Current Issue : October-December Volume : 2025 Issue Number : 4 Articles : 5 Articles
Vector-borne diseases pose a significant public health challenge in tropical regions, where complex interactions between hosts, vectors, and the environment drive epidemic dynamics. In this study, we develop a spatio-temporal mathematical model to describe the spread of such diseases, incorporating population dynamics and spatial–temporal factors affecting pathogen transmission. We conduct a theoretical analysis of the model, proving the existence, uniqueness, and positivity of solutions. Additionally, we examine equilibrium states and key epidemiological parameters, including the basic reproduction number. Our findings provide mathematical insights into epidemic propagation and offer a foundation for designing effective control strategies....
Fuzzy time series forecasting has gained significant attention for its accuracy, robustness, and interpretability, making it widely applicable in practical prediction tasks. In classical fuzzy time series models, the lag order plays a crucial role, with variations in order often leading to markedly different forecasting results. To obtain the best performance, we propose a mixed-order fuzzy time series model, which incorporates fuzzy logical relationships (FLRs) of different orders into its rule system. This approach mitigates the uncertainty in fuzzy forecasting caused by empty FLRs and FLR groups while fully exploiting the fitting advantages of different-order FLRs. Theoretical analysis is provided to establish the mathematical foundation of the mixed-order model, and its superiority over fixed-order models is demonstrated. Simulation studies reveal that the proposed model outperforms several classical time series models in specific scenarios. Furthermore, applications to real-world datasets, including a COVID-19 case study and a TAIEX financial dataset, validate the effectiveness and applicability of the proposed methodology...
In this work, we prove that the initial value problem for the Schrödinger– Korteweg–de Vries (SKdV) system is locally well posed in Gevrey spaces for s > −34 and k ≥ 0. This advancement extends recent findings regarding the well posedness of this model within Sobolev spaces and investigates the regularity properties of its solutions....
The method of particular solutions using polynomial basis functions (MPS-PBF) has been extensively used to solve various types of partial differential equations. Traditional methods employing radial basis functions (RBFs)—such as Gaussian, multiquadric, and Matérn functions—often suffer from accuracy issues due to their dependence on a shape parameter, which is very difficult to select optimally. In this study, we adopt the MPS-PBF to solve the time-dependent Schrödinger equation in two dimensions. By utilizing polynomial basis functions, our approach eliminates the need to determine a shape parameter, thereby simplifying the solution process. Spatial discretization is performed using the MPS-PBF, while temporal discretization is handled via the backward Euler and Crank–Nicolson methods. To address the ill conditioning of the resulting system matrix, we incorporate a multi-scale technique. To validate the efficacy of the proposed scheme, we present four numerical examples and compare the results with known analytical solutions, demonstrating the accuracy and robustness of the scheme....
This study innovatively explores vibrational control with reference to elliptical thickness variation. Traditionally, plate vibrations have been analysed by incorporating circular, linear, parabolic, and exponential thickness variations. However, these variations often fall short in optimizing vibrational characteristics. So, we develop a new formula specifically for orthotropic as well as isotropic plates with elliptical thickness profiles and employ the Rayleigh–Ritz method to calculate the vibrational frequencies of the plate. This research demonstrates that elliptical variation significantly reduces vibrational frequencies compared to conventional thickness profiles. The findings indicate that this unique configuration enhances vibrational control, offering potential applications in engineering fields where vibration reduction is essential. The results provide a foundation for further exploration of non-standard thickness variations in the design of advanced structural components. The study reveals that the elliptical variation in tapering parameter is a much better choice than other variation parameters studied in the literature for the purpose of optimizing the vibrational frequency of plates....
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