陽明交通大學應用數學系

Abstract. The global navigation satellite system (GNSS) has been widely used in positioning, navigation, and timing. The GNSS satellite orbit serves as a reference datum in connection to the International GNSS Service (IGS)-defined reference frame, not only for GNSS ranging measurements but also for the so-called precise point positioning (PPP) technique. Therefore, the accuracy of the reference orbit is crucial for precise geodetic applications. On the other hand, in recent years, with the rapid development of the space satellite industry, countries around the world have been actively promoting the research, development, and application of Low Earth Orbit (LEO) satellites. These satellites have been widely utilized in scientific research and commercial sectors and are quickly advancing toward commercialization. LEO satellites refer to satellites operating at altitudes of approximately 200 to 2,000 kilometers above the Earth’s surface. Compared to medium- and high-orbit satellites, LEO satellites offer advantages such as lower orbital altitude, reduced latency, and higher coverage accuracy. As technology progresses and demand increases, the application scope of LEO satellites continues to expand, particularly playing a critical role in Positioning, Navigation, and Timing (PNT) as well as in communication services.

Abstract. Exploring the mathematical principles behind remote sensing, starting with how to define the location using Earth Coordinate Systems and Geodetic Coordinate Systems, and demonstrate how to map satellite images to a Ground Coordinate System. The presentation will also introduce image processing techniques for both optical and Synthetic-aperture radar (SAR) images, including radiometric calibration and geometric correction. Finally, I'll showcase specific applications such as Total Variation (TV) models, image fusion using neural networks and SAR image denoising.

Abstract. Computational galaxy formation has been remarkably successful in recreating realistic galaxies on a supercomputer using the so-called “cosmological simulations”, where a smooth mixture of gas and dark matter in the early Universe gradually evolves into thousands of galaxies similar to those observed today. The key to this success lies in the physical processes (collectively referred to as "feedback") that drive the cycling of gas in and around galaxies. However, all existing cosmological simulations face a fundamental limitation due to their empirical "sub-resolution" models. In this talk, I will introduce the successes and challenges in this field and discuss exciting recent progress on high-resolution, small-scale simulations that aim to tackle the problem by directly modeling the physics in the interstellar medium. I will also discuss the critical role of innovative numerical algorithms in advancing our field.

Abstract.
Mean field games (MFGs) are formulated as nonlinear coupled systems of partial differential equations, consisting of the Fokker–Planck equation, which governs the density distribution of agents, and the Hamilton–Jacobi–Bellman equation, which describes the temporal evolution of their control inputs. Such systems arise in a broad range of applications, including crowd dynamics, control of autonomous vehicle fleets, mathematical biology, engineering, and economics. Since MFGs are typically posed as space–time boundary value problems, numerical schemes designed for standard initial value problems cannot be directly applied. This motivates the development of new computational methods together with a rigorous mathematical foundation. In this talk, I present an implementation-friendly approach based on a generalized conditional gradient (GCG) method and discuss its convergence properties. In particular, I report recent results, obtained in collaboration with H. Nakamura, for MFGs with local coupling terms.

Abstract
Given a graph and a function on its vertices, how do we partition the vertices into clusters so that (1) vertices with similar function values are in the same cluster and (2) the induced subgraph on each cluster is connected as much as possible? Such a problem has applications in detecting the sources of air pollution, image segmentation, and so on. We will go through the theoretical background of this algorithm and demonstrate some of its applications.

Abstract
The Quantic Tensor Train (QTT) is a tensor network framework that provides highly compact representations of high-dimensional functions and operators. This makes it a promising tool for tackling nonlinear partial differential equations that are otherwise computationally demanding. In this work, we explore the use of QTT for solving the Gross–Pitaevskii equation (GPE), a fundamental nonlinear model describing Bose–Einstein condensates and related quantum systems. By using QTT, we significantly reduce the computational complexity compared to conventional discretization methods, achieving efficient and scalable solutions. Our results demonstrate the potential of QTT to extend tensor network techniques beyond linear problems, opening the door to new applications in nonlinear quantum dynamics and many-body physics.

Abstract：
1. Operation method of MOSFET and memory devices
2. Recent development of 3-Dimensional devices (Flash memory & DRAM)
3. Reliability issues of Flash memory
(limitation of number of rewrite cycles and the difficulty to analyze)
4. Short review of my reliability studies