Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

Infinitesimal Bialgebras, Pre-lie and Dendriform Algebras

We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...

Copies of a rooted weighted graph attached to an arbitrary weighted graph and applications

Ela Copies of a Rooted Weighted Graph Attached to an Arbitrary Weighted Graph and Applications

The spectrum of the Laplacian, signless Laplacian and adjacency matrices of the family of the weighted graphs R{H}, obtained from a connected weighted graph R on r vertices and r copies of a modified Bethe tree H by identifying the root of the i-th copy of H with the i-th vertex of R, is determined.