Linear Systems And Signals 3rd Edition Pdf Download Fixed
Click Here >>> https://shoxet.com/2tahar
The goal of this paper is to firstly describe and evaluate a novel approach for the solution of multidimensional linear systems using a canonical form. Secondly, this novel approach is applied to the blood flow problem, for which it provides a more accurate description of the flow than the traditional technique based on the system matrix. Finally, the validity of a new non-linear index derived from the system matrix is also investigated.
The multidimensional analysis of wave propagation in the aorta is first presented. These analyses are based on the solution of a general boundary problem, which result in a matrix eigenvalue problem for the system matrix, and a canonical system of eigenvectors for the system matrix. The analysis is then applied to the specific problem of interest, namely the wave propagation in the ascending aorta, resulting in a detailed description of the aortic circulation. Several linear and non-linear indices are derived from the resulting eigenvectors, demonstrating the feasibility of this approach.
The second part of the paper is devoted to the comparison between the results obtained using the linear canonical system of eigenvectors and those obtained by using the traditional analysis based on the system matrix. This comparison is performed on two case studies, namely the inflow (ascending aorta) and the outflow (descending aorta) waves. The comparison demonstrates that the analysis based on the canonical eigenvectors results in a more reliable flow description.
The third part of the paper is devoted to the derivation of a non-linear index based on the linear canonical eigenvectors. This index is compared with the traditional non-linear methods of analysis, namely the non-linear correlation dimension and the Lyapunov exponent. These comparisons were performed on the example of the aortic inflow, demonstrating that the index derived from the linear canonical eigenvectors provides a better flow description. In this case the new method not only improves the description of the flow but also leads to an improved description of the non-linear dynamics.
In this paper, we show how the set of possible static symmetries of a linear multidimensional system can be determined using a direct linearization technique. We also perform a thorough examination of the interplay between the different possible static symmetries and a certain class of non linear transformations, previously introduced by one of the authors. This last study reveals that a specific class of static symmetry can be represented as a periodic non linear transformation associated with a certain multidimensional oscillator. This leads us to the natural question as to what other possible static symmetries can be related to a multidimensional oscillator, and we show that the concept can be extended to any non linear symmetry that can be represented as a static transformation, with a corresponding oscillator. We also show, by means of a simple example, how this extension allows to gain deeper insights into the structure of a multidimensional system. 827ec27edc