A Theoretical Exploration of Paraletrix Calculus as an Extension of Rhotrix Mathematics
Article Sidebar
Page Numbers:
94-103
Digital Object Identifier:
10.58578/amjsai.v3i1.9100
Viewed: 84 times
Downloaded: 64 times
LYAS Publisher cordially invites qualified professionals to serve as Editors or Reviewers. Your expertise will make an important contribution to maintaining and strengthening the academic quality of our publications. Interested applicants are kindly requested to complete the application form at the following link: Editors & Reviewers
Please feel free to contact us if you need any further information about the submission process or if you have any additional questions.
Authors:Isa Yahaya1, Salisu Lukunti2, Umar Mujahid Aliyu3, Imafidor Hassan Ibrahim4, Mohammed Abubakar Kolo5, Sulaiman Ahmad6, Nura Hashim7, Mohammed Yusuf Marafa8
Copyright :Authors retain copyright and grant the journal right of first publication.
Main Article Content
Abstract
This paper, titled A Theoretical Exploration of Paraletrix Calculus as an Extension of Rhotrix Mathematics, builds upon earlier studies in generalized matrix theory by extending the structural and operational framework of non-standard matrix-like objects. Atanassov and Shannon [1] first introduced matrix-tertions and matrix-ngittrets as entities that interpolate between 2-dimensional vectors and 2×2 matrices, thereby enriching the conceptual landscape of generalized matrices. Ajibade [2] subsequently advanced the field by proposing thotrices as intermediates between 2×2 and 3×3 matrices, while further developments in rhotrix theory have established various multiplication techniques, such as heart-oriented and row–column multiplications—and yielded several important results. Recognizing the diversity of both rectangular and square matrices, the paraletrix structure was formulated as a generalization of the thotrix, allowing unequal numbers of rows and columns and thus providing a more flexible algebraic setting. This study extends the mathematical framework by introducing differentiation and integration within paraletrix calculus, defining these operations for paraletrix-valued functions with respect to an independent variable. In doing so, it lays the groundwork for a coherent calculus on paraletrices as a theoretical extension of rhotrix mathematics and generalized matrix theory.
Citation Metrics:
Downloads
Citation Metrics & Similar Scopus Articles
-
Mirzahosseini M. (2027)A Review of Constitutive Modeling of Unsaturated SoilsIranian Journal of Geophysics, 20(3), 81-128
-
Carvalho T. (2027)Bifurcation analysis of the tangential switching mode in a non-monotonic tumor growth modelNonlinear Analysis Real World Applications, 94
-
Adam A.H.A. (2027)QLRUN: Integrating Q-learning and covariance matrix learning into Runge–Kutta optimization for engineering design problemsUnconventional Resources, 16
Article Details
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
References
[2]. Ajibade, A. O. (2003). The concept of rhotrix in mathematical enrichment. International Journal of Mathematical Education in Science and Technology, 34(2), 175–179. https://doi.org/10.1080/0020739021000053828
[3]. Sani, B. (2004). An alternative method for multiplication of rhotrices. International Journal of Mathematical Education in Science and Technology, 35(5), 777–781. https://doi.org/10.1080/00207390410001716577
[4]. Sani, B. (2007). The row–column multiplication of high dimensional rhotrices. International Journal of Mathematical Education in Science and Technology, 38(5), 657–662. https://doi.org/10.1080/00207390601035245
[5]. Aminu, A., & Michael, O. (2014). An introduction to the concept of paraletrix, a generalization of rhotrix. Afrika Matematika. Advance online publication. https://doi.org/10.1007/s13370-014-0251-1
[6]. Aminu, A., & Michael, O. (2015). An introduction to the concept of paraletrix, a generalization of rhotrix. Afrika Matematika, 26(5–6), 871–885. https://doi.org/10.1007/s13370-014-0251-1
[7]. Ndubuisi, R. U., Abubakar, R. B., & Udoaka, O. G. (2024). Some results on heart-oriented paraletrix ring. Journal of Applied Mathematics and Computation, 8(1), 1–6. https://doi.org/10.26855/jamc.2024.03.001