DSpace Community:http://oasis.postech.ac.kr/handle/2014.oak/3832018-06-20T22:30:01Z2018-06-20T22:30:01ZOn Hecke L-functions attached to half-integral weight modular formsCHOIE, YOUNG JUhttp://oasis.postech.ac.kr/handle/2014.oak/389352018-06-11T07:20:53Z2018-12-01T00:00:00ZTitle: On Hecke L-functions attached to half-integral weight modular forms
Authors: CHOIE, YOUNG JU2018-12-01T00:00:00ZHolomorphic Automorphic forms and CohomologyCHOIE, YOUNG JUBruggeman, RoelofDiamantis, Nikolaoshttp://oasis.postech.ac.kr/handle/2014.oak/409252018-05-02T06:15:41Z2018-04-01T00:00:00ZTitle: Holomorphic Automorphic forms and Cohomology
Authors: CHOIE, YOUNG JU; Bruggeman, Roelof; Diamantis, Nikolaos
Abstract: t. We investigate the correspondence between holomorphic automorphic
forms 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 apply
it to complex weights that are not an integer at least 2. We show that for these
weights the generalized Eichler integral gives an injection into the first cohomology
group with values in a module of holomorphic functions, and characterize
the image. We impose no condition on the growth of the automorphic
forms at the cusps. Our result concerns arbitrary cofinite discrete groups with
cusps, and covers exponentially growing automorphic forms, like those studied
by Borcherds, and like those in the theory of mock automorphic forms.
For real weights that are not an integer at least 2 we similarly characterize
the space of cusp forms and the space of entire automorphic forms. We give a
relation between the cohomology classes attached to holomorphic automorphic
forms of real weight and the existence of harmonic lifts.
A tool in establishing these results is the relation to cohomology groups with
values in modules of “analytic boundary germs”, which are represented by harmonic
functions on subsets of the upper half-plane. It turns out that for integral
weights at least 2 the map from general holomorphic automorphic forms to cohomology
with values in analytic boundary germs is injective. So cohomology with
these coefficients can distinguish all holomorphic automorphic forms, unlike the
classical Eichler theory2018-04-01T00:00:00ZThe Fokker-Planck equation with absorbing boundary conditions in bounded domainsHWANG, HYUNG JUJang,JuhiJung,Jaewoohttp://oasis.postech.ac.kr/handle/2014.oak/501042018-06-07T01:01:26Z2018-03-01T00:00:00ZTitle: 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 plasmasYUN, GUNSUHWANG, HYUNG JUhttp://oasis.postech.ac.kr/handle/2014.oak/411762018-05-04T02:33:19Z2018-02-01T00:00:00ZTitle: 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