DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical SciencesMon, 21 Jun 2021 11:18:29 GMT2021-06-21T11:18:29ZDegree 3 unramified cohomology of classifying spaces for exceptional groups
http://hdl.handle.net/10203/285403
Title: Degree 3 unramified cohomology of classifying spaces for exceptional groups
Authors: Baek, Sanghoon
Abstract: Let G be a reductive group defined over an algebraically closed field of characteristic 0 such that the Dynkin diagram of G is the disjoint union of diagrams of types G(2), F-4, E-6, E-7, E-8. We show that the degree 3 unramified cohomology of the classifying space of G is trivial. In particular, combined with articles by Merkurjev [11] and the author [1], this completes the computations of degree 3 unramified cohomology and reductive invariants for all split semisimple groups of a homogeneous Dynkin type. (C) 2021 Elsevier B.V. All rights reserved.Fri, 01 Oct 2021 00:00:00 GMThttp://hdl.handle.net/10203/2854032021-10-01T00:00:00ZComponentwise linearity of projective varieties with almost maximal degree
http://hdl.handle.net/10203/282869
Title: Componentwise linearity of projective varieties with almost maximal degree
Authors: Cuong, Doan Trung; Kwak, Sijong
Abstract: The degree of a projective subscheme has an upper bound deg(X) <= ((e+r)(e)) in terms of the codimension eand the reduction number r. It was proved in [3] that deg(X) = ((e r)(e)) if and only if Xis arithmetically Cohen-Macaulay and has an (r+ 1)-linear resolution. Moreover, if the degree of a projective variety Xsatisfies deg(X) = ((e+r)(e)) - 1, then the Betti table is described with some constraints. In this paper, we build on this work to show that most of such varieties are componentwise linear and the componentwise linearity is particularly suitable for understanding their Betti tables. As an application, the graded Betti numbers of those varieties with componentwise linear resolutions are computed. (C) 2021 Elsevier B.V. All rights reserved.Wed, 01 Sep 2021 00:00:00 GMThttp://hdl.handle.net/10203/2828692021-09-01T00:00:00ZDiscontinuous bubble immersed finite element method for Poisson-Boltzmann-Nernst-Planck model
http://hdl.handle.net/10203/285558
Title: Discontinuous bubble immersed finite element method for Poisson-Boltzmann-Nernst-Planck model
Authors: Kwon, In; Kwak, Do Young; Jo, Gwanghyun
Abstract: We develop a numerical scheme for Poisson-Boltzmann-Nernst-Planck (PBNP) model. We adopt Gummel's method to treat the nonlinearity of PBNP where Poisson-Boltzmannequation and Nernst-Planckequation are iteratively solved, and then the idea of discontinuous bubble (DB) to solve the Poisson-Boltzmannequation is exploited [6]. First, we regularize the solution of Poisson-Boltzmannequation to remove the singularity. Next, we introduce the DB function as in [6] to treat the nonhomogeneous jump conditions of the regularized solution. Then, we discretize the discontinuous bubble and the bilinear form of Poisson-Boltzmannequation and solve the discretized linear problem by the immersed finite element method. Once Poisson-Boltzmannequation is solved, we apply the control volume method to solve Nernst-Planckequation via an upwinding concept. This process is repeated by updating the previous approximation until the total residual of the system decreases below some tolerance. We provide our numericalexperiments. We observe optimal convergence rates for the concentration variable in all examples having analytic solutions. We observe that our scheme reflects well without oscillations the effect on the distribution of electrons caused by locating the singular charge close to the interface. (C) 2021 Elsevier Inc. All rights reserved.Sun, 01 Aug 2021 00:00:00 GMThttp://hdl.handle.net/10203/2855582021-08-01T00:00:00ZObstructions for bounded shrub-depth and rank-depth
http://hdl.handle.net/10203/285298
Title: Obstructions for bounded shrub-depth and rank-depth
Authors: Kwon, O-joung; McCarty, Rose; Oum, Sang-il; Wollan, Paul
Abstract: Shrub-depth and rank-depth are dense analogues of the tree-depth of a graph. It is well known that a graph has large tree-depth if and only if it has a long path as a subgraph. We prove an analogous statement for shrub-depth and rank-depth, which was conjectured by Hlineny et al. (2016) [11]. Namely, we prove that a graph has large rank-depth if and only if it has a vertex-minor isomorphic to a long path. This implies that for every integer t, the class of graphs with no vertex-minor isomorphic to the path on t vertices has bounded shrub-depth. (C) 2021 Elsevier Inc. All rights reserved.Thu, 01 Jul 2021 00:00:00 GMThttp://hdl.handle.net/10203/2852982021-07-01T00:00:00Z