Authors : Ismail Abbas

Volume/Issue : Volume 9 - 2024, Issue 10 - October

Google Scholar : https://tinyurl.com/k3vce7sf

Scribd : https://tinyurl.com/5csunhts

DOI : https://doi.org/10.38124/ijisrt/IJISRT24OCT1091

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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 useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as 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. No wonder these definitions/assumptions are ugly 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 catastrophic inaccurate assumptions existing in current classical mathematics, resulting from the use of 3D+t manifold space to specify initial conditions, boundary conditions and the source/sink term. Fortunately, these inaccurate assumptions that start with an ugly 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 ugliest 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 of statistical transition matrix chains. By complex and untold history, we mean that useless and misleading mathematics dominated scientific research and education throughout the 20th century, so much so that the accumulated legacy of misconceptions became a huge, complex mountain, almost impossible to eliminate. Fortunately, the numerical theory of Cairo techniques and the Laplacian theorem constitute an advanced and exhaustive form of the energy continuity equation and thus can create new logical mathematics. This is also the case of the famous Schrödinger time- dependent PDE.  The Laplacian theorem is one of the most important products created by the numerical statistical theory called Cairo techniques. In previous articles we introduced and briefly explained the so-called Laplacian theorem in the 4D x-t unit space, while in this article we highlight its importance and how it can generate new mathematics in more detail. The Laplacian partial differential equation that interests us is the one having a well-defined exclusive form and living in an isolated sample spatial control volume surrounded by a closed surface (A) and subject to Dirichlet boundary conditions. This very particular case of Laplacian PDE is always treated mathematically in a classical D^4 variety which is lazy and misleading. Finally, this article collects, studies, identifies and analyzes the dozen most common current useless mathematical events and presents an effective and adequate alternative.

References :

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2. I. Abbas, An effective alternative to current mathematics, IJISRT journal, Sep 2024.
3. I. Abbas, Useless mathematics, ResearchGate, Sep 2024.
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7. I. Abbas, IJISRT, Time Dependent Numerical Statistical Solution of the Partial Differential Heat Diffusion Equation, Volume6, Issue , January – 2021.
8. Abbas, How nature works in four-dimensional space: the complex and untold story, ResearchGate, IJISRT journal, May 2023.
9. I. Abbas, An effective alternative to current mathematics, Useless mathematics, IJISRT journal, ResearchGate, Sep 2024.
10. I. Abbas, Useless mathematics, ResearchGate, IJISRT review, Sep 2024.
11. I. Abbas, Effective unconventional approach to statistical differentiation and statistical integration, ResearchGate, IJISRT journal, November 2022.
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13. I. Abbas, Theory and Design of Audio Rooms: Physical Formulation, September 2024, International Journal of Innovative Science and Research Technology DOI: 10.38124/ijisrt/IJISRT24AUG547
14. I.Abbas, Theory and design of audio rooms-of audio rooms-Reformulation of Sabines formula, ResearchGate, IJISRT journal, Oct 2021.
15. Chiara Visentin, et al., A numerical and experimental validation of the theory of acoustic diffusion inside long rooms https://hal.science/hal-00845722, July 2013
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20. I. Abbas Cairo Techniques Solution of Schrödinger's Partial Differential Equation -Time Dependence, March 2024, International Journal of Innovative Science and Research Technology, DOI: 10.38124/ijisrt/IJISRT24MAR911
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