DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272019-11-16T22:48:20Z2019-11-16T22:48:20Zl-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficientsHamacher, PaulKim, Wansuhttp://hdl.handle.net/10203/2518972019-03-19T02:01:12ZTitle: l-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
Authors: Hamacher, Paul; Kim, WansuA logarithmic chemotaxis model featuring global existence and aggregationDesvillettes, LaurentKim, Yong-JungTrescases, ArianeYoon, Changwookhttp://hdl.handle.net/10203/2643212019-08-20T05:20:03Z2019-12-01T00:00:00ZTitle: A logarithmic chemotaxis model featuring global existence and aggregation
Authors: Desvillettes, Laurent; Kim, Yong-Jung; Trescases, Ariane; Yoon, Changwook
Abstract: The global existence of a chemotaxis model for cell aggregation phenomenon is obtained. The model system belongs to the class of logarithmic models and takes a Fokker-Planck type diffusion for the equation of cell density. We show that weak solutions exist globally in time in dimensions n is an element of {1, 2, 3} and for large initial data. The proof covers the parameter regimes that constant steady states are linearly stable. It also partially covers the other parameter regimes that constant steady states are unstable. We also find the sharp instability condition of constant steady states and provide numerical simulations which illustrate the formation of aggregation patterns. (C) 2019 Elsevier Ltd. All rights reserved.2019-12-01T00:00:00ZLimit properties of continuous self-exciting processesKim, GunheeChoe, Geon Hohttp://hdl.handle.net/10203/2679472019-10-14T06:20:04Z2019-12-01T00:00:00ZTitle: Limit properties of continuous self-exciting processes
Authors: Kim, Gunhee; Choe, Geon Ho
Abstract: We introduce a self-exciting continuous process based on Brownian motion, and derive its limit properties. We find conditions when the limit behaviors of the given process and its associated Hawkes process agree. The Kolmogorov-Smirnov test was applied to check the statistical similarity of the two processes. (C) 2019 Elsevier B.V. All rights reserved.2019-12-01T00:00:00ZHardy's inequality in a limiting case on general bounded domainsByeon, JaeyoungTakahashi, Futoshihttp://hdl.handle.net/10203/2683182019-11-11T06:20:05Z2019-12-01T00:00:00ZTitle: Hardy's inequality in a limiting case on general bounded domains
Authors: Byeon, Jaeyoung; Takahashi, Futoshi
Abstract: In this paper, we study Hardy's inequality in a limiting case: integral(Omega) vertical bar del u vertical bar(N) dx >= C-N(Omega) integral(Omega) vertical bar u(x)vertical bar(N)/vertical bar x vertical bar(N)(log R/vertical bar x vertical bar)(N) dx for functions u is an element of W-0(1,N) (Omega), where Omega is a bounded domain in RN with R = sup(x is an element of Omega)vertical bar x vertical bar. We study the attainability of the best constant C-N(Omega) in several cases. We provide sufficient conditions that assure C-N(Omega) > CN(B-R) and CN(Omega) is attained, here B-R is the N-dimensional ball with center the origin and radius R. Also, we provide an example of Omega subset of R-2 such that C-2(Omega) > C-2(B-R) = 1/4 and C-2(Omega) is not attained.2019-12-01T00:00:00Z