https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/665 2026-07-04T07:11:17Z 2026-07-04T07:11:17Z Ahn, Jungho Kim, Jinha Kwon, O-joung https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/215896 2026-06-25T02:00:22Z 2026-08-01T00:00:00Z

Title: Unified almost linear kernels for generalized covering and packing problems on nowhere dense classes Authors: Ahn, Jungho; Kim, Jinha; Kwon, O-joung Abstract: Let F be a family of graphs and r≥0 be an integer. For a graph G and an integer k, (r,F)-COVERING asks whether there is a set D⊆V(G) of size at most k such that every induced subgraph of G isomorphic to a graph in F is at distance at most r from D. (r,F)-PACKING asks whether G has k induced subgraphs H1,…,Hk such that each Hi is isomorphic to a graph in F and the distance between distinct V(Hi) and V(Hj) in G is more than r. We show that for every fixed nonempty finite family F of connected graphs and r≥0, (r,F)-COVERING and (r,F)-PACKING admit almost linear kernels on every nowhere dense class of graphs, parameterized by the solution size k. As corollaries, we prove that DISTANCE-r VERTEX COVER, DISTANCE-r MATCHING, F-FREE VERTEX DELETION, and INDUCED-F-PACKING for any fixed finite family F of connected graphs admit almost linear kernels on every nowhere dense class of graphs. Our results extend the results for DISTANCE-r DOMINATING SET by Drange et al. (2016) [17] and Eickmeyer et al. (2017) [20] and for DISTANCE-r INDEPENDENT SET by Pilipczuk and Siebertz (2021) [41].

2026-08-01T00:00:00Z Choi, Geunsu Jung, Mingu Lee, Han Ju Roldan, Oscar https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/210924 2026-02-25T04:30:29Z 2026-06-01T00:00:00Z

Title: Linear structures of norm-attaining Lipschitz functions and their complements Authors: Choi, Geunsu; Jung, Mingu; Lee, Han Ju; Roldan, Oscar Abstract: We solve two main questions on linear structures of (non-)norm-attaining Lipschitz functions. First, we show that for every infinite metric space M , the set consisting of Lipschitz functions on M which do not strongly attain their norm and the zero function contains an isometric copy of ℓ<inf>∞</inf>, and moreover, those functions can be chosen not to attain their norm as functionals on the Lipschitz-free space over M . Second, we prove that for every infinite metric space M , neither the set of strongly norm-attaining Lipschitz functions on M nor the union of its complement with zero is ever a linear space. Furthermore, we observe that the set consisting of Lipschitz functions which cannot be approximated by strongly norm-attaining ones and the zero element contains ℓ<inf>∞</inf> isometrically in all the known cases. Some natural observations and spaceability results are also investigated for Lipschitz functions that attain their norm in one way but do not in another.

2026-06-01T00:00:00Z Yang, Seung Jee Jeong, Jaehong https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/213371 2026-06-18T06:00:12Z 2026-06-01T00:00:00Z

Title: Spatiotemporal modeling of wind speed fields over the Korean Peninsula using 3D-CNN and β-VAE for probabilistic forecasting Authors: Yang, Seung Jee; Jeong, Jaehong Abstract: Accurate and uncertainty-aware spatiotemporal modeling of wind speed fields is essential for optimizing wind energy operations and identifying suitable turbine deployment sites. This study proposes a data-driven generative framework based on a 3D-CNN combined with a beta-Variational Autoencoder (beta-VAE) to produce probabilistic 1-hour-ahead wind field forecasts over the Korean Peninsula. The fiveyear ERA5 dataset is split into three years for training and two subsequent years for validation and testing. Three-dimensional convolutions are used to capture both spatial and temporal dependencies, and the parameter beta controls the trade-off between reconstruction fidelity and latent space regularization. A sensitivity analysis indicates that beta = 0.01 provides a favorable balance for forecasting. Using Root Mean Square Error, Continuous Ranked Probability Score, Variogram Score, and Probability Integral Transform-based diagnostics, we evaluated the trained model and found that it reproduces the ensemble statistics and spatial dependence structures of the observed wind fields. The model also yields reasonably well-calibrated probabilistic forecasts. Compared to the ConvLSTM beta-VAE and 2D-CNN beta-VAE baselines, the 3D-CNN beta-VAE provides comparable skill at a 1-hour lead time and noticeably better probabilistic forecast performance and spatial consistency at longer lead times. These results suggest that the 3D-CNN beta-VAE could serve as a scalable tool for offshore wind energy resource assessment and short-term turbine operation planning.

2026-06-01T00:00:00Z Hosseini, Amin Park, Choonkil Karizaki, Mehdi Mohammadzadeh https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/214343 2026-06-23T01:30:14Z 2026-06-01T00:00:00Z

Title: On the characterization and Automatic continuity of (σ, τ)-ternary derivations Authors: Hosseini, Amin; Park, Choonkil; Karizaki, Mehdi Mohammadzadeh Abstract: Let A and B be two algebras, and let sigma, tau : A -> B be two linear mappings. A linear mapping d(1) : A -> B is called a (sigma, tau)-ternary derivation if there exist the linear mappings d(2), d(3) : A -> B which satisfy d(1)(ab) = d(2)(a)sigma(b) +tau(a)d(3)(b) for all a, b is an element of A. By a (d(2), sigma, tau, d(3))-derivation, we mean a (sigma, tau)-ternary derivation d1 associated with the mappings d(2) and d(3). The main purpose of this article is to study the characterization and automatic continuity of such derivations on Banach algebras and C-& lowast;-algebras.

2026-06-01T00:00:00Z