Vol. 32 No. 2 (2025)

Open Access

Article

Article ID: 2343

Using learning and cognitive models for assessing quality of content hosted into websites
by Shahida Tasneem Shaik, Hima Bindu Duddempudi, Kunal Sana, Kodanda Rama Sastry Jammalamadaka, Sasi Bhanu Jammalamadaka, Balakrishna Kamesh Duvvuri

Advances in Differential Equations and Control Processes, Vol.32, No.2, 2025;

DOI: https://doi.org/10.59400/adecp2343

The quality of a WEB site is based on 42 different factors. Out of those factors, the quality of content is the key factor. Different types of content are hosted on websites, including text, data, text data, images, videos, graphics, and animations. There are also interrelations among the content sources. The element-level connectivity and hierarchical element connectivity of content sources dictate the quality of content hosted on the website. The number of content elements, connectivity among the elements and the number of hierarchies existing on a website are many and, therefore, require a framework using which the quality of content is computed. This paper presents a framework based on an expert and ANN model. Using the framework, the quality of content hosted on a website is computed considering all sub-factors determining the quality of the factor “Content”. Using the framework proposed in this paper, the quality of the content was estimated accurately to 91.80.

show more
- PDF
Open Access

Article

Article ID: 2712

Stabilizing Schrödinger—ODE systems with boundary delay for industrial process optimization
by Ya-Ru Xie, Yu-Wen Chen, Cong-Yue Tian, Rui-Qing Gao, Li Zhang

Advances in Differential Equations and Control Processes, Vol.32, No.2, 2025;

DOI: https://doi.org/10.59400/adecp2712

In this paper, we focus on the stabilization of a Schrödinger-ODE cascaded system with boundary delayed control. The system is stabilized through the utilization of integral-type feedback control, in which the integral kernel functions serve as parameters. The objective is to identify an appropriate set of kernel functions that ensure exponential stability characteristics of the closed-loop system. The initial step is to select a target system that must be exponentially stable. We propose an auxiliary system for the task at hand. Initially, we need to establish the equivalence between the auxiliary system and the original controlled time-delay system. This stage is primarily concerned with the elimination of the influence of input memory. The second system is leveraged to ascertain the equivalence between stable target system and the auxiliary system. This paper presents a method to choose parameter functions to create an exponentially stable feedback controller.

show more
- PDF
Open Access

Article

Article ID: 2818

Weak fault diagnosis method for rotorcraft bearings based on whale optimization algorithm—Optimized simplistic geometry mode decomposition and maximum correlated kurtosis deconvolution
by Liang Gao, Changhong Li

Advances in Differential Equations and Control Processes, Vol.32, No.2, 2025;

DOI: https://doi.org/10.59400/adecp2818

Early fault signals of the rolling bearing in the rotor are weak and present the characteristics of non-periodic and non-stationary; it is more difficult to carry out fault diagnosis on it. In this regard, this paper proposes a weak rolling bearing fault diagnosis algorithm based on whale optimization algorithm, simplistic geometry mode decomposition, and maximum correlated kurtosis deconvolution (WOA-SGMD-MCKD). Firstly, the vibration signal of the rotor platform is obtained, and the Symmetric Geometric Mode Decomposition (SGMD) is used to reconstruct the vibration signal. To obtain the best decomposition effect of the SGMD and overcome modal aliasing, the Whale Optimization Algorithm (WOA) is used to optimize the embedding dimension. Secondly, for the reconstructed vibration signal, the Maximum Correlated Kurtosis Deconvolution (MCKD) is used to extract its impulse component, and the WOA is used to optimize the filter length and deconvolution period of the MCKD so that the frequency envelope spectrum of the vibration signal can be obtained, which can provide the basis for the fault diagnosis of rolling bearings. Finally, the effectiveness and feasibility of the algorithm proposed are verified by a non-periodic and non-stationary simulation platform and rotor maneuvering platform in this paper.

show more
- PDF
Open Access

Article

Article ID: 2873

Global dynamics of an HBV-HIV co-infection model incorporating latent reservoirs
by Ahmed Elaiw, Abdulaziz Alhmadi, Aatef Hobiny

Advances in Differential Equations and Control Processes, Vol.32, No.2, 2025;

