https://scholar.gist.ac.kr/handle/local/7945 Wed, 13 May 2026 14:56:47 GMT 2026-05-13T14:56:47Z https://scholar.gist.ac.kr/handle/local/33610 Title: 첫 통과/마지막 통과 알고리즘에 대하여 Author(s): Hwang, Chi-Ok Tue, 28 Feb 2023 15:00:00 GMT https://scholar.gist.ac.kr/handle/local/33610 2023-02-28T15:00:00Z https://scholar.gist.ac.kr/handle/local/32013 Title: α-Mean curvature flow of non-compact complete convex hypersurfaces and the evolution of level sets Author(s): Kang, Hyunsuk; Lee, Kiahm; Lee, Taehun Abstract: We consider the α -mean curvature flow for convex graphs in Euclidean space. Given a smooth, complete, strictly convex, non-compact initial hypersurface over a strictly convex projected domain, we derive uniform curvature bounds, which are independent of the height of a graph, to give C 2 {C}^{2} -estimates for convex graphs. Consequently, these height-independent estimates imply that all the derivatives for level sets converge uniformly. Furthermore, with these estimates on level sets, the boundary of the domain of a graph, which demonstrates the behavior of level sets as the height tends to infinity, is shown to be a smooth solution for the α -mean curvature flow of codimension two in the classical sense. © 2025 Elsevier B.V., All rights reserved. Thu, 31 Jul 2025 15:00:00 GMT https://scholar.gist.ac.kr/handle/local/32013 2025-07-31T15:00:00Z https://scholar.gist.ac.kr/handle/local/16505 Title: Yang-Lee Zeros of the Triangular Ising Antifeffomagnets Author(s): Hwang, Chi-Ok; Seung-Yeon Kim Abstract: In our previous research, by combining both the exact enumeration method (microcanonical transfer matrix) for a small system () with the Wang–Landau Monte Carlo algorithm for large systems (to ) we obtained the exact and approximate densities of states , as a function of the magnetization and exchange energy , for a triangular-lattice Ising model. In this paper, based on the density of states , the precise distribution of the Yang–Lee zeros of triangular-lattice Ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature for a 9×9 lattice system. Also, the feasibility of the Yang–Lee zero approach combined with the Wang–Landau algorithm is demonstrated; as a result, we obtained the magnetic exponents for triangular Ising antiferromagnets at various temperatures. Tue, 30 Nov 2010 15:00:00 GMT https://scholar.gist.ac.kr/handle/local/16505 2010-11-30T15:00:00Z https://scholar.gist.ac.kr/handle/local/10512 Title: WELL-MIXING VERTICES AND ALMOST EXPANDERS Author(s): Chakraborti, Debsoumya; Kim, Jaehoon; Kim, Jinha; Kim, Minki; Liu, Hong Abstract: We study regular graphs in which the random walks starting from a positive fraction of vertices have small mixing time. We prove that any such graph is virtually an expander and has no small separator. This answers a question of Pak [SODA: Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002, pp. 321-328]. As a corollary, it shows that sparse (constant degree) regular graphs with many well-mixing vertices have a long cycle, improving a result of Pak. Furthermore, such cycle can be found in polynomial time. Secondly, we show that if the random walks from a positive fraction of vertices are well-mixing, then the random walks from almost all vertices are well-mixing (with a slightly worse mixing time). Wed, 30 Nov 2022 15:00:00 GMT https://scholar.gist.ac.kr/handle/local/10512 2022-11-30T15:00:00Z