Journal of Intelligent Communication

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Fractal Dimension (Df) Theory of Ismail’s Entropy (IE) with Potential Df Applications to Structural Engineering

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https://doi.org/10.54963/jic.v4i1.258
A Mageed, I. (2024). Fractal Dimension (Df) Theory of Ismail’s Entropy (IE) with Potential Df Applications to Structural Engineering. Journal of Intelligent Communication, 3(2), 111–123. https://doi.org/10.54963/jic.v4i1.258
Volume 3 Issue 2 (2024): In Progress
Copyright (c) 2024 Ismail A Mageed
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Authors

As an ultimate generalisation to several kinds of generalised entropy in the literature, a novel entropy measure, namely, Ismail’s entropy, or (IE), is presented. This article spotlights the significance of fractal dimension, through highlighting several possible applications of fractal dimension to structural engineering. In addition to several difficult open problems and the next step of inquiry, the paper ends with some concluding observations.

Keywords:

information theory structural engineering

Author Biography

Dr. Ismail A Mageed, University of Bradford, United Kingdom.

Dr. Ismail A Mageed obtained his doctorate in Applied Probability at The University of Bradford, United Kingdom. Dr Mageed has been nominated by numerous high-profile academic institutions to the world prestigious ABEL PRIZE(NOBLE PRIZE OF MATHEMATICS) FOR THE ACADEMIC YEAR 2025, based on his great services to humanity through revolutionary mathematical applications to advance several scientific disciplines, including Engineering, Computer Science and much more. His current research interests include the unification of queueing theory with information theory and information geometry. His leading research on the relativisation of queuing theory and discovering the geodesic  equation of motion for transient queues was greatly received by the world research community, based on spotlighting novel avenues for a UNIFIED THEOREM ON EVERYTHING. Mageed’s research on finding the analytic solutions of the longstanding simulative approach of The Pointwise Stationary Fluid Flow Approximation theory (PSFFA) was an exceptional discovery to advance PSFFA theory. Dr Mageed has published numerous papers in many highly reputable journals and IEEE conferences. He is also a reviewer  and a member of the editorial board to many international prominent journals. Mageed’s research has been internationally recognized as being revolutionary by providing several breakthroughs and solving many longstanding open problems. He is currently an active member at the NetPen Research Group, which is the strongest research group in queueing networks in the world. Dr Mageed has published a chapter in a book of the best eight queueing theorists in the world, entitled:

Queueing Theory 2: Advanced Trends

By the world-renowned Publishing Company, ISTE WILLEY, which was translated into French by the same Publishing Company. He has also published another chapter in a high-profile book, entitled:

Fractal Analysis - Applications and Updates

By the world leading open access publishing house, IntechOpen. He is currently coaching numerous volunteering  several research teams worldwide to deliver more insights on employing research to serve humanity. He is also a fellow of the Royal Statistical Society (RSS),the OR Society of the United Kingdom, a member of INTISCC (Austria), IEANG (world council of engineering) and a life member of the Islamic Society of Statistical Sciences. 

Highlights

  • In this exposition, the fractal dimension theory of Ismail’s entropy, namely IE, is revealed for the first time ever.
  • More potentially, this study has revealed how this discovery reveals the dominancy of IE, especially from a fractal dimension perspective.
  • On another applicative note, some applications of fractal dimension to structural engineering are addressed.
  • Having addressed these two potential applications, the frontiers are full of hopes to proceed with more and more , yet to explore, especially to enhance space industry and other unprecedented applications.

