorphisms connecting these extended brackets and their “differentials” as well. The method used is based on the “unification” techniques introduced by the second author.