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All Journal YASIN: Jurnal Pendidikan dan Sosial Budaya International Journal of Education, Management, and Technology
N. H. Manjak
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Computer Science & IT Education Electrical & Electronics Engineering Engineering Materials Science & Nanotechnology Social Sciences Other

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Quantum Wreath Products of Transformation Semigroups: Associativity, Distributivity, and Faithful Embeddings into C*-Algebras B. S. Abbas; I. B Mshelia; N. H. Manjak
International Journal of Education, Management, and Technology Vol 4 No 2 (2026): International Journal of Education, Management, and Technology
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ijemt.v4i2.9271

Abstract

Connecting discrete semigroup theory with quantum C*-algebras requires a rigorous account of how semigroup constructions are preserved in operator-algebraic settings. This study develops a framework for embedding the direct and wreath products of transformation semigroups into quantum C*-algebras. Through algebraic verification and operator-theoretic construction, the study first establishes that the wreath product of transformation semigroups is associative and distributes over the direct product under appropriate conditions. Faithful representations of these products are then constructed as operators on Hilbert spaces, yielding explicit C*-algebraic isomorphisms. The results show that the direct product admits an embedding as a direct sum of C*-algebras, whereas the wreath product corresponds to a crossed product involving tensor products and the C*-algebras of the acting semigroup. They further demonstrate that semigroup-level isomorphisms lift to the associated C*-algebras and that the wreath product distributes over direct sums in the C*-algebraic setting. Necessary and sufficient conditions are established under which these embeddings preserve both algebraic structures and operator-theoretic properties. By connecting transformation semigroup constructions with noncommutative geometry, this framework provides an operator-algebraic foundation for analyzing direct and wreath products through faithful quantum representations.
Hybrid Yang Transform Method for Fractional Nonlinear Partial Differential Equations I. M. Waziri; N. H. Manjak; A. M. Kwami; M. S. Adamu; Okai J. O
YASIN Vol 5 No 3 (2025): YASIN: Jurnal Pendidikan dan Sosial Budaya
Publisher : Lembaga Yasin AlSys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/yasin.v5i3.5382

Abstract

This work evaluates the performance of the YTAP and New Iterative Method (NIM) in approximating solutions to both linear and nonlinear partial differential equations (PDEs). Through comparative analysis involving exact solutions, numerical tables, and graphical illustrations, the results demonstrate that both methods are highly effective, with YTAP generally yielding smaller approximation errors. Specifically, in the case of a linear PDE (Example 2), YTAP exhibits superior accuracy, while NIM also performs reliably. For nonlinear PDEs (Example 3), YTAP proves to be a robust and efficient method, successfully generating recursive solutions that closely match the exact results. These findings underscore the reliability of YTAP as a powerful tool for solving a wide range of PDEs.
Co-Authors A. M. Kwami B. S. Abbas I. B Mshelia I. M. Waziri M. S. Adamu Okai J. O