We recall the history of the transportation (Kantorovich) metric and the Monge–Kantorovich problem. We also describe several little-known applications: the first one concerns the theory of decreasing sequences of partitions (tower of measures and iterated metric), the second one relates to Ornstein's theory of Bernoulli automorphisms (¯ d-metric), and the third one is the formulation of the str...

We propose a constructive approach to solve the Monge-Kantorovich problem for chains of infinite order on a finite alphabet with an additive cost function. From this constructive description of the Kantorovich coupling we obtain, for any ǫ > 0, a perfect simulation algorithm for sampling from an ǫ-approximating coupling which assigns to the cost function an expectation which is ǫ-close to the m...

Solutions to Monge-Kantorovich equations, expressing optimality condition in mass transportation problem with cost equal to distance, are stationary points of a critical-slope model for sand surface evolution. Using a dual variational formulation of sand model, we compute both the optimal transport density and Kantorovich potential as t → ∞ limit of evolving sand flux and sand surface, respecti...

The research is supported by Zhejiang Provincial Education Department Research Projects (Y201016421) Abstract We achieve that the optimal solutions according to Kantorovich-Rubinstein-Wasserstein Lp−distance (p > 2) (abbreviation: KRW Lp−distance) in a bounded region of Euclidean plane satisfy a partial differential equation. We can also obtain the similar results about Monge-Kantorovich proble...

This paper concerned with applicability of the method of Kantorovich majorants to nonlinear singular integral equations with Hilbert kernel . The results are illustrated in Hölder space. RESUMEN Este art́ıculo es concerniente a la aplicabilidad del método de mayorantes de Kantorovich para ecuaciones integrales singulares no lineales con núcleo de Hilbert. Los resultados son aplicaciones en espac...

This paper deals with the nonlinear free vibration of thick annular functionally graded material plates. The thickness is assumed to be constant. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on the first-order shear deformation plate theory and...

In contrast to its wealth of applications in mathematics, the Kantorovich metric started to be noticed in computer science only in recent years. We give a brief survey of its applications in probabilistic concurrency, image retrieval, data mining, and bioinformatics. This paper highlights the usefulness of the Kantorovich metric as a general mathematical tool for solving various kinds of proble...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

In the present paper we prove a Besicovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices. Mathematics Subject Classification: 37A30, 47A35, 46B42, 46E30, 46G10.