Version 1
: Received: 3 August 2020 / Approved: 5 August 2020 / Online: 5 August 2020 (03:43:11 CEST)
Version 2
: Received: 12 September 2021 / Approved: 13 September 2021 / Online: 13 September 2021 (13:27:39 CEST)
Version 3
: Received: 26 October 2022 / Approved: 26 October 2022 / Online: 26 October 2022 (09:39:11 CEST)
How to cite:
Abdullahi, K.B. Kabirian-based Optinalysis: Its Paradigm, Theorems, and Properties. Preprints2020, 2020080072. https://doi.org/10.20944/preprints202008.0072.v3
Abdullahi, K.B. Kabirian-based Optinalysis: Its Paradigm, Theorems, and Properties. Preprints 2020, 2020080072. https://doi.org/10.20944/preprints202008.0072.v3
Abdullahi, K.B. Kabirian-based Optinalysis: Its Paradigm, Theorems, and Properties. Preprints2020, 2020080072. https://doi.org/10.20944/preprints202008.0072.v3
APA Style
Abdullahi, K.B. (2022). Kabirian-based Optinalysis: Its Paradigm, Theorems, and Properties. Preprints. https://doi.org/10.20944/preprints202008.0072.v3
Chicago/Turabian Style
Abdullahi, K.B. 2022 "Kabirian-based Optinalysis: Its Paradigm, Theorems, and Properties" Preprints. https://doi.org/10.20944/preprints202008.0072.v3
Abstract
The conceptual and theoretical backbones of symmetry/asymmetry detections or similarity/dissimilarity, and identity/unidentity study are automorphism or isomorphism respectively. However, the development of equations and methods for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures deviates from these backbones. In this article, an equation was proposed for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures, and proved that its isoreflective pairs-points are functionally bijective and inverse. The proposal, called Kabirian-based optinalysis, is based on the conceptual and theoretical frameworks of automorphism and isomorphism. The Kabirian-based optinalysis is also proven and characterized as invariant (robust) under translation (i.e., scaling and location shift), and rotation or reflection. Computing codes were written in python language for Kabirian-based optinalysis to serve as working codes for application and verification.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
26 October 2022
Commenter:
Kabir Bindawa Abdullahi
Commenter's Conflict of Interests:
Author
Comment: The previous version of the manuscript has been revised for the following: 1. the tittle has been modified to fit the content's scope, 2. the mathematical expressions and annotations were edited and improved, 3. the mathematical proves were justified and presented in details, 4. the article's sections and content presentation were re-structured and edited, 5. computing codes (python codes) were provided for the proposal.
Commenter: Kabir Bindawa Abdullahi
Commenter's Conflict of Interests: Author
1. the tittle has been modified to fit the content's scope,
2. the mathematical expressions and annotations were edited and improved,
3. the mathematical proves were justified and presented in details,
4. the article's sections and content presentation were re-structured and edited,
5. computing codes (python codes) were provided for the proposal.