Understanding the limiting distributions of translates of measures on submanifolds of homogeneous spaces of Lie groups lead to very interesting number theoretic and geometric applications. We explore this theme in various generalities, and in specific cases. Our main tools are Ratner’s theorems on unipotent flows, nondivergence theorems of Dani and Margulis, and dynamics of linear actions of se...

stochastic approach to vehicle routing problem: development and theories abstract in this article, a chance constrained (ccp) formulation of the vehicle routing problem (vrp) is proposed. the reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. knowing that reliable computer software for lar...

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...

In this paper, we present two quite general approximation theorems for the propagators of higher order (in time) abstract Cauchy problems, which extend largely the classical Trotter-Kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions. Then, we apply the approximation theorems to deal with the second order dynamical boundary value problems.