This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-pose...

The nonlocal boundary value problem for elliptic difference equations in an arbitrary Banach space is considered. The well-posedness of this problem is investigated. The stability, almost coercive stability and coercive stability estimates for the solutions of difference schemes of the second order of accuracy for the approximate solutions of the nonlocal boundary value problem for elliptic equ...

generally, this article deals with the challenges and solutions facing the internet security. first, the article discusses the following subjects: the security of communication and information networks, the importance of the networks, the networks security precedence internet and computers crimes, the beginning of computer crimes, classifying computer crimes as well as the solutions proposed to...

We formulate a minimax game which is equivalent to the Nehari problem in the sense that this minimax game is well-posed if and only if the Hankel norm of a given operator is less than a prescribed constant. This game and the dual game provide us with physical interpretations of the Riccati operators that are commonly used in the solution of the Nehari problem.

We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed ...

Electroencephalography is a non-invasive technique for detecting the brain activity from the measure of the electric potential on the head surface. In mathematical terms, it reduces to an inverse problem in which one wants to determine the source that has generated the electric field by measuring the boundary value of the electric potential [1]. Since the timevariation of the electric and magne...

The optimal transport problem studies how to one measure another in the most cost-effective way and has wide range of applications from economics machine learning. In this paper, we introduce study an information constrained variation problem. Our yields a strengthening generalization Talagrand’s celebrated transportation cost inequality. Following Marton’s approach, show that new inequality ca...