Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspo...

The connection matrix theory for Morse decompositions is introduced. The connection matrices are matrices of maps between the homology indices of the sets in the Morse decomposition. The connection matrices cover, in a natural way, the homology index braid of the Morse decomposition and provide information about the structure of the Morse decomposition. The existence of connection matrices of M...

Let G be a Lie groupwith Lie algebra g. On the trivial principal G-bundle over g there is a natural connection whose curvature is the Lie bracket of g. The exponential map of G is given by parallel transport of this connection. If G is the diffeomorphism group of a manifold M , the curvature of the natural connection is the Lie bracket of vectorfields on M . In the case that G = SO(3) the motio...

Proof-Nets (Roorda 1990) are a good device for processing with eategorial grammars, mainly because they avoid spurious ambiguities. Nevertheless, they do not provide easily readable structures and they hide the true proximity between Categorial Grammars and Dependency Grammars. We give here an other kind of Proof-Nets which is much related to Dependency Structures similar to those we meet in, f...

A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular, we prove that, under some natural assumptions, any ksymplectic manifold admits an Ehresmann connection, discuss some corollaries of this result and find vanishing theorems for characteristic classes on a k-symplectic...

this paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. the classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number