Exponential convergence for one dimensional contact processes

The complete convergence theorem implies that starting from any initial distribution the one dimensional contact process converges to a limit ast. In this paper we give a necessary and sufficient condition on the initial distribution for the convergence to occur with exponential rapidity.This work was discussed while the authors were visiting the Nankai Mathematics Institute in Tianjin.Partially supported by the National Science Foundation, the Army Research Office through the Mathematical Sciences Institute at Cornell University, and a Guggenheim fellowship.Research supported by the National Science Foundation of China.     

A study of a possible unified potential model

The various properties of quarkonium systems have been studies in the framework of a recently proposed potential model, which combines the asymptotic freedom at the largeQ ₂ and the multigluon effect at the lowerQ ₂ regions with the confinement at the large distance. Good agreements with experiments are found, including \(c\bar c\) and \(b\bar b\) energy levels, leptonic decay widths, and in particular the fine and hyperfine splittings. We also analyze the Lorentz structure of the confinement potential with reference to the charmonium and bottomium fine and hyperfine splittings. Our analyses conclude that almost pure scalar confinement is favored. The properties of \(t\bar t\) spectroscopies are studied over a wide range of \(M_{t\bar t}\) values (from 80 GeV to 200 GeV).