In the present paper some different types of boundedness in fuzzy normed linear spaces of type $(X,N,\ast )$ , where ∗ is an arbitrary t-norm, are considered. These boundedness concepts are very general and some of them have no correspondent in the classical topological metrizable linear spaces. Properties of such bounded sets are given and we make a comparative study among these types of boundedness. Among them there are various concepts concerning symmetrical properties of the studied objects arisen from the classical setting appropriate for this journal topics. We establish the implications between them and illustrate by examples that these concepts are not similar.

In this paper a system derived by an optimal control problem for the ball-plate dynamics is considered. Symplectic and Lagrangian realizations are given and some symmetries are studied. The image of the energy-Casimir mapping is described and some connections with the dynamics of the considered system are presented.

In this paper the n-tuples of commuting isometric semigroups on a Hilbert space and the product semigroup generated by them are considered. Properties of the right defect spaces and characterizations of the semigroups of type ?s? are given. Also, the Wold-type decompositions with 3n summands for n-tuples of commuting isometric semigroups are introduced. The existence and uniqueness of such decompositions are analysed and several connections with the Wold decompositions of each semigroup and their product semigroup are presented.