Emmanuel Akaligwo

It is our aim to propose a new iterative algorithm with an inertial term involving asymptotically nonexpansive mapping in the framework of Hilbert spaces. Let T : H ⟶ H be asymptotically nonexpansive mapping with F ( T ) ≠ ∅ ∅ and let be defined by x _{n +1} = σ _n z _n + b _n ( T ⁿ σ _n z _n − σ _n z _n ) + ε _n , ∀ n ≥ 1. T satisfies an additional mild condition, then the sequence converges strongly to . Our main contribution lies in establishing a strong convergence theorem for this method, without relying on the assumption that . Our strong convergence theorems extend the corresponding convergence theorems in literature for nonexpansive maps to a more general class of asymptotically nonexpansive maps. Furthermore, our proposed algorithm is implemented by finding the fixed point of common solutions to a variational inequality problem and η −inverse‐strongly monotone mapping in Hilbert space. Numerical illustrations showed some improvements over existing results in literature.

Keeping track of the human population is essential for proper planning for facilities such as healthcare, infrastructure, education, and other essential needs. There are various ways by which the government can ensure that service provision is improved and maintained for its citizens and very often this starts by knowing the changes in demography as a function of time. In this work, mathematical modeling and simulations are used to study the population dynamics of Abuja. The models are used for prediction of the population and how its dynamics change over time. With approximate growth rate at 9.3% per annum, the projected population of Abuja will hit 30,220,701 million by the year 2039 all things being equal. Parameter sensitivity analysis was performed using population census data, and the results show a huge influence of variations in the model parameters. The results indicate that the difference between the per capita birth and death rate parameters is crucial for changes in the population. Such findings can also be analogously applied to other cities with a similar population structure and economy.

Noise and vibration pose significant challenges in built-up structures, affecting structural integrity and occupant comfort. Traditional materials often fail to address these issues effectively across all relevant frequencies, particularly in urban and industrial environments. This paper presents a mathematical modeling approach and virtual design framework for developing metamaterials specifically tailored to mitigate noise and vibration in built-up structures. By leveraging finite element analysis, dynamic energy analysis, and optimization algorithms, the study demonstrates how metamaterials can create frequency-specific barriers. Comparative analyses with previous studies, performance metrics, and sensitivity evaluations reveal the robustness and unique contributions of this approach. Validation through simulations and benchmarking confirms the model’s effectiveness, enhancing structural resilience and human comfort in complex environments. Additionally, this study surveys natural metamaterials and the urban environment. The major findings highlight the effectiveness of natural metamaterials (NMs) in ground vibration attenuation, offering diverse applications and proposing a roadmap for developing natural materials for clean and quiet environments

Noise and vibration are pervasive challenges in built-up structures, impacting structural integrity, operational efficiency, and occupant well-being. These issues are particularly pronounced in urban and industrial settings, where traditional materials often struggle to deliver effective mitigation across the broad range of relevant frequencies. This paper introduces an integrated mathematical modeling and virtual design framework for the development of advanced metamaterials aimed at reducing noise and vibration in such complex structures. The approach combines finite element analysis, dynamic energy analysis, and optimization algorithms to design metamaterials with frequency-selective properties that create targeted barriers to acoustic and vibrational disturbances. The study not only develops a systematic methodology for designing these metamaterials but also validates their efficacy through comprehensive simulations and benchmarking against established solutions. The results highlight the advantages of the proposed metamaterials in terms of adaptability, efficiency, and performance robustness across various operating conditions. Sensitivity analyses and comparative evaluations further underscore the superiority of the framework in addressing frequency-dependent challenges, offering significant improvements over conventional materials. A unique aspect of this research is the inclusion of natural metamaterials (NMs) as a sustainable alternative for mitigating ground vibrations. The study reviews the potential of NMs for diverse functionalities, particularly in attenuating ground vibrations in urban environments. These findings emphasize the versatility and eco-friendliness of natural materials, providing a roadmap for their development and application in achieving clean and quiet environments. The proposed framework, therefore, bridges theoretical advancements with practical applications, paving the way for resilient and sustainable solutions to noise and vibration challenges in built-up structures.

In this paper, we extended the well-known alternating direction method of multipliers (ADMM) for optimization problems to generalized Nash equilibrium problems (GNEP) with shared constraints. We developed an ADMM-type algorithm with fixed regularization to tackle the problem (GNEP) where an upper estimate for the operator norm is not known and then we apply a multiplier-penalty in order to get rid of the joint constraints. We equipped the Hilbert space with an appropriate weighted scalar product and it turns out to be weakly convergent under a lipschitz and monotonicity assumption. A proximal term is then added to improve the convergence properties. Furthermore, a comparative analysis of quasi-variational inequality method, interior point method, penalty method and the proposed method are discussed.