The Schrödinger equation for N particles interacting through effective pair potentials is derived from the massless Nelson model with ultraviolet cutoffs. We consider a scaling limit where the particles are slow and heavy, but, in contrast to earlier work [6], no “weak coupling” is assumed. To this end we prove a space-adiabatic theorem without gap condition which gives, in particular, control ...

For a strictly stationary sequence of regularly varying random variables we study functional weak convergence of partial sum processes in the space D[0, 1] with the Skorohod J1 topology. Under the strong mixing condition, we identify necessary and sufficient conditions for such convergence in terms of the corresponding extremal index. We also give conditions under which the regular variation pr...

Abstract The purpose of this paper to establish the semilocal convergence analysis three-step Kurchatov method under weaker conditions in Banach spaces. We construct recurrence relations assumption that involved first-order divided difference operators satisfy $$\omega $$ ω condition. Theorems are given for e...

this paper has examined the phenomenon of convergence of per capita out put levels across the ic countries for the 1960-1998 periods. three concepts of convergence, i.e., sigma beta and relative beta, have been used. the estimated beta values reveals only a very weak convergence (?=.0014) across ic for 1960-1998 period. but when a more homogeneous group of countries were selected, the results s...

We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely , to answer in the affirmative to the open question posed by Tan and Xu [1] even in a general setup.     1 1 n n c x      