Abstract: We present a study of the Adomian's Decomposition Method (ADM) applied to the Hamilton-Jacobi equations ut + H (ux) = 0. We recall the well known characteristics methods in the case of this type of equations to justify the existence or not of solutions. This yields that the ADM gives efficient solutions in time only in ]0; T *[, where T * is the critical time of our equation.
Abstract: In this work we present some matrix operators named circulant operators and their action on square matrices. This study on square matrices provides new insights into the structure of the space of square matrices. Moreover it can be useful in various fields as in agents networking on Grid or large-scale distributed self-organizing grid systems.
Abstract: This work initiates a systematic investigation into the matrix forms of the Pascal triangle as mathematical objects in their own right. The present paper is especially devoted to the so-called G-matrices, i.e. the set of the twelve (n+1)×(n+1) triangular matrix forms that can be derived from the Pascal triangle expanded to the level View the MathML source. For n=1, the G-matrix set reduces to a set of four distinct matrices. The twelve G-matrices are defined and the classic Pascal recursion is reformulated for each of the twelve G-matrices. Three sets of matrix transformations are then introduced to highlight different relations between the twelve G-matrices and for generating them from appropriately chosen subsets.
Abstract: This paper presents a framework of multimodel based approach for interconnected components network by finite state machine model. The main concept on which we base our approach is the fact that, in a context of interconnected components, due to the influence of some components named here key-components the system can switch from one mode to another. The influence of these components can be measured by the level of involvement in the switching events. The proposed approach can be applied to embedded systems in which we propose to consider the controller as a part of the system.
Abstract: This paper presents a finite state machine approach of grid system, for tracking the state of involved components in a given behavior of this system. In large system context, classic methods such as state composition become time- consuming and cumbersome due to the explosion problem of combinatorial states. The approach presented in this paper tend to overcome this problem, using finite state machines constructed with median symmetry operators as transition alphabet, and matrices of local components state as vertices.
