This paper sets out to review a study of the set of affine controllable systems connexity denoted by Ca.
Abstract
Purpose
This paper sets out to review a study of the set of affine controllable systems connexity denoted by Ca.
Design/methodology/approach
With each affine system a homogeneous system is associated. Jurdjevic and Sallet proved that, if a homogeneous system is controllable in R2−{0} and, if the affine system has not a fixed point, then the affine system is controllable in R2.
Findings
It is shown that these systems are denoted by S, and are dense in Ca.
Research limitations/implications
Allows one to tackle the problem by using the connexity of a dense set in S.
Originality/value
Succeeds in completing a study of the set of affine controllable systems connexity denoted by Ca.
Details
Keywords
The paper presents a method for solving the 3D steady state, linear transport equation in bounded domain.
Abstract
Purpose
The paper presents a method for solving the 3D steady state, linear transport equation in bounded domain.
Design/methodology/approach
The method can be extended easily to general linear transport problem.
Findings
The idea of using the spectral method for searching solutions to the multi‐dimensional transport problems, leads us to a solution for all values of the independent variables.
Research limitations/implications
The procedure is based on the development of the angular flux in a truncated series of Chebyshev polynomials in the spatial variables.
Practical implications
The methodology used will permit us to transform the 3D problem into a set of 1D problems. The convergence of this approach is studied in the context of the discrete‐ordinates method.
Originality/value
An adaptation of this method for the convergence of the spectral solution within the framework of the analytical solution to study and prove convergence is relatively new.