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- ItemCharacterization of Signed Symmetric Group in Inner Product Spaces(Adamawa State University, 2019) Usamot, IF;; Rauf, K;; Bakare, GN;; Ibrahim, G. RThis paper provides some characterizations of signed symmetric group (SSn) using the notion of orthogonality in inner product spaces. The concepts of ortho-stochastic and reflection were introduced on SSn and results were established with some examples.
- ItemCombinatorics Properties of Order-preserving Full Contraction Transformation Semigroup by Their Equivalence Classes(Department of Mathematics and Statistics, University of Victoria, Canada., 2013) Ibrahim, G. R; Makanjuola, S. OIn this paper the cardinalities of equivalence classes of starred Green’s relations in order-preserving full contraction transformation semigroup of a finite set(OCT) and the elements in each equivalence classes were investigated. For each class tables were formed, elements were arrange based on their kernel and image sets, patterns of arrangement observed and formulae were deduced in each case through the combinatorial principles.
- ItemSome characterizations of equivalence relation on contraction mappings(Elsevier, 2020) Akinwunmi, S. A;; Mogbonju, M. M;; Ibrahim, G. RLet T n be the set of full transformations and P n be the set of partial transformations. It is shown that T n form a semi-group of order n n and P n form a semi-group of order (n+ 1) n. Let ρ (n, m) be a binary relation then we define the image set of ρ (n, m), I (ρ):{n| n∈ N a n d t h e r e e x i s t s m∈ M:(m, n)∈ ρ} whenever (≡ ρ):≡ ρ on a set M is called an equivalence relation if≡ ρ is reflexive, symmetric and transitive. Then, For all m∈ M, we let [m] equivalence class denote the set [m]={n∈ M| n≡ ρ m} with respect to≡ ρ determine by m. Furthermore, we show that D= L∘ R= R∘ L= L υ R implies L⊆ J and R⊆ J. Therefore, D is the minimum equivalence relation class containing L and R. Hence, D⊆ J. If n∈ X m:{n∈ X m| n x n= n; n x= x n} then n∈ D c l a s s is regular. We also show that for L c l a s s, R c l a s s and H c l a s s for all m, n∈ D (α) we have α such that D (α)⊆ M implies I (α)⊆ M. Then for any transformation of …
- ItemSome 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.
- ItemMathematical Model for Mycobacterium Tuberculosis(Tekirdağ Namık Kemal University Institute of Science, 2024) LAWAL, O. J; ZHIRI, A. B.,; MURITALA, F.; IBRAHIM, G. R.; LUKONDE, A. P.To demonstrate the dynamics of the Mycobacterium tuberculosis disease population, a mathematical model was presented. The model has five compartments, and the resulting equations were resolved. While multiple cases of illness transmission were simulated using the compartmental model of infectious disease spread for a structured population model, the fundamental reproduction number was found using the next-generation matrix. Based on the results of the simulations, the system’s disease-free and endemic equilibrium was created by presenting, analyzing, and graphing the various subpopulations across time. The Homotopy Perturbation Method (HPM) analytical technique was then used to resolve the model.