DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical Sciences2017-04-18T16:35:04ZInterlacing of zeros of certain weakly holomorphic modular forms for Gamma(+)(0)(2)
http://hdl.handle.net/10203/220844
Title: Interlacing of zeros of certain weakly holomorphic modular forms for Gamma(+)(0)(2)
Authors: Choi, SoYoung; Im, Bo-Hae
Abstract: We prove that zeros of each basis element of the space of weakly holomorphic modular forms of weight k for the Fricke group Gamma(+)(0)(2) of level 2 interlace, extending the result for SL2(Z) of Jenkins and Pratt [4].
(c) 2016 Elsevier Inc. All rights reserved.2017-05-01T00:00:00ZCLASSIFICATION OF REAL BOTT MANIFOLDS AND ACYCLIC DIGRAPHS
http://hdl.handle.net/10203/220432
Title: CLASSIFICATION OF REAL BOTT MANIFOLDS AND ACYCLIC DIGRAPHS
Authors: Choi, Suyoung; Masuda, Mikiya; Oum, Sang-il
Abstract: We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism between the real Bott manifolds.
Our characterization can also be described in terms of graph operations on directed acyclic graphs. Using this combinatorial interpretation, we prove that the decomposition of a real Bott manifold into a product of indecomposable real Bott manifolds is unique up to permutations of the indecomposable factors. Finally, we produce some numerical invariants of real Bott manifolds from the viewpoint of graph theory and discuss their topological meaning. As a byproduct, we prove that the toral rank conjecture holds for real Bott manifolds.2017-04-01T00:00:00ZAn Immersed Finite Element Method for the Elasticity Problems with Displacement Jump
http://hdl.handle.net/10203/222678
Title: An Immersed Finite Element Method for the Elasticity Problems with Displacement Jump
Authors: Kyeong, Daehyeon; Kwak, Do Young
Abstract: In this paper, we propose a finite element method for the elasticity problems which have displacement discontinuity along the material interface using uniform grids. We modify the immersed finite element method introduced recently for the computation of interface problems having homogeneous jumps [20, 22]. Since the interface is allowed to cut through the element, we modify the standard Crouzeix-Raviart basis functions so that along the interface, the normal stress is continuous and the jump of the displacement vector is proportional to the normal stress. We construct the broken piecewise linear basis functions which are uniquely determined by these conditions. The unknowns are only associated with the edges of element, except the intersection points. Thus our scheme has fewer degrees of freedom than most of the XFEM type of methods in the existing literature [1,8,13]. Finally, we present numerical results which show optimal orders of convergence rates.2017-04-01T00:00:00ZCHOW GROUPS OF PRODUCTS OF SEVERI-BRAUER VARIETIES AND INVARIANTS OF DEGREE 3
http://hdl.handle.net/10203/220445
Title: CHOW GROUPS OF PRODUCTS OF SEVERI-BRAUER VARIETIES AND INVARIANTS OF DEGREE 3
Authors: Baek, Sanghoon
Abstract: We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension 2 Chow groups of a product of Severi-Brauer varieties. In particular, for any n >= 2 we completely determine the degree 3 invariants of a split semisimple group, the quotient of (SL2)(n) by its maximal central sub-group, as well as of the corresponding split reductive group. We also provide an example illustrating that a modification of our method can be applied to find the semi-decomposable invariants of a split semisimple group of type A.2017-03-01T00:00:00Z