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Mikailalsys Journal of Mathematics and Statistics
Published by Lembaga Yasin Alsys
ISSN : 30308399     EISSN : 3030816X     DOI : https://doi.org/10.58578/mjms
Core Subject : Education, Engineering,
Engineering Mathematics Mechanical Engineering
The journal contains scientific articles covering topics such as mathematical theory, statistical methods, the application of mathematics in various disciplines, and statistical data analysis. The primary objective of this journal is to promote a better understanding of mathematical and statistical concepts and to encourage advancements in the methods and applications of mathematics and statistics in various contexts. The journal serves as a platform for researchers, academics, and practitioners to share knowledge and the latest research findings in the fields of mathematics and statistics. MJMS publishes three editions a year in February, June, and October.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 79 Documents
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Maximum Works Performed by Signed Partial Transformations of a Finite Set Tal, Pokalas P.; Chibueze, Eze; Sanda, Yulari
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.5962

Abstract

Let Xn and Xn* be the finite sets {1, 2, 3, ..., n} and {±1, ±2, ±3, ..., ±n} respectively. A map from Xn to Xn is called a transformation on Xn. We call a map a signed transformation if it maps from Xn to Xn*. Let Pn~ be the set of all signed partial transformations on Xn. This set consists of all transformations in Pn~ for which the domain of the transformation is a subset of Xn. The work w(alpha) performed by a transformation alpha is defined as the sum of all distances |i - alpha(i)| for each i in the domain of alpha. In this paper, we characterize all transformations in Pn~ that attain maximum and minimum works, and we deduce formulas for these minimum and maximum values. We further present a range for the values of w(alpha) for all transformations in Pn~.
Fixed Point Results on Generalized Weakly Quasi-Type Contractive Operators Chiroma, Rhoda; Shagari, Mohammed Shehu; Tanto, Ezra Emmanuel
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6046

Abstract

This study introduces and investigates generalized weakly quasi-type contractive operators within the context of b-metric-like spaces, aiming to establish rigorous conditions for the existence and uniqueness of fixed points. While weakly contractive mappings have been widely examined in standard metric spaces, their behavior in b-metric-like spaces remains underexplored. Addressing this gap, the paper extends existing theoretical frameworks and contributes novel results relevant to this generalized setting. The proposed assertions are substantiated through non-trivial comparative examples, and several corollaries are presented to illustrate how the main findings generalize and unify various established results in fixed point theory. These contributions enhance the understanding of contractive mappings in non-standard metric-like structures and open pathways for further applications.
A Graph-Theoretic Characterization of Orbits in the Finite Full Transformation Semigroup Mbah, M. A.; C., Eze; Tal, Pokalas P.; Kasim, S.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6073

Abstract

This paper investigates the orbit structures of elements in the full transformation semigroup TnT_n through the framework of digraph connectivity. Transformations are characterized based on whether their associated functional digraphs are strongly connected, weakly connected, or unilateral. It is shown that strong connectivity corresponds precisely to transformations whose orbits form a single nn-cycle. In contrast, unilateral connectivity arises when orbits constitute directed paths terminating in a unique cycle, and weak connectivity is identified when all elements belong to a single weakly connected component. Furthermore, the paper provides enumeration results, proving that there are exactly (n−1)!(n - 1)! transformations with strongly connected (cyclic) orbits and n!(n−1)n!(n - 1) transformations with unilateral orbit structures. These findings offer new structural and enumerative insights into the full transformation semigroup by analyzing the connectivity patterns of its orbit representations.
A Novel Probability Distribution: Mathematical Derivation and Validation of the Poisson Hamza Model Alao, Bamigbala Olateju; Alhaji, Magaji Umar; Bawuro, Fadimatu Mohammed; Bature, Gambo Innga
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6106

