DSpace Community: KAIST Dept. of Mathematical SciencesKAIST Dept. of Mathematical Scienceshttp://hdl.handle.net/10203/5272019-10-17T06:43:56Z2019-10-17T06:43:56Zl-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.2019-12-01T00:00:00ZThe transcendence of zeros of canonical basis elements of the space of weakly holomorphic modular forms for Gamma(0)(2)Choi, SoYoungIm, Bo-Haehttp://hdl.handle.net/10203/2643232019-08-22T03:20:06Z2019-11-01T00:00:00ZTitle: The transcendence of zeros of canonical basis elements of the space of weakly holomorphic modular forms for Gamma(0)(2)
Authors: Choi, SoYoung; Im, Bo-Hae
Abstract: We consider the canonical basis elements f(k,m)(epsilon) for the space of weakly holomorphic modular forms of weight k for the Hecke congruence group Gamma(0)(2) and we prove that for all m >= c(k) for some constant c(k), if z(0) in a fundamen- tal domain for Gamma(0)(2) is a zero of f(k,m)(epsilon), then either z(0) is in {i/root 2, - 1/2 + i/2, 1/2 + i/2, -1+i root 7/4, 1+i root 7/4} or z(0) is transcendental. (C) 2019 Elsevier Inc. All rights reserved.2019-11-01T00:00:00Z