DSpace 集合:
https://scholars.lib.ntu.edu.tw/handle/123456789/32193
2024-03-29T08:56:31ZSynchronization of Kuramoto–Sakaguchi model with the distributed time-delayed interactions
https://scholars.lib.ntu.edu.tw/handle/123456789/638963
標題: Synchronization of Kuramoto–Sakaguchi model with the distributed time-delayed interactions
作者: CHUN-HSIUNG HSIA; Jung, Chang Yeol; Kwon, Bongsuk; Moon, Sunghwan
摘要: The synchronous behavior of Kuramoto–Sakaguchi models with distributed time-delayed interactions is investigated. We prove complete and partial phase synchronization for both the distributed semi time-delay model and the full time-delay model. Additionally, we present several numerical experiments supporting our main results and illustrating interesting patterns.2024-02-01T00:00:00ZAn effective method for identifying clusters of robot strengths
https://scholars.lib.ntu.edu.tw/handle/123456789/638958
標題: An effective method for identifying clusters of robot strengths
作者: Teng, Jen Chieh; CHIN-TSANG CHIANG; Lim, Alvin
摘要: In the analysis of qualification stage data from FIRST Robotics Competition (FRC) championships, the ratio (1.67–1.68) of the number of observations (110–114 matches) to the number of parameters (66–68 robots) in each division has been found to be quite small for the most commonly used winning margin power rating (WMPR) model. This usually leads to imprecise estimates and inaccurate predictions in such three-on-three matches that FRC tournaments are composed of. With the recognition of a clustering feature in estimated robot strengths, a more flexible model with latent clusters of robots was proposed to alleviate overparameterization of the WMPR model. Since its structure can be regarded as a dimension reduction of the parameter space in the WMPR model, the identification of clusters of robot strengths is naturally transformed into a model selection problem. Instead of comparing a huge number of competing models (7.76 × 10 67 to 3.66 × 10 70) , we develop an effective method to estimate the number of clusters, clusters of robots and robot strengths in the format of qualification stage data from the FRC championships. The new method consists of two parts: (i) a combination of hierarchical and non-hierarchical classifications to determine candidate models; and (ii) variant goodness-of-fit criteria to select optimal models. In contrast to existing hierarchical classification, each step of our proposed non-hierarchical classification is based on estimated robot strengths from a candidate model in the preceding non-hierarchical classification step. A great advantage of the proposed methodology is its ability to consider the possibility of reassigning robots to other clusters. To reduce overestimation of the number of clusters by the mean squared prediction error criteria, corresponding Bayesian information criteria are further established as alternatives for model selection. With a coherent assembly of these essential elements, a systematic procedure is presented to perform the estimation of parameters. In addition, we propose two indices to measure the nested relation between clusters from any two models and monotonic association between robot strengths from any two models. Data from the 2018 and 2019 FRC championships and a simulation study are also used to illustrate the applicability and superiority of our proposed methodology.2023-01-01T00:00:00Z2D Serre-Green-Naghdi Equations over Topography: Elliptic Operator Inversion Method
https://scholars.lib.ntu.edu.tw/handle/123456789/638951
標題: 2D Serre-Green-Naghdi Equations over Topography: Elliptic Operator Inversion Method
作者: Gavrilyuk, Sergey; KEH-MING SHYUE
摘要: Multidimensional Serre-Green-Naghdi equations are numerically solved by using a natural hyperbolic-elliptic splitting. The hyperbolic step is solved by semidiscret finite volume methods. The elliptic step is related to recovering nonhydrostatic pressure. One-dimensional (1D) and two-dimensional (2D) test problems (i.e., 1D solitary wave propagation, 2D dam-break problem, solitary wave overstep and overhump) are considered.2024-01-01T00:00:00ZLandis-type conjecture for the half-Laplacian
https://scholars.lib.ntu.edu.tw/handle/123456789/638950
標題: Landis-type conjecture for the half-Laplacian
作者: Pu-Zhao Kow; JENN-NAN WANG
摘要: In this paper, we study the Landis-type conjecture, i.e., unique continuation
property from infinity, of the fractional Schr\"{o}dinger equation with drift
and potential terms. We show that if any solution of the equation decays at a
certain exponential rate, then it must be trivial. The main ingredients of our
proof are the Caffarelli-Silvestre extension and Armitage's Liouville-type
theorem.2021-06-11T00:00:00Z