International Journal of Mathematical Sciences and Optimization: Theory and Applications

A Deterministic Model Analysis for Youth Involvement in Yahoo-Yahoo (Cybercrime) and Yahoo+ (Ritualism)

2025-08-20T14:25:59+00:00

The rising involvement of young people in yahoo-yahoo (cybercrime) and yahoo+ (ritualism) has become a major societal concern, particularly in Nigeria, where economic instability and peer pressure drive vulnerable individuals into these illicit activities. This study develops a deterministic compartmental model to analyze the transition of youths through different stages: vulnerability, engagement in yahoo-yahoo, progression into yahoo+ (ritualism), and recovery through rehabilitation. The model accounts for key factors such as recruitment rates, peer influence, the probability of transitioning to ritualistic practices, rehabilitation effectiveness, and relapse risks. A stability analysis of the equilibrium points, which are the yahoo-free and endemic, provides insight into long-term trends based on the basic reproduction number, $R_{0}$ , determining whether yahoo-yahoo (cybercrime) and yahoo+ (ritualism) persist or decline. Numerical simulations reveal potential strategies to reduce youth participation in these activities. Based on the model’s findings, the study offers policy recommendations to support sustainable youth development and mitigate this growing societal threat.

Hyper-Homomorphisms in Obic Algebras

2025-08-13T16:21:31+00:00

In this paper, hyper-homomorphisms of Obic algebras, which are generalizations of homomorphisms in Obic algebras, are introduced. Their properties are investigated. It is shown that homomorphisms of Obic algebras preserve oscillation. Furthermore, it is established that with a suitably defined binary operation, the collection of hyper-homomorphisms in Obic algebras is also an Obic algebra. Moreover, monics, regular and preserving maps of Obic algebras are studied through their hyper-homomorphisms.

Optimizing Neural Networks with Linearly Combined Activation Functions: A Novel Approach to Enhance Gradient Flow and Learning Dynamics

2025-08-13T16:21:31+00:00

Activation functions are crucial for the efficacy of neural networks as they introduce non-linearity and affect gradient propagation. Traditional activation functions, including Sigmoid, ReLU, Tanh, Leaky ReLU, and ELU, possess distinct advantages but also demonstrate limits such as vanishing gradients and inactive neurons. This research introduces an innovative method that linearly integrates five activation functions using linearly independent coefficients to formulate a new hybrid activation function. This integrated function seeks to harmonize the advantages of each element, alleviate their deficiencies, and enhance network training and generalization. Our mathematical study, graphical visualization, and hypothetical tests demonstrate that the combined activation function provides enhanced gradient flow in deeper layers, expedited convergence, and improved generalization relative to individual activation functions. Quantitative metrics demonstrate enhanced gradient flow, expedited convergence, and improved generalization relative to individual activation functions. Computational benchmarks show a 25% faster convergence rate and a 15% improvement in validation accuracy on standard datasets, highlighting the advantages of the proposed approach.

A Note on Transmuted Exponentiated Inverse Exponential Distribution and Application to Breast Cancer Data

2025-08-13T12:38:58+00:00

The Transmuted Exponentiated Inverse Exponential (TEIE) Distribution has been derived using Exponentiated Inverse Exponential (EIE) distribution and the Quadratic Rank Transmutation Map (QRTM). The developed distribution is more flexible and adaptable in modeling data exhibiting different shapes of the hazard function than its sub-models. The mathematical expressions and shapes of the distribution function, probability density function, hazard rate function, and reliability function are studied. The parameters of the TEIE distribution are estimated by the method of maximum likelihood. Finally, the TEIE distribution is applied to breast cancer data set and found to have a better fit than the Transmuted Inverse Exponential (TIE) distribution and the Inverse Exponential (IE) distribution.

On Quasi-Nilpotents in Finite Partial Transformation Semigroups

2025-08-13T13:00:11+00:00

Let $X_{n}$ be the finite set ${1, 2, 3, \dots, n}$ and $P_{n}$ be the partial transformation on $X_{n}$ . A transformation $α$ in $P_{n}$ is called quasi-nilpotent if when $α$ is raised to some certain power it reduces to a constant map, i.e., $α^{m}$ reduces to a constant map for $m \geq 1$ . We characterize quasi-nilpotents in $P_{n}$ and show that the semigroup $P_{n}$ is quasi-nilpotent generated. Moreover, if $K (n, r)$ is the subsemigroup of $P_{n}$ consisting of all elements of height $r$ or less, where the height of an element $α$ is defined as $∣ im α ∣$ , we obtain the quasi-nilpotent rank of $K (n, r)$ , that is, the cardinality of a minimum quasi-nilpotent generating set for $P_{n}$ , as the Stirling number of the second kind $S (n + 1, r + 1)$ , which is the same as its idempotent rank.

