Abstract For any multi-graph $G$ with edge weights and vertex potential, its universal covering tree ${\mathcal{T}}$, we completely characterize the point spectrum of operators $A_{{\mathcal{T}}}$ on ${\mathcal{T}}$ arising as pull-backs local, self-adjoint $A_{G}$ $G$. This builds work Aomoto, includes an alternative proof necessary condition for derived in [ 5]. Our result gives a finite time...

in this paper in order to determine performance point (pp) in a simply way, a program has been introduced using excel software. actually, to determine the pp point, using capacity spectrum, a lot of and error and efforts to be done. unfortunately this method does not give an accurate value. most of engineers use simple methods such as, method of ratio as given in codes of practice, but the resu...

contrary to the long period ground motions that can be predicted and estimated, high frequency ground motions have random character and behave stochastically. stochastic modeling methods are usually used for the modeling of high frequency ground motions where there are not strong ground motion records. stochastic methods are of two kinds: in the first one, the seismic source is considered as a ...

We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in [1]. We establish by cut-and-join methods that the number of partial chord diagrams filtered by the boundary length and point spectrum satisfies a recursion relation, which combined with an initial condition determines these numbers uniquely. This recursi...