Journal of Mathematics Research, Issue: Vol.18, No.1

A Split Mixed Finite Element Method for Fourth-Order Hyperbolic Equations

Mon, 23 Mar 2026 23:46:06 +0000

Fourth-order hyperbolic equations model complex vibration and wave phenomena, and have broad applications in physics and engineering. This paper investigates a split mixed finite element method for such equations. By introducing intermediate variables, the fourth-order differential equation is reformulated as a system of lower-order equations. A semi-discrete split scheme is constructed, and the existence and uniqueness of its solution are established. Error estimates are derived using elliptic projection and the $L^2$-projection operator. A fully discrete split mixed finite element scheme is developed by applying the central difference method to discretize the time derivatives. The stability and convergence of the scheme are analyzed. Numerical experiments for a one-dimensional fourth-order hyperbolic equation validate the theoretical results.

Modeling and Mathematical Analysis of the Interactions Between the Leafhopper Amrasca Biguttula and Cotton Using Caputo's Fractional Approach

Tue, 24 Mar 2026 00:03:01 +0000

In this paper, we propose a fractional order mathematical model in the sense of Caputo for the transmission dynamics of cotton disease caused by the jassid Amrasca biguttula. In this model, which takes into account disease transmission through vegetative reproduction, the cotton population is divided into susceptible (S_c), latent (L_c), and infected (I_c) individuals. The Amrasca biguttula jassid population is divided into susceptible (S_a) and infected (I_a) individuals. Through the mathematical analysis of the model, we show that the system is well posed from both the mathematical and epidemiological perspectives. After determining the basic reproduction number R_0 and the disease-free equilibrium E_s, we study the local and global stability of the equilibrium point. Sensitivity analysis is performed to identify the most influential parameter of the model, particularly for disease prevention. Finally, numerical simulations are carried out to illustrate and validate the analytical results.

Low-Regret Control of a Nonlinear Hyperbolic Problem With Missing Data

Tue, 24 Mar 2026 00:15:43 +0000

In this paper, we characterise the control of an ill-posed nonlinear evolution problem. More precisely, we study the low-regret control of a system governed by a hyperbolic operator by using the regularisation approach, which makes it possible to generate missing data. We obtain singular optimal systems characterising the low-regret control and the no-regret control of the hyperbolic problem.

Construction of Covering Sets

Wed, 25 Mar 2026 00:10:58 +0000

With the aid of computers, this paper is devoted to investigate the optimization of covering sets. Many concrete examples are provided. We also generalize the study to Gaussian integers.

Integrated Modeling for the Optimization of Air Transport Networks Under Multiple Constraints

Tue, 31 Mar 2026 00:05:39 +0000

This paper presents an integrated multi-objective optimization model for air transport networks in the West African Economic and Monetary Union (WAEMU) region, addressing the challenges of fragmented infrastructure and regulatory constraints. By simultaneously optimizing route planning, fleet assignment, scheduling, demand management, and operational costs, the framework minimizes expenses while maximizing passenger satisfaction. The model is empirically validated using data from the World Bank and African Civil Aviation Commission, incorporating passenger traffic, socioeconomic indicators, and fleet specifications. Computational simulations using Python's PuLP library demonstrate trade-offs across scenarios, including high demand, fleet expansion, cost sensitivities, and a supplementary carbon-price sensitivity aligned with ICAO's CORSIA framework. Validation against airline benchmarks yields a mean absolute percentage error (MAPE) of 9.7% and an R^2 of 0.91 for cost estimates. Results highlight optimal fleet allocations, with wide-body aircraft preferred for high-demand routes, and show that carbon pricing shifts the Pareto frontier upward by about 2-5% under typical WAEMU operating-cost ranges. The work bridges gaps in existing literature by offering a holistic, data-driven approach tailored to African regional dynamics.

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 18, No. 1

Tue, 31 Mar 2026 00:10:53 +0000

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 18, No. 1