Mathematical Model for Ions Transport Optimization in an Animal Cell Using MATLAB

2025-08-13T16:21:31+00:00

The increasing world population has raised significant concerns about matching food production to demand, prompting extensive research in scientific fields aimed at enhancing plant and animal productivity. However, some of these advances have introduced unintended consequences, such as uncontrolled cell growth that leads to cancer. Effective regulation of cell size is essential to maintaining organismal health. This study focuses on the utilization of a numerical method to develop a mathematical model that optimizes ion transport within an animal cell as a mechanism to ensure a physiologically healthy cell. Through this model, optimal ion concentrations were identified using MATLAB-SIMULINK. The results were validated using experimental data to ensure that they promote healthy cell growth and stability. The results provide valuable insights for treating disorders associated with abnormal cell growth initiated by unregulated ions concentration. This research contributes to understanding cellular homeostasis and lays the groundwork for future bioengineering applications.

On the Fixed Points of Springer Varieties in Type A

2025-08-13T13:22:54+00:00

Springer varieties are sub-varieties of the full (complete) flag variety $F ℓ_{n} (C)$ , which can be thought of as the fiber over $X$ of the Springer resolution of singularities of the cone of nilpotent endomorphisms $X : V ⟶ V$ , where $X$ is a nilpotent endomorphism in its Jordan canonical form of type $λ$ and $V$ is an $n$ -dimensional vector space over $C$ ( $V = C^{n}$ for convenience). The geometry of Springer varieties is reviewed in this article, along with their $S^{k}$ -fixed points. We accomplish this by briefly reviewing nilpotent orbits in type $A$ within the framework of integer partitions.

Assessing Asset Value Changes Using a System of Stochastic Models with Constant Terms and Periodic Drift Coefficients

2025-08-13T16:21:31+00:00

The Stochastic Differential Equation (SDE) is a well-known mathematical tool used for estimating asset values over time. This paper focuses on stochastic systems with an emphasis on variations in stock parameters. The problems were solved analytically using Itô's method, providing precise measures for assessing asset values. The study empirically analyzes the behavior of asset values under increasing volatility, presenting results in tables and graphs. Key findings include: increased volatility decreases asset values, periodic parameters cause fluctuations in asset assessments, and the average asset value over time impacts financial markets in time-varying investments. This work introduces a novel approach by modeling stock drift coefficients with constants and periodic event parameters, offering unique insights for financial market investors.

Fixed Point Theorems for Some Iteration Processes with Generalized Zamfirescu Mappings in Uniformly Convex Banach Spaces

2025-08-13T16:12:40+00:00

This paper establishes fixed point theorems for certain iteration processes in uniformly convex Banach spaces using generalized Zamfirescu mappings. The results improve upon recent findings in the literature. The study focuses on iterative schemes such as Mann and Ishikawa, demonstrating their strong convergence to fixed points under generalized Zamfirescu contractive conditions. The work contributes to the broader understanding of fixed point theory in uniformly convex Banach spaces and provides a foundation for further research in this area.

On the Solutions of Optimal Control Problems Constrained by Ordinary Differential Equations with Vector-Matrix Coefficients Using FICO Xpress Mosel

2025-08-13T16:20:03+00:00

This study addresses a general class of quadratic optimal control problems (OCPs) constrained by ordinary differential equations (ODEs) with vector-matrix coefficients. Due to the intractability of analytical solutions for complex dynamic systems, the focus is on developing and comparing efficient numerical methods. An analytical framework is first established by applying first-order optimality conditions to the Hamiltonian, yielding a system of first-order ODEs. The associated Riccati differential equation is then solved using a state transformation approach. For numerical solutions, the objective functional is discretized using Simpson's $3 1$ rule, and the system dynamics are approximated using a fifth-order implicit integration scheme. The discretized problem is reformulated as an unconstrained optimization problem via the Augmented Lagrangian Method and solved using both the CGM and FICO Xpress Mosel. Comparative results reveal that FICO Xpress Mosel provides faster convergence and greater numerical stability, especially for high-dimensional problems. These findings underscore the effectiveness of commercial solvers like FICO Xpress Mosel in solving large-scale quadratic OCPs with enhanced accuracy and efficiency.