THEORY OF B-MATRIX AND HYPERCUBE


Authors : Dr. Ismail Abbas

Volume/Issue : Volume 6 - 2021, Issue 5 - May

Google Scholar : http://bitly.ws/9nMw

Scribd : https://bit.ly/2RYyNTa

We introduce and define a theory of the Bstochastic transition matrix other than the Markov stochastic transition matrix. We also define and explain the main assumptions and principles essential to its validity as well as its inherent characteristics. We compare the characteristics of matrices B and Markov matrix and show that both matrices can be real or imaginary and that their chains work in both real and imaginary spaces. In particular, matrix B has a striking advantage of being easy to formulate and simple to manage for 2D and 3D spatiotemporal diffusion problems with any arbitrary boundary conditions BC and any arbitrary configuration of source / sink terms such as case of Poisson and Laplace partial differential equations as well as heat diffusion PDE. Finally, we propose a modeling of the 16 vertices of the 4D hypercube in the cartisian space x, y, z, w by a super symmetrical matrix B of 16 inputs and 16 outputs.

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