DOI: https://doi.org/10.59400/adecp2873

HBV and HIV are both blood-borne viruses with overlapping transmission routes, leading to higher HBV prevalence among people with HIV. While mathematical models have been extensively used to study each virus individually, co-infection dynamics have been relatively underexplored in research. This study presents a new within-host co-infection model for HIV and HBV that includes latent reservoirs. It accounts for HIV infecting both CD4+ T cells and hepatocytes, while HBV targets only hepatocytes. The model features both latent and active infection states for each cell type, along with free viral particles for both viruses. The model undergoes a qualitative analysis, leading to the derivation of four threshold parameters (R_i, i = 0, 1, 2, 3) that govern the existence and stability of its four equilibrium points. The stability conditions for each equilibrium of the model are determined through the construction of Lyapunov functions. Computational simulations are performed to confirm the key theoretical findings, while sensitivity analysis assesses how various parameters influence the basic reproductive numbers for HIV (R₀) and HBV (R₁) single-infections. The impact of anti-HIV and anti-HBV drugs is examined, and the critical efficacy thresholds for both therapies are identified. If the treatment effectiveness exceeds these thresholds, complete eradication of both HIV and HBV can be achieved.

show more
- PDF
Open Access

Article

Article ID: 3054

Generating directional attractors based on multiple subdivision
by Baoxing Zhang, Hongchan Zheng, Yuanyuan Xie

Advances in Differential Equations and Control Processes, Vol.32, No.2, 2025;

DOI: https://doi.org/10.59400/adecp3054

The connection between self-similar fractals and subdivision shows that self-similar fractals can be generated as attractors by an extended family of subdivision schemes. This paper aims to equipe these attractors with directions. Such directional attractors in this paper are generated based on a kind of multiple subdivision, which owns several anisotropic subdivision operators and generate surfaces with directions. For the multiple subdivision, we derive an iterated function system for each anisotropic subdivision operator to get a multiple function system, which can be arranged in a tree structure. Then by controlling the paths in the tree, attractors with different directions can be generated. Several examples are given to illustrate these new directional attractors.

show more
- PDF

Early fault signals of the rolling bearing in the rotor are weak and present the characteristics of non-periodic and non-stationary; it is more difficult to carry out fault diagnosis on it. In this regard, this paper proposes a weak rolling bearing fault diagnosis algorithm based on whale optimization algorithm, simplistic geometry mode decomposition, and maximum correlated kurtosis deconvolution (WOA-SGMD-MCKD). Firstly, the vibration signal of the rotor platform is obtained, and the Symmetric Geometric Mode Decomposition (SGMD) is used to reconstruct the vibration signal. To obtain the best decomposition effect of the SGMD and overcome modal aliasing, the Whale Optimization Algorithm (WOA) is used to optimize the embedding dimension. Secondly, for the reconstructed vibration signal, the Maximum Correlated Kurtosis Deconvolution (MCKD) is used to extract its impulse component, and the WOA is used to optimize the filter length and deconvolution period of the MCKD so that the frequency envelope spectrum of the vibration signal can be obtained, which can provide the basis for the fault diagnosis of rolling bearings. Finally, the effectiveness and feasibility of the algorithm proposed are verified by a non-periodic and non-stationary simulation platform and rotor maneuvering platform in this paper.

Numerical solution of a 3D mathematical model for the progression of tumor angiogenic factor in a tissue

In this work, the movement of tumor angiogenic factor in a three-dimensional tissue is obtained by the Method of Lines. This method transforms a partial differential equation into a system of ordinary differential equations together with the initial and boundary conditions. The more the number of lines is increased, the more the accuracy of the method increases. This method results in very accurate numerical solutions for linear and non-linear problems in contrast with other existing methods. We present Matlab-generated figures, which are the movement of tumor angiogenic factor in porous medium and explain the biological importance of this progression. The computer codes are also provided.

Mathematical modelling and controllability analysis of fractional order coal mill pulverizer model

This paper investigates the controllability of nonlinear dynamical systems and their applications, with a focus on fractional-order systems and coal mill models. A novel theorem is proposed, providing sufficient conditions for controllability, including constraints on the steering operator and nonlinear perturbation bounds. The theorem establishes the existence of a contraction mapping for the nonlinear operator, enabling effective control strategies for fractional systems. The methodology is demonstrated through rigorous proof and supported by an iterative algorithm for controller design. Additionally, the controllability of a coal mill system represented as a nonlinear differential system, is analyzed. The findings present new insights into the interplay of fractional dynamics and nonlinear systems, offering practical solutions for real-world control problems.