References

  1. Mageed, I.A.; Zhang, Q. An Introductory Survey of Entropy Applications to Information Theory, Queuing Theory, Engineering, Computer Science, and Statistical Mechanics. In Proceedings of the 2022 27th International Conference on Automation and Computing, Bristol, UK, 1–3 September 2022.
  2. Mageed, I.A.; Zhang, Q. An Information Theoretic Unified Global Theory for a Stable $ M/G/1$ Queue with Potential Maximum Entropy Applications to Energy Works. In Proceedings of the 2022 Global Energy Conference, Batman, Turkey, 26–29 October 2022.
  3. Kouvatsos, D.D.; Mageed, I.A.; Anisimov, V.; Limnios, N. Non-extensive Maximum Entropy Formalisms and Inductive Inferences of Stable M/G/1 Queue with Heavy Tails. Adv. Trends Queue. Theory 2021, 2.
  4. Mageed, I.A.; Bhat, A.H. Generalized Z-Entropy (Gze) and Fractal Dimensions. Appl. Math. Inf. Sci. 2022, 16, 829–834.
  5. Zhou, L.; Johnson, C.R.; Weiskopf, D. Data-Driven Space-Filling Curves. IEEE Trans. Visualization Comput. Graphics 2020, 27, 1591–1600.
  6. Wang, W.J.; Xu, X.; Shao, Y.; Liao, J.W.; Jian, H.X.; Xue, B.; Yang, S.G. Fractal Growth of Giant Amphiphiles in Langmuir-Blodgett Films. Chin. J. Polym. Sci. 2022, 40, 556–566.
  7. Sadem, Z.; Fathi, B.; Mustapha, L. Image Edge Detection and Fractional Calculation. Int. J. Adv. Nat.Sciences Eng. Res. 2023, 7, 222–225.
  8. Nayak, S.R.; Mishra, J. Analysis of medical images using fractal geometry. In Research Anthology on Improving Medical Imaging Techniques for Analysis and Intervention; Medical Information Science Reference; IGI Global: Hershey, PA, USA, 2023; pp. 1547–1562.
  9. Gao, X.L.; Shao, Y.H.; Yang, Y.H.; Zhou, W.X. Do the Global Grain Spot Markets Exhibit Multifractal Nature? Chaos, Solitons Fractals 2022, 164, 112663.
  10. Zhao, T.; Li, Z.; Deng, Y. Information Fractal Dimension of Random Permutation Set. Chaos, Solitons Fractals 2023, 174, 113883.
  11. Pons, F.; Messori, G.; Faranda, D. Statistical Performance of Local Attractor Dimension Estimators in Non-Axiom A Dynamical Systems. Chaos: An Interdiscip. J. Nonlinear Sci. 2023, 33.
  12. Mageed, I.A.; Zhang, Q. The Rényian-Tsallisian Formalisms of the Stable M/G/1 Queue with Heavy Tails Entropian Threshold Theorems for the Squared Coefficient of Variation. Electron. J. Comput. Sci. Inf. Technol. 2023, 9, 7–14.
  13. Mageed, I.A.; Zhang, Q. Inductive Inferences of Z-Entropy Formalism (ZEF) Stable M/G/1 Queue with Heavy Tails. In Proceedings of the 2022 27th International Conference on Automation and Computing, Bristol, UK, 1–3 September 2022.
  14. Mageed, I.A. Fractal Dimension (Df) Theory of Ismail’s Second Entropy () with Potential Fractal Applications to ChatGPT, Distributed Ledger Technologies (DLTs) and Image Processing (IP). In Proceedings of the 2023 International Conference on Computer and Applications, Cairo, Egypt, 28–30 November 2023.
  15. Mageed, I.A. Fractal Dimension (Df) of Ismail’s Fourth Entrop () with Fractal Applications to Algorithms, Haptics, and Transportation. In Proceedings of the 2023 International Conference on Computer and Applications, Cairo, Egypt, 28–30 November 2023.
  16. Anwar, A.; Adarsh, S. A Review on Fractal Analysis and its Applications in Structural Engineering. In Proceedings of the IOP Conference Series: Materials Science and Engineering, Kerala, India, 14–15 July 2020.
  17. Ebrahimkhanlou, A.; Farhidzadeh, A.; Salamone, S. Multifractal Analysis of Crack Patterns in Reinforced Concrete Shear Walls. Struct. Health Monit. 2016, 15, 81–92.
  18. Rezaie, A.; Mauron, A.J.; Beyer, K. Sensitivity Analysis of Fractal Dimensions of Crack Maps on Concrete and Masonry Walls. Automation Const. 2020, 117, 103258.
  19. Feldman, D.P. Chaos and Fractals: An Elementary Introduction, 1st ed.; Oxford University Press: Oxford, UK, 2012.
  20. Almeida, J.; Prodan, O.; Rosso, A.; Beyer, K. Tests on Thin Reinforced Concrete Walls Subjected to in-Plane and Out-of-Plane Cyclic Loading. Earthquake Spectra 2017, 33, 323–345.
  21. Autodesk Education Resources. Available online: http://students.autodesk.com/ (accessed on 25 July 2024).
  22. Petry, S.; Beyer, K. Cyclic Test Data of Six Unreinforced Masonry Walls with Different Boundary Conditions. Earthquake Spectra 2015, 31, 2459–2484.
  23. Petry, S.; Beyer, K. Scaling Unreinforced Masonry for Reduced-Scale Seismic Testing. Bull. Earthquake Eng. 2014, 12, 2557–2581.
  24. Xiao, J.; Long, X.; Li, L.; Jiang, H.; Zhang, Y.; Qu, W. Study on the Influence of Three Factors on Mass Loss and Surface Fractal Dimension of Concrete in Sulfuric Acid Environments. Fractal Fract. 2021, 5, 146.
  25. Zhou, H.W.; Xie, H. Direct Estimation of the Fractal Dimensions of a Fracture Surface of Rock. Surf. Rev. Lett. 2003, 10, 751–762.