DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical Sciences2017-09-30T14:44:22ZSpectral Resolution of the Neumann-Poincar, Operator on Intersecting Disks and Analysis of Plasmon Resonance
http://hdl.handle.net/10203/225800
Title: Spectral Resolution of the Neumann-Poincar, Operator on Intersecting Disks and Analysis of Plasmon Resonance
Authors: Kang, Hyeonbae; Lim, Mikyoung; Yu, Sang Hyeon
Abstract: The purpose of this paper is to investigate the spectral nature of the Neumann-Poincar, operator on the intersecting disks, which is a domain with the Lipschitz boundary. The complete spectral resolution of the operator is derived, which shows, in particular, that it admits only the absolutely continuous spectrum; no singularly continuous spectrum and no pure point spectrum. We then quantitatively analyze using the spectral resolution of the plasmon resonance at the absolutely continuous spectrum.2017-10-01T00:00:00ZNear equipartitions of colored point sets
http://hdl.handle.net/10203/225586
Title: Near equipartitions of colored point sets
Authors: Holmsen, Andreas E.; Kyncl, Jan; Valculescu, Claudiu
Abstract: Suppose that nk points in general position in the plane are colored red and blue, with at least n points of each color. We show that then there exist n pairwise disjoint convex sets, each of them containing k of the points, and each of them containing points of both colors. We also show that if P is a set of n(d + 1) points in general position in R-d colored by d colors with at least n points of each color, then there exist n pairwise disjoint d-dimensional simplices with vertices in P, each of them containing a point of every color. These results can be viewed as a step towards a common generalization of several previously known geometric partitioning results regarding colored point sets.2017-10-01T00:00:00ZEven-cycle decompositions of graphs with no odd-K-4-minor
http://hdl.handle.net/10203/226118
Title: Even-cycle decompositions of graphs with no odd-K-4-minor
Authors: Huynh, Tony; Oum, Sang-il; Verdian-Rizi, Maryam
Abstract: An even-cycle decomposition of a graph G is a partition of E(G) into cycles of even length. Evidently, every Eulerian bipartite graph has an even-cycle decomposition. Seymour (1981) proved that every 2-connected loopless Eulerian planar graph with an even number of edges also admits an even-cycle decomposition. Later, Zhang (1994) generalized this to graphs with no K-5-minor. Our main theorem gives sufficient conditions for the existence of even-cycle decompositions of graphs in the absence of odd minors. Namely, we prove that every 2-connected loopless Eulerian odd-K-4-minor-free graph with an even number of edges has an even-cycle decomposition. This is best possible in the sense that 'odd-K-4-minor-free' cannot be replaced with 'odd-K-5-minor-free.' The main technical ingredient is a structural characterization of the class of odd-K-4-minor-free graphs, which is due to Lovasz, Seymour, Schrijver, and Truemper. (C) 2017 Elsevier Ltd. All rights reserved.2017-10-01T00:00:00ZInviscid traveling waves of monostable nonlinearity
http://hdl.handle.net/10203/224020
Title: Inviscid traveling waves of monostable nonlinearity
Authors: Choi, Sun-Ho; Chung, Jaywan; Kim, Yong-Jung
Abstract: Inviscid traveling waves are ghost-like phenomena that do not appear in reality because of their instability. However, they are the reason for the complexity of the traveling wave theory of reaction diffusion equations and understanding them will help to resolve related puzzles. In this article, we obtain the existence, the uniqueness and the regularity of inviscid traveling waves under a general monostable nonlinearity that includes non-Lipschitz continuous reaction terms. Solution structures are obtained such as the thickness of the tail and the free boundaries. (C) 2017 Elsevier Ltd. All rights reserved.2017-09-01T00:00:00Z