Abstract

This study introduces the Poisson Hamza Distribution (PHD), a novel probability distribution developed from the classical Poisson framework to address limitations in modeling count data. While the Poisson distribution is a standard tool for modeling rare events, its inherent assumptions, particularly equidispersion, limit its applicability in complex, real-world contexts. The PHD introduces enhanced modeling flexibility by accommodating overdispersion, thereby extending the utility of Poisson-based models. A comprehensive mathematical formulation of the PHD is presented, along with derivations of its key statistical properties, including moments, variance, standard deviation, skewness, and kurtosis. Theoretical validation is supported by empirical analysis, demonstrating the distribution’s robustness and practical relevance. These contributions offer a valuable extension to existing statistical methodologies and provide researchers and practitioners with an alternative model for analyzing overdispersed count data.
On the Connectivity and Eulerian Properties of Cayley Digraphs in Transformation Monoids Danlami, Kazaik Benjamin; Eze, Chibueze; O., Olaiya O.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6134

Abstract

This paper establishes fundamental connections between the graph-theoretic properties of Cayley digraphs and the algebraic structure of transformation monoids. Our main contributions include a complete characterization of strong connectivity in transformation monoids, proving that for a transformation monoid T acting on a finite set X, the Cayley digraph Cay(T, S) with respect to a generating set S ⊆ T is strongly connected if and only if T contains the full symmetric group S(X); and a classification of Eulerian properties in symmetric groups, demonstrating that for the symmetric group Sn with any generating set S, the Cayley digraph Cay(Sn, S) is Eulerian precisely when it is strongly connected. We provide concrete examples illustrating these theorems, including detailed Cayley graph constructions for S3 with explicit generating sets. Our results reveal deep connections between monoid theory and graph theory, showing how algebraic properties manifest in combinatorial structures. The proofs employ techniques from semigroup theory, algebraic graph theory, and finite group theory, offering new insights into the representation of transformation monoids through their generator-dependent digraphs. This work contributes to the broader understanding of how algebraic structures can be studied through their associated graphs.
Mathematical Analysis of Cryptosporidium Outbreak W, Ayanrinola O.; A, Odebiyi O.; M, Ogidiolu O.; O, Fagbemiro; O, Ogidiolu O.; O, Adeyemi M.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6136

Abstract

Cryptosporidium is a waterborne pathogen that transmits through various routes, including contact with the feces of infected individuals, contaminated environments, unsafe water, unsanitized food, raw or unpasteurized milk, animal exposure, and recreational water bodies. This study formulates and analyzes five compartmental models to propose effective strategies for controlling the spread of cryptosporidiosis. The models were assessed for biological and mathematical validity using the theory of positivity and were confirmed to be epidemiologically well-posed. The basic reproduction number was derived using the next generation matrix method and found to be less than unity, suggesting that the infection has the potential to be eliminated from the population. Stability analysis of the disease-free equilibrium was conducted using the Jacobian matrix method and confirmed local asymptotic stability. Sensitivity analysis identified the contact rate between susceptible and infected individuals as the most influential parameter affecting the basic reproduction number. This highlights the importance of reducing contact rates as a key intervention strategy. Numerical simulations performed using Maple 22 provided supportive insights and interpretations of the model dynamics, reinforcing the analytical findings.
On the Comparison of PAR, DARMA, and INAR in Modeling Count Time Series Data Buba, Haruna; Abdulkadir, Ahmed; Lasisi, Kazeem E.; Bishir, A.; Mashat, Strong Yusuf
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6312

