DSpace Community:
http://oasis.postech.ac.kr/handle/2014.oak/383
2018-07-18T23:13:21ZOn Hecke L-functions attached to half-integral weight modular forms
http://oasis.postech.ac.kr/handle/2014.oak/38935
Title: On Hecke L-functions attached to half-integral weight modular forms
Authors: CHOIE, YOUNG JU2018-12-01T00:00:00ZHolomorphic Automorphic forms and Cohomology
http://oasis.postech.ac.kr/handle/2014.oak/40925
Title: Holomorphic Automorphic forms and Cohomology
Authors: CHOIE, YOUNG JU; Bruggeman, Roelof; Diamantis, Nikolaos
Abstract: t. We investigate the correspondence between holomorphic automorphicforms on the upper half-plane with complex weight and parabolic cocycles.For integral weights at least 2 this correspondence is given by the Eichler integral.We use Knopp’s generalization of this integral to real weights, and applyit to complex weights that are not an integer at least 2. We show that for theseweights the generalized Eichler integral gives an injection into the first cohomologygroup with values in a module of holomorphic functions, and characterizethe image. We impose no condition on the growth of the automorphicforms at the cusps. Our result concerns arbitrary cofinite discrete groups withcusps, and covers exponentially growing automorphic forms, like those studiedby Borcherds, and like those in the theory of mock automorphic forms.For real weights that are not an integer at least 2 we similarly characterizethe space of cusp forms and the space of entire automorphic forms. We give arelation between the cohomology classes attached to holomorphic automorphicforms of real weight and the existence of harmonic lifts.A tool in establishing these results is the relation to cohomology groups withvalues in modules of “analytic boundary germs”, which are represented by harmonicfunctions on subsets of the upper half-plane. It turns out that for integralweights at least 2 the map from general holomorphic automorphic forms to cohomologywith values in analytic boundary germs is injective. So cohomology withthese coefficients can distinguish all holomorphic automorphic forms, unlike theclassical Eichler theory2018-04-01T00:00:00ZThe Fokker-Planck equation with absorbing boundary conditions in bounded domains
http://oasis.postech.ac.kr/handle/2014.oak/50104
Title: The Fokker-Planck equation with absorbing boundary conditions in bounded domains
Authors: HWANG, HYUNG JU; Jang,Juhi; Jung,Jaewoo
Abstract: In this paper, we study the initial-boundary value problem of the Fokker-Planck equation with absorbing boundary conditions in multidimensional bounded domains. First, we establish a well-posedness theory by constructing a solution for the regularized equation and passing to the limit by uniform L-1 and L-infinity estimates. Second, for a general multidimensional domain with a smooth boundary, we show that the solution is smooth far from the singular set and locally Holder continuous up to the singular set.2018-03-01T00:00:00ZEffect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas
http://oasis.postech.ac.kr/handle/2014.oak/41176
Title: Effect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas
Authors: YUN, GUNSU; HWANG, HYUNG JU
Abstract: We propose a phenomenological yet general model in a form of extended complex Ginzburg-Landau equation to understand edge-localized modes (ELMs), a class of quasi-periodic fluid instabilities in the boundary of toroidal magnetized high-temperature plasmas. The model reproduces key dynamical features of the ELMs (except the final explosive relaxation stage) observed in the high-confinement state plasmas on the Korea Superconducting Tokamak Advanced Research: quasi-steady states characterized by field-aligned filamentary eigenmodes, transitions between different quasi-steady eigenmodes, and rapid transition to non-modal filamentary structure prior to the relaxation. It is found that the inclusion of time-varying perpendicular sheared flow is crucial for reproducing all of the observed dynamical features.2018-02-01T00:00:00Z