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...

We study the extreme and periodic $L_2$ discrepancy of plane point sets. The is based on arbitrary rectangles as test sets whereas periodic uses “periodic intervals”, which can be seen intervals t

Let f be an orientation preserving homeomorphism of the disc D which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2π/3 or 4π/3, or J has a periodic point of least period n for each n ∈ N∗.