Journals: Abdelhafid Boussouf University Center of Mila, Algeria
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Introduction of modified root finding approaches and their comparative study with existing methods
Full text linkRoot-finding in nonlinear equations is a fundamental problem in numerical analysis with applications in mathematics and engineering. Traditional methods like the Bisection and False Position methods have been widely used, but they often face challenges related to convergence speed, stability, and computational efficiency. This paper presents two novel numerical root-finding methods that combine the robustness of the Bisection method with the efficiency of the False Position method, improving both convergence rates and stability. Furthermore, we illustrate some numerical applications to discuss error analysis, convergence analysis, and comparisons with existing methods. These findings contribute to the advancement of numerical computation by providing more reliable and efficient root-finding techniques
Nonlinear dynamics and chaos control of a discrete Rosenzweig-MacArthur prey-predator model
Full text linkThis paper investigates the nonlinear dynamics and chaos control of a discrete Rosenzweig-MacArthur predator-prey model. We first conduct a thorough dynamical analysis, identifying the system\u27s equilibrium points and examining their stability conditions. The study reveals the occurrence of Flip and Neimark-Sacker bifurcations, which represent critical qualitative changes in population dynamics. Specifically, Flip bifurcations lead to period-doubling phenomena, while Neimark-Sacker bifurcations indicate the emergence of quasi-periodic oscillations, both of which are crucial for understanding the onset of complex behaviors such as cycles and oscillations in ecological systems. To address the chaotic dynamics induced by these bifurcations, two control strategies are applied: the Ott-Grebogi-Yorke (OGY) method and feedback control. The results demonstrate the effectiveness of both approaches in stabilizing the system\u27s dynamics, with the OGY method proving to be more effective in achieving faster stabilization. These findings provide valuable insights into the management and preservation of ecological systems where predator-prey interactions exhibit instability and chaos
An approach to functional description of mass-operational characteristics in the tasks of quality control of raw materials
Full text linkThe paper presents a mathematical approach to solving an applied problem, namely determining the content of metal-containing impurities in the building industry. An example involving the magnetic control of a quartz sand sample is considered. The results are presented graphically and additionally processed in semi-logarithmic coordinates. Using the proposed method, the total mass of impurities in the sample was calculated, as well as the mass removed during a limited number of operations for extracting metal impurities, and the consistency of the control was assessed
Stability and sensitivity analysis of an infectious respiratory disease with vaccination and use of face masks
Full text linkMathematical modeling serves as a vital tool in public health, enabling policymakers to synthesize evidence, forecast disease trends, and assess intervention strategies. This study investigated the combined effects of face masks, quarantine, social distancing, and vaccination in controlling infectious respiratory diseases. The reproduction number was derived using the next-generation matrix (NGM). Local stability analysis utilized the Gershgorin Circle Theorem, while global stability was analyzed through the Quadratic Lyapunov Theorem. Sensitivity analysis was conducted using the normalized forward sensitivity index, and numerical simulations were performed with Python libraries such as \textit{scipy, numpy}, and \textit{matplotlib.pyplot}. Bifurcation analysis was carried out using the Center Manifold Theorem. The findings revealed that while these measures effectively reduced infection spread, they were insufficient to completely eliminate disease transmission. This study underscores the importance of implementing multiple strategies concurrently to effectively control the transmission of infectious diseases and guide public health interventions
Some spectral problems of a diffusion operator under Paley-Wiener-based high-order approximations
Full text linkIn this study, we acquired spectral results for the diffusion operator under higher-order approximations. We reconstruct the well-known techniques and derive the essential results for the presented problem. The spectral results for the diffusion operator with high-order approximations were evaluated, focusing on solutions in the Paley-Wiener space. Additionally, we consider theorems that involve solutions belonging to the Paley-Wiener space and the applications of Shannon\u27s sampling theorem. We also examine and evaluate the diffusion operator under more general separable boundary conditions
A new approach to hyper dual numbers with tribonacci and tribonacci-Lucas numbers and their generalized summation formulas
Full text linkMotivated by the definition of Tribonacci quaternions, we define hyper-dual numbers whose components involve Tribonacci and Tribonacci-Lucas numbers. We refer to these new numbers as hyper-dual Tribonacci numbers and hyper-dual Tribonacci-Lucas numbers, respectively.
In this paper, we also establish some properties of these numbers and present useful identities involving them. Furthermore, we investigate formulas for the generalized sum and the sum with alternating signs for Tribonacci and Tribonacci-Lucas numbers using a new method. Based on these results, we derive the corresponding formulas for the generalized and alternating sign sums of hyper-dual Tribonacci and hyper-dual Tribonacci-Lucas numbers
The extended Exton\u27s quadruple hypergeometric function and its properties
No full textIn this paper, we introduce the extended Exton\u27s hypergeometric function using the extended beta function given by \"{O}zergin et al. For this extended function, we derive various properties, including integral representations, recurrence relations, generating functions, transformation formulas, and summation formulas. Some special cases of the main results are also considered
Investigating the impact of vaccination on COVID-19 dynamics and resurgence risks
Full text linkCOVID-19 emerged in December 2019 and became a global threat, prompting heightened global surveillance from 2020 to 2022. Although COVID-19 continues to circulate and evolve, global surveillance has substantially reduced. The reduction in surveillance came after the introduction of vaccines worldwide. We formulated a mathematical model to investigate how incorporating vaccines impacts the dynamics of COVID-19 transmission. The study qualitatively analyzed the model and calculated the basic reproduction numbers (). We estimated the model\u27s parameters by fitting the model to real COVID-19 case data and using maximum likelihood estimation. To determine which parameters have the greatest impact on the spread and transmission of disease, a sensitivity analysis is carried out. The analysis revealed that the transmission rate is the most important factor responsible for the spread of COVID-19, while the vaccination rate has the most significant impact on controlling the disease. The numerical simulations showed that a high vaccination rate significantly reduces exposed, asymptomatic, symptomatic, and hospitalized individuals, reducing the impact of the virus on the community. It is crucial to consider the rate of immunity loss, as neglecting it could negate the benefits of vaccination
Optimal control via FBSDE with dynamic risk penalization: a structuring formulation based on Pontryagin\u27s principle
Full text linkThis paper introduces an innovative framework for dynamically optimizing consumption and investment decisions by integrating a risk penalization mechanism directly into the system’s dynamics. Leveraging Forward-Backward Stochastic Differential Equations (FBSDEs), our approach enables adaptive risk regulation in response to market fluctuations. We formulate the optimization problem, analyze the associated adjoint equations, and derive explicit characterizations of optimal strategies. Numerical simulations across multiple scenarios validate the robustness of the proposed method, demonstrating a significant reduction in terminal wealth variance compared to classical approaches. Our model thus offers a promising advance in dynamic financial risk management
Refining Euler and fourth-order Runge-Kutta methods using curvature-based adaptivity
Full text linkThis paper introduces curvature-adaptive variants of both the Euler and Runge-Kutta methods for solving ordinary differential equations (ODEs). By incorporating local curvature information into step size selection, the proposed Curvature-Adaptive Euler (CAE) and Curvature-Adaptive fourth-order Runge-Kutta (CARK4) methods achieve a superior balance between accuracy and computational efficiency compared to their fixed-step counterparts. The unified curvature adaptation framework presented in this work enhances classical ODE solvers by leveraging the geometric properties of the solution curve, resulting in more efficient numerical integration schemes