An easy consequence of Kantorovich-Rubinstein duality is the following: if f : [ 0 , 1 ] d → R Lipschitz and { x … N } ⊂ then | ∫ ( ) − ∑ k = ≤ ‖ ∇ L ∞ ⋅ W δ where denotes 1−Wasserstein (or Earth Mover's) Distance. We prove a similar inequality with smaller norm on larger Wasserstein distance instead ). Our sharp when points are very regular, i.e. ∼ / . This prompts question whether these two i...

First time, an analytical two-dimensional (2D) elasticity solution for arbitrarily supported axially functionally graded (FG) beam is developed. Linear gradation of the material property along the axis of the beam is considered. Using the strain displacement and constitutive relations, governing partial differential equations (PDEs) is obtained by employing Ressiner mixed var...

Received: January 6, 2011 Accepted: January 24, 2011 doi:10.5539/jmr.v3n2p66 The research is supported by Zhejiang Provincial Education Department research projects (Y201016421) Abstract Monge-Kantorovich transportation problem in a bounded region of Euclidean space is transferred into a partial differential equations group. And then the explicit formula of the optimal coupling is achieved. The...

This article aims to propose the short-term cost-based pricing method of supply chain network with the consideration of value-added tax (VAT) and corporate income tax. First, the average cost function of each business unit in supply chain network is given, and the average cost function is taken as the monotone mapping in n-dimensional space. According to Kantorovich theorem, the existence and u...

A new algorithm for real root isolation of polynomial equations based on hybrid computation is presented in this paper. Firstly, the approximate (complex) zeros of the given polynomial equations are obtained via homotopy continuation method. Then, for each approximate zero, an initial box relying on the Kantorovich theorem is constructed, which contains the corresponding accurate zero. Finally,...

The goal of this paper is to present a local convergence analysis of Newton’s method for approximating a locally unique solution of an equation in a Banach space setting. Using the gauge function theory and our new idea of restricted convergence regions we present an extended and unified convergence theory. Key–Words: Newton’s method, Banach space, semilocal convergence, gauge function, converg...

We discuss a new notion of distance on the space of finite and nonnegative measures on Ω ⊂ Rd, which we call Hellinger–Kantorovich distance. It can be seen as an infconvolution of the well-known Kantorovich–Wasserstein distance and the HellingerKakutani distance. The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and...

The purpose of this paper is to give a survey of the progress, advantages and limitations of various operator inequalities involving improved Young's and its reverse inequalities related to the Kittaneh-Manasrah inequality. We also present our new progress to the related research topics. New scalar versions of Young's inequalities are promoted, the operator version and the Hilbert-Schmidt form ...