This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \cite{Cont} , where velocity field viscous incompressible fluid written as expected value stochastic process. Our contribution to establish this probabilistic representation formula for mild solutions $\mathbb{R}^{d} $.

lunar and mars landing is a crucial part of any exploration mission. its importance is manifested by the considerable interest in the past couple of decades. solution of lunar descent can be either numerical or analytical. numerical solutions are iterative and computationally demanding and some of them might not be suitable for on-board implementation. on the other hand, analytical solutions ar...

This paper presents a method to improve the accuracy of DC Optimal Power Flow problem, based on evaluating some nodal shares of transmission losses, and illustrates its efficiency through comparing with the conventional DCOPF solution, as well as the full AC one. This method provides three main advantages, confirming its efficiency: 1- It results in such generation levels, line flows, and noda...