9,778 research outputs found
Relative Severi inequality for fibrations of maximal Albanese dimension over curves
Let be a relatively minimal fibration of maximal Albanese
dimension from a variety of dimension to a curve defined over
an algebraically closed field of characteristic zero. We prove that , which was conjectured by Barja in [2]. Via the strategy
outlined in [5], it also leads to a new proof of the Severi inequality for
varieties of maximal Albanese dimension. Moreover, when the equality holds and
, we prove that the general fiber of has to satisfy the
Severi equality that . We also prove
some sharper results of the same type under extra assumptions.Comment: Comments are welcom
Modelling the Self-similarity in Complex Networks Based on Coulomb's Law
Recently, self-similarity of complex networks have attracted much attention.
Fractal dimension of complex network is an open issue. Hub repulsion plays an
important role in fractal topologies. This paper models the repulsion among the
nodes in the complex networks in calculation of the fractal dimension of the
networks. The Coulomb's law is adopted to represent the repulse between two
nodes of the network quantitatively. A new method to calculate the fractal
dimension of complex networks is proposed. The Sierpinski triangle network and
some real complex networks are investigated. The results are illustrated to
show that the new model of self-similarity of complex networks is reasonable
and efficient.Comment: 25 pages, 11 figure
- β¦