Browsing by Author "Bakare, G.N."

Now showing 1 - 5 of 5
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    Green’s Equivalence Classes in Full Transformation Semigroups: A Height-based Approach
    (Department of Mathematics, Universitas Negeri Gorontalo, Indonesia, 2025-04-08) Usamot, I. F.; Ibrahim, G.R.; Bakare, G.N.; Adeshola, A.D.; Aliu, T. O.
    Green’s relations constitute five distinct equivalence classes that serve to define the elements of a semigroup. In this work, the equivalence classes within the Full Transformation Semigroup (Tκ) were systematically enumerated according to their respective heights, and the findings derived were subsequently generalized through the application of a combinatorial assertion and their graphical representations included to substantiate the theoretical results
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    RESULTS ON ORDER DECREASING FULL TRANSFORMATION SEMIGROUP VIA TROPICAL GEOMETRY
    (Canadian University Dubai, UAE, 2022) Bakare, G.N.; Ibrahim, G.R.; Usamot, I.F; Oyebo, Y. T.
    Abstract. Let DΥη be the subsemigroup of order decreasing full transforma tion on Ωη = {1, 2, · · · , η} . In this paper, the tropical geometry were applied on DΥη for 1 ≤ η ≤ 4. The elements in DΥη of classical algebra were degen erated into tropical polynomial and some results were obtained through their tropical curve.
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    Some Combinatorial Results on Star-Like Transformation Semigroup T αω∗
    (Mathematical Association of Nigeria, 2022) Ibrahim, G.R.; Lawal, O.J.; Akinwunmi, S. A.; Bakare, G.N.; Adeshola, A.D
    Let Xn be a finite set and star-like full transformation semi group T αω∗Tn of Xn. Let Height of α∗ be H+(α) = | Imα∗|, Fixed ) = | {x ∈ X : xα∗ = x} |, Idem potent of αn were character ized using the general method and definitions. The methods employed in carrying out this research work were that the elements in each of the functions were listed and some tables were formed for H+(α), J
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    Some Properties Of Symmetric Inverse Semigroup and Some Of it's Subsemigroup
    (Mathematical Association Of Nigeria(MAN), 2013) Ibrahim, G.R.; Bakare, G.N.
    In this paper, we studied the number of Nilpotent elements of order-preserving one-one partial transformation semigroup and number of Nilpotent elements of order decreasing +order preserving partial transformation semigroup . also, we showed that every idempotent of partial one-one transformation semigroup is contraction mapping.
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    Sum-Difference Model for Production of a Star-Like Harmonic Oscillator Transformation Semigroup
    (NIPES Pub., 2025-05-20) Akinwunmi, S. A.; Bakare, G.N.; Ogbu, A.O.; Garba, R.I
    This study introduces a novel sum-difference model for generating a star-like harmonic oscillator transformation semigroup, based on combinatorial properties of partial transformations over the finite set ?? = {1, 2, 3… , ?}. A partial transformation on ?? is defined as a mapping from a subset ?∗ . Using this framework, we construct a generalized two-dimensional star-like harmonic structure to produce ordered sequences and visualizable transformations. Specifically, for transformations ?∗, ?∗, ?∗ ∈ ??? ∗ , the cardinality |??? ∗ | is modeled as 1 2 ??∗ = ??∗−??∗ 2 4?∗?∗ which governs the generation of star-like sequences and image mappings. The paper presents a unified analytical approach to deriving these results using a star-like sumdifference operator. We further establish new harmonic oscillator relations within the semigroup, supported by proofs of key combinatorial functions. This research contributes to the development of algebraic methods in harmonic transformation theory and lays a foundation for future applications in signal modeling, automata theory, and abstract algebraic systems.