Authors : Ismail Abbas

Volume/Issue : Volume 9 - 2024, Issue 9 - September

Google Scholar : https://tinyurl.com/vwm6tfnr

Scribd : https://tinyurl.com/bdcw4z94

DOI : https://doi.org/10.38124/ijisrt/IJISRT24SEP1243

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Abstract : If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By effective alternative to current mathematics, we mean working in a more complete mathematical space than the classical 3D+t variety which is inadequate for generating well-defined definitions and hypotheses as well as its limited ability to solve time-dependent partial differential equations. The current classical discrete 3D+t space PDE, in which time is an external controller and not integrated into the 3D geometric space, cannot be integrated digitally. This space is logically incomplete and misleading in the production of definitions and hypotheses as well as in the resolution itself of time- dependent PDEs. It is no wonder that these definitions/assumptions are confusing and result in weak or intractable mathematics, leading to all kinds of misunderstandings, from horrible notations to undisciplined length of theorems containing a considerable amount of black magic and ending with a gray nature of the mathematical result obtained. In this article, we present some of the most inaccurate assumptions and definitions in current classical mathematics that arise from using the 3D+t manifold space to specify initial conditions, boundary conditions, and the source/sink term. Fortunately, these inaccurate assumptions that start with inadequate space for boundary conditions, initial conditions, and source/sink term can be spotted and analyzed via 4D unitary numerical statistical theory called Cairo techniques in the format of transition chains of matrix B to complete what is missing. In other words, we present how to spot some of the worst mathematical conclusions of classical 3D geometry plus t as an external control numerical space, and then show how to correct them via the 4D unit space which is the subject of this article.

References :

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