The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler’s inequality.

In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is based on a formulation of the discretized equations in vector form using only matrix-vector products and componentwise operations. By applying simple matrix-bas...

The resolution of transport equations is shown to be intimately related to the Monge-Kantorovich optimal mass transportation theory. Existence results for linear systems of transport equations in divergence form are given at the end of the paper.

The article deals with problems of generating desired illumination patterns, formulated in a special way. More precisely, we consider that can be reformulated as Monge–Kantorovich mass transfer problem some cost function. For all this type, uniformly formulate the support quadric method and show it coincides gradient for finding maximum certain concave

We describe a significant extension of the finite element method (FEM) that allows finite element analysis (FEA) to be performed in situ, on a native geometric representation of a solid domain. The proposed method, called Scan&Solve, is a particular implementation of the solution structure method (SSM) that builds on the classical ideas of Kantorovich and Rvachev. It can be applied to any geome...