Abstract

This study evaluates the forecasting and fitting performance of three advanced models—Poisson Autoregressive (PAR), Discrete Autoregressive Moving Average (DARMA), and Integer-Valued Autoregressive (INAR) for count time series data exhibiting complex features such as autocorrelation, overdispersion, and zero inflation. Both simulated and empirical datasets were analyzed, and model performance was assessed using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). The results indicate that PAR models significantly outperform DARMA and INAR models, achieving substantially lower AIC (482.53 vs. >5,310,479) and RMSE (3,742 vs. 246,682), highlighting their robustness in handling periodic trends and autocorrelation. In contrast, standard Poisson regression performs poorly under overdispersion, with an AIC approaching 5.3 million, while zero-inflated datasets compromise error metrics such as MAPE due to division by zero. Although DARMA and INAR models perform comparably, they are less effective in capturing extreme fluctuations or sudden spikes. These findings emphasize the limitations of conventional models and point to the need for more flexible approaches, such as hybrid ZIP-INAR models or Bayesian methods, to effectively manage overdispersion and zero inflation. The study concludes with a practical recommendation to prioritize PAR models when modeling autocorrelated count data.
A Hybrid of Adomian Decomposition Method for the Solution of Logistic Equations Waziri, I. M.; Waziri, Usman; S., Kamfa A.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6403

Abstract

This study introduces a novel analytical technique that integrates the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) to solve nonlinear differential equations, with particular emphasis on logistic growth models. The proposed hybrid method leverages the recursive decomposition mechanism of ADM alongside the correction functional framework of VIM to improve both the convergence rate and the accuracy of the solutions. To assess its effectiveness, the method is applied to selected cases of the logistic differential equation. The resulting approximate solutions exhibit strong agreement with known exact solutions, demonstrating the method's reliability and potential in addressing complex nonlinear problems in applied mathematics. This approach offers a robust alternative for researchers and practitioners seeking efficient analytical tools for nonlinear modeling.
Statistical Quality Control as a Tool for Monitoring and Improving Dimensional Accuracy in Soap Manufacturing Ayenigba, Alfred Ayo
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6431

Abstract

This study examines the application of Statistical Quality Control (SQC) techniques to enhance dimensional consistency, specifically in length and weight in the production of Sunlight Soap at Unilever’s Aba Plant. Data were collected from 20 production batches in January 2024 and analyzed using X̅ and R control charts, along with process capability indices (Cₚ and Cₚₖ). Analysis revealed that both dimensions were statistically in control, with no significant variation across batches (p = 0.9875 for length; p = 0.939 for weight). However, while weight measurements exhibited excellent process capability (Cₚ = 2.35, Cₚₖ = 2.31), length measurements reflected poor capability (Cₚ = 0.412, Cₚₖ = 0.301), indicating excessive variability. To address this inconsistency, the study recommends equipment recalibration, real-time monitoring, and targeted staff training. The findings contribute a replicable quality control framework aimed at improving product uniformity within fast-moving consumer goods (FMCG) manufacturing environments.
Modelling Measles Reoccurrence in Vaccinated Infants Adeboye, O. A.; Adewale, S. O.; Odebiyi, O. A.; Oladejo, J. K.
Mikailalsys Journal of Mathematics and Statistics Vol 3 No 3 (2025): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v3i3.6537

Abstract

Measles is a highly contagious viral disease caused by the morbillivirus, marked by symptoms including fever, cough, runny nose, conjunctivitis, and a characteristic widespread rash. In severe cases, especially among young children and pregnant women, it can lead to complications such as ear infections, pneumonia, encephalitis, and death. This study develops a six-compartment deterministic mathematical model, expressed as a system of ordinary differential equations, to investigate the transmission dynamics of measles in human populations. The model was demonstrated to be both mathematically and epidemiologically well-posed. The basic reproduction number (R₀) was derived, and the stability analysis of the disease-free equilibrium showed it to be locally and globally asymptotically stable when R₀ < 1, and unstable when R₀ > 1. Sensitivity analysis using normalized forward sensitivity indices revealed the impact of various parameters on R₀. Specifically, parameters with negative indices, such as the vaccination rate and treatment rate reduce R₀ when increased, while those with positive indices, such as the effective contact rate increase R₀ when increased. These findings underscore the importance of increasing vaccination coverage, enhancing treatment efforts, and isolating infected individuals to control and prevent measles outbreaks. The model provides a theoretical framework for designing effective public health strategies to minimize the disease burden in the population.

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