DSpace Collection:http://scholars.ntou.edu.tw/handle/123456789/111112024-08-06T16:22:31Z2024-08-06T16:22:31ZOptimal Shape Factor and Fictitious Radius in the MQ-RBF: Solving Ill-Posed Laplacian ProblemsLiu, Chein-ShanKuo, Chung-LunChang, Chih-Wenhttp://scholars.ntou.edu.tw/handle/123456789/247162024-03-06T03:51:35Z2024-01-01T00:00:00ZTitle: Optimal Shape Factor and Fictitious Radius in the MQ-RBF: Solving Ill-Posed Laplacian Problems
Authors: Liu, Chein-Shan; Kuo, Chung-Lun; Chang, Chih-Wen
Abstract: To solve the Laplacian problems, we adopt a meshless method with the multiquadric radial basis function (MQRBF) as a basis whose center is distributed inside a circle with a fictitious radius. A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function. A sample function is interpolated by the MQ-RBF to provide a trial coefficient vector to compute the merit function. We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm. The novel method provides the optimal values of parameters and, hence, an optimal MQ-RBF; the performance of the method is validated in numerical examples. Moreover, nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition; this can overcome the problem of these problems being ill-posed. The optimal MQ-RBF is extremely accurate. We further propose a novel optimal polynomial method to solve the nonharmonic problems, which achieves high precision up to an order of 10-11.2024-01-01T00:00:00ZMemory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value ProblemLiu, Chein-ShanChang, Chih-WenKuo, Chung-Lunhttp://scholars.ntou.edu.tw/handle/123456789/247042024-03-06T03:51:32Z2024-01-01T00:00:00ZTitle: Memory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value Problem
Authors: Liu, Chein-Shan; Chang, Chih-Wen; Kuo, Chung-Lun
Abstract: In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values f '(r), f ''(r), and f '''(r) of a nonlinear equation f(x) = 0 with r being its simple root. We can achieve high values of the efficiency index (E.I.) over the bound 2(2/3) = 1.587 with three function evaluations and over the bound 2(1/2) = 1.414 with two function evaluations. The third-degree Newton interpolatory polynomial is derived to update these critical values per iteration. We introduce relaxation factors into the Dzunic method and its variant, which are updated to render fourth-order convergence by the memory-accelerating technique. We developed six types optimal one-step iterative schemes with the memory-accelerating method, rendering a fourth-order convergence or even more, whose original ones are a second-order convergence without memory and without using specific optimal values of the parameters. We evaluated the performance of these one-step iterative schemes by the computed order of convergence (COC) and the E.I. with numerical tests. A Lie symmetry method to solve a second-order nonlinear boundary-value problem with high efficiency and high accuracy was developed.2024-01-01T00:00:00ZPseudo and anisotropic MFS for Laplace equation and optimal sources using maximal projection method with a substitution functionLiu, Chein-ShanKuo, Chung-Lunhttp://scholars.ntou.edu.tw/handle/123456789/246922024-03-06T02:05:12Z2023-01-01T00:00:00ZTitle: Pseudo and anisotropic MFS for Laplace equation and optimal sources using maximal projection method with a substitution function
Authors: Liu, Chein-Shan; Kuo, Chung-Lun
Abstract: The paper creates two new families of fundamental solutions for the 3D Laplace equation, presented into two parts. For the first part in terms of a planar line as a new coordinate the derived 2D like fundamental solution has a logarithmic singularity, which results in a method of pseudo fundamental solutions. We propose two methods to determine the optimal values of the offset parameter used to locate the source points. In the second part, an anisotropic distance function r(g) in terms of a symmetric non-negative anisotropic metric tensor is introduced, which satisfies a certain quadratic matrix equation, and then ln r(g) is proved to be a new fundamental solution. Using a unit orientation vector we can derive the metric tensor in closed-form, and prove that it is a singular projection operator. Given the unit orientation vector satisfying a cone condition, a method of anisotropic fundamental solutions is developed. They are distinct from the traditional 3D MFS. Owing to a weaker singularity than that of 1/r appeared in the 3D MFS, the method of pseudo fundamental solutions and the method of anisotropic fundamental solutions outperform the 3D MFS. Some numerical experiments explore the performance of these two novel methods.2023-01-01T00:00:00ZAn Overview of the Potential of Food-Based Carbon Dots for Biomedical ApplicationsWang, Chen-YowNdraha, NodaliWu, Ren-SiangLiu, Hsin-YunLin, Sin-WeiYang, Kuang-MinLin, Hung-Yunhttp://scholars.ntou.edu.tw/handle/123456789/246802024-03-06T01:10:07Z2023-01-01T00:00:00ZTitle: An Overview of the Potential of Food-Based Carbon Dots for Biomedical Applications
Authors: Wang, Chen-Yow; Ndraha, Nodali; Wu, Ren-Siang; Liu, Hsin-Yun; Lin, Sin-Wei; Yang, Kuang-Min; Lin, Hung-Yun
Abstract: Food-based carbon dots (CDs) hold significant importance across various fields, ranging from biomedical applications to environmental and food industries. These CDs offer unique advantages over traditional carbon nanomaterials, including affordability, biodegradability, ease of operation, and multiple bioactivities. This work aims to provide a comprehensive overview of recent developments in food-based CDs, focusing on their characteristics, properties, therapeutic applications in biomedicine, and safety assessment methods. The review highlights the potential of food-based CDs in biomedical applications, including antibacterial, antifungal, antivirus, anticancer, and anti-immune hyperactivity. Furthermore, current strategies employed for evaluating the safety of food-based CDs have also been reported. In conclusion, this review offers valuable insights into their potential across diverse sectors and underscores the significance of safety assessment measures to facilitate their continued advancement and application.2023-01-01T00:00:00Z