Browsing by Author "Ibrahim, G. R."

Now showing 1 - 6 of 6
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    Analytical Solution of Some Non – Linear Delay Differential Equations Using Adomian Decomposition Method
    (Department of Computer Engineering, Sigma University , Vadodara Gujarat, India, 2024) Lawal1*, O.J; Muraina, S.; Ibrahim, G. R.; Faruk ,M.; Idris, S.
    This study examined some Non-linear Delay Differential Equation problems with known exact solutions and solved them using the Adomian Decomposition Method. We then observed the results and compared them with the corresponding exact solutions, and ultimately found that the two results agree. In addition, we discussed the phenomena that occur in real life and are described by Non-linear Differential Equations.
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    Application of Lattice Theory on Order-Preserving Full Transformation
    (Faculty of physical Science , University of Ilorin, 2023) Ibrahim, G. R.; Bakare, G. N.; Akinwunmi. S. A.
    Let be a finite set, Tn be full transformation semigroup and OTn be subsemigroup of Tn of all order-preserving full transformation semigroup. Let transformation α ∈ OTn ∀x, y ∈ α, if x ≤ y then α(x) ≤ α(y), then α is called order-preserving transformation. This paper focuses on the notion of fixed points which are elements that remain unchanged under this transformation. The existence of fixed points were explored and emphasizing their role in establishing a lattice structure. The lattice of fixed points exhibits two essential operations: meet and join. These operations enable us to compute the greatest and least elements of fixed points. Beyond pure mathematics, the study of fixed points and their lattice structure has applications in dynamical systems, economics, computer science, and several other domains, making it both a theoretical and practical subject.
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    Application of Tropical Geometry on Subsemigroup of Order-preserving Full Transformation
    (Science Association of Nigeria, 2018) Bakare G. N.,; Ibrahim, G. R.; Usamot I. F.,; Ahmed B. M.
    This work ties together the tropical geometry and semigroup. We applied tropical geometry on subsemigroup of order-preserving full transformation (OTn) by degenerating the elements of classical algebra into tropical algebra in which the multiplicities were deduced through their tropical curves.
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    Characterization of quasi idempotent in semigroups of full contraction mappings
    (Nigerian Society of Physical Sciences, 2024) A. D. Adeshola,∗; , S. O Akandea; Ibrahim, G. R.
    Let Tn be the semigroup of full transformation of a finite set and let Xn = {1, 2, · · · , n}. A transformation α : Domα ⊂ Xn →Im(α) ⊂ Xn is said to be full or total transformation if Domα = Xn. A transformation β ∈ CT n is said to be full contraction mapping if ∀ x, y ∈ Domα, |xα − yα| ≤ |x − y| ∀ x, y ∈ Domα. Let CT n be the semigroup of full contraction transformation and let QCT n be its quasi-idempotent of full contraction transformation of Xn. In this paper, we characterized quasi-idempotent elements into matching blocks, non-matching blocks and self matching blocks of CT n and later come up with a strong and useful theorem
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    CONJUGACY CLASSES OF THE ORDER-PRESERVING AND ORDER-DECREASING PARTIAL ONE-TO-ONE TRANSFORMATION SEMIGROUPS
    (FUTMINA, 2019) UGBENE, I. J.,; BAKARE, G. N.; Ibrahim, G. R.
    In this paper ą is considered to be the partial one-to-one transformation semigroup on X n = {1,2,L,n}. The order-preserving and order-decreasing partial one-to-one transformation semigroup ą1 ) is defined to be the subsemigroups of ą . The nilpotent and idempotent elements of ą1 were then obtained from its conjugacy classes using path structure to be n+1 and *恼馁жi − ж 2 respectively. The index and period of each conjugacy classes were also found. More so, some properties of conjugacy classes were stated.
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    Some algebraic properties of order-preserving full contraction transformation semigroup
    (SCIK publisher, 2019) Ibrahim, G. R.; A.T Imam,; AD Adeshola,; GN Bakare
    Let be a finite set, the semigroup of full contraction and order-preserving full contraction transformation semigroup of a finite set. In this paper the Local and global U-depth as well as the status of were investigated where U is the generating set. The local and global depth were found from the known generating Set of and also, the status of the semigroup was obtained from the product of global depth and the order of generating of . For , local depth of α is equal to its defect, global depth and status of are and respectively. We also look at the structure of Green’s relations of order-preserving full contraction transformation semigroup.