for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

The notion of stability can be generalised to point processes by defining the scaling operation in a randomised way: scaling a configuration by t corresponds to letting such a configuration evolve according to a Markov branching particle system for -log t time. We prove that these are the only stochastic operations satisfying basic associativity and distributivity properties and we thus introdu...

Since branching region of an active nerve fiber is an abrupt widening of the structure, two concepts emerge: first, the stimulating current must be sufficient to raise the outgrowing fibers above the thresh¬old, and secondly, the stimulating current will be divided in proportion to the characteristic admittance of the branches. On the other hand, blocking of the nerve impulse in this region is ...

Since branching region of an active nerve fiber is an abrupt widening of the structure, two concepts emerge: first, the stimulating current must be sufficient to raise the outgrowing fibers above the thresh¬old, and secondly, the stimulating current will be divided in proportion to the characteristic admittance of the branches. On the other hand, blocking of the nerve impulse in this region is ...