A simple procedure to map two probability measures in R is the so-called Knothe-Rosenblatt rearrangement, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the...

In this paper, a new analogue of Bernstein-Kantorovich operators as (p, q)-Bernstein-Kantorovich operators are introduced. We discuss approximation properties for these operators based on Korovkin’s type approximation theorem and we compute the order of convergence using usual modulus of continuity and also the rate of convergence when the function f belongs to the class LipM (α). Moreover, the...

The paper establishes that a generalization of Monge–Kantorovich equation gives rise to necessary and sufficient optimality condition for the Kantorovich dual problem minimal flow associated with very degenerate Finsler metric without any assumption on coerciveness.

in this study prediction of the steady-state flow of branched polymer melts in pipe geometry with finite volume method is presented. our analysis in this study revealed that;for normal-stress tqq , the xpp model can predict this tensor unlike the other viscoelastic models such as ptt or gieskus which can not predict tqq for viscoelastic fluid in two dimensional pipe flows. the fluid is modelled...

a new approach is proposed to model a crack in orthotropic composite media using the extended finite element method (xfem). the xfem uses the concept of partition of unity in addition to meshless basic idea of approximating a field variable by its values at a set of surrounding nodes. as a result, higher order approximations can be designed with the same total number of degrees of freedom. in t...