The problem of optimal transportation between a set of sources and a set of wells has become recently the object of new mathematical models generalizing the Monge-Kantorovich problem. These models are more realistic as they predict the observed branching structure of communication networks. They also define new distances between measures. The question arises of how these distances compare to th...

In this paper, we deal with Stancu operators which depend on a non-negative integer parameter. Firstly, define Kantorovich extension of the operators. For functions belonging to space Lp [0, 1] , 1 ? p < ?, obtain convergence in norm by sequence Stancu-Kantorovich operators, and give an estimate for rate via first order averaged modulus smoothness. Moreover, operators; search variation detra...

The aim of this paper is to study the convergence and approximation properties of the bivariate operators and GBS operators of Kantorovich type.

We consider two variational evolution problems related to MongeKantorovich mass transfer. These problems provide models for collapsing sandpiles and for compression molding. We prove the following connection between these problems and nonlocal geometric curvature motion: The distance functions to surfaces moving according to certain nonlocal geometric laws are solutions of the variational evolu...

The Newton–Kantorovich hypothesis (15) has been used for a long time as a sufficient condition for convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space setting. Recently in [3], [4] we showed that this hypothesis can always be replaced by a condition weaker in general (see (18), (19) or (20)) whose verification requires the same computational cos...

A probabilistic method for solving the Monge-Kantorovich mass transport problem on R is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle with an optimal transport cost as its rate function. As a consequence, new approximation results for the optimal cost function and the optimal transport plans ar...

The chaotic order A B among positive invertible operators A,B > 0 on a Hilbert space is introduced by logA≥ logB. Using Uchiyama’s method and Furuta’s Kantorovich-type inequality, we will point out that A B if and only if ‖BpA−p/2B−p/2‖Ap ≥ Bp holds for any 0 < p < p0, where p0 is any fixed positive number. On the other hand, for any fixed p0 > 0, we also show that there exist positive invertib...

By a classical result of Gray et al. (1975) the %̄ distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product spaces. This is a modification of the optimal coupling problem from Monge–Kantorovich theory. In this paper we derive some general classes of examples of optimal stationary couplings whi...

The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information on the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated electrons has been based on the calculation of comotion functions with the help of semianalytic formulations. This procedure is system-specific and has been ...

The original transport problem is to optimally move a pile of soil to an excavation. Mathematically, given two measures of equal mass, we look for an optimal map that takes one measure to the other one and also minimizes a given cost functional. Kantorovich relaxed this problem by considering a measure whose marginals agree with given two measures instead of a bijection. This generalization lin...