• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.993-1002
• /
• 2017

Let ${\Omega}$ be a bounded, uniformly totally pseudoconvex domain in ${\mathbb{C}}^2$ with the smooth boundary b${\Omega}$. Assuming that ${\Omega}$ satisfies the negative ${\bar{\partial}}$ property. Let M be a positive, finite area divisor of ${\Omega}$. In this paper, we will prove that: if ${\Omega}$ admits a maximal type F and the ${\check{C}}eck$ cohomology class of the second order vanishes in ${\Omega}$, there is a bounded holomorphic function in ${\Omega}$ such that its zero set is M. The proof is based on the method given by Shaw [27].

• Kyungpook Mathematical Journal
• /
• v.63 no.3
• /
• pp.413-424
• /
• 2023

The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ², for 1 < p < ∞, the Bergman projection 𝓟 is bounded from L^p(Ω, dV ) to the Bergman space A^p(Ω); from L^∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L¹(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

• Structural Engineering and Mechanics
• /
• v.67 no.4
• /
• pp.317-326
• /
• 2018

The iterative decomposition coupling formulation of the precise integration finite element method (FEM) and the time domain boundary element method (TD-BEM) is presented for elstodynamic problems. In the formulation, the FEM node and the BEM node are not required to be coincident on the common interface between FEM and BEM sub-domains, therefore, the FEM and BEM are independently discretized. The force and displacement converting matrices are used to transfer data between FEM and BEM nodes on the common interface between the FEM and BEM sub-domains, to renew the nodal variables in the process of the iterations for the un-coincident FEM node and BEM node. The iterative coupling formulation for elastodynamics in current paper is of high modeling accuracy, due to the semi-analytical solution incorporated in the precise integration finite element method. The decomposition coupling formulation for elastodynamics is verified by examples of a cantilever bar under a Heaviside-type force and a harmonic load.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.541-548
• /
• 2015

Let R be a commutative ring. An R-module M is called a w-Noetherian module if every submodule of M is of w-finite type. R is called a w-Noetherian ring if R as an R-module is a w-Noetherian module. In this paper, we present an exact version of the Eakin-Nagata Theorem on w-Noetherian rings. To do this, we prove the Formanek Theorem for w-Noetherian rings. Further, we point out by an example that the condition (${\dag}$) in the Chung-Ha-Kim version of the Eakin-Nagata Theorem on SM domains is essential.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1241-1249
• /
• 2020

Let Ω be a domain in ℂⁿ. Suppose that ∂Ω is smooth pseudoconvex of D'Angelo finite type near a boundary point ξ₀ ∈ ∂Ω and the Levi form has corank at most 1 at ξ₀. Our goal is to show that if the squeezing function s_Ω(𝜂_j) tends to 1 or the Fridman invariant h_Ω(𝜂_j) tends to 0 for some sequence {𝜂_j} ⊂ Ω converging to ξ₀, then this point must be strongly pseudoconvex.

• Korean Journal of Mathematics
• /
• v.23 no.4
• /
• pp.631-636
• /
• 2015

Let D be an integral domain and w be the so-called w-operation on D. In this note, we introduce the notion of *(w)-domains: D is a *(w)-domain if $(({\cap}(x_i))({\cap}(y_j)))_w={\cap}(x_iy_j)$ for all nonzero elements $x_1,{\ldots},x_m$; $y_1,{\ldots},y_n$ of D. We then show that D is a $Pr{\ddot{u}}fer$ v-multiplication domain if and only if D is a *(w)-domain and $A^{-1}$ is of finite type for all nonzero finitely generated fractional ideals A of D.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.1
• /
• pp.127-134
• /
• 2000

Let $\Omega$ be a bounded pseudoconvex domain in$C^{n}$ with smooth defining function r and let$z_0\; {\in}\; b{\Omega}$ be a point of finite type. We also assume that $\Omega$ is convex in a neighborhood of $z_0$. Then we prove that all the holomorphic sectional curvatures of the Bergman metric of $\Omega$ are bounded below by a negative constant near $z_0$.

• Structural Engineering and Mechanics
• /
• v.14 no.1
• /
• pp.99-118
• /
• 2002

The scaled-boundary finite element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one coordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) coordinate direction. These coordinate directions are defined by the geometry of the domain and a scaling centre. This paper presents a general development of the scaled boundary finite-element method for two-dimensional problems where two boundaries of the solution domain are similar. Unlike three-dimensional and axisymmetric problems of the same type, the use of logarithmic solutions of the weakened differential equations is found to be necessary. The accuracy and efficiency of the procedure is demonstrated through two examples. The first of these examples uses the standard finite element method to provide a comparable solution, while the second combines both solution techniques in a single analysis. One significant application of the new technique is the generation of transition super-elements requiring few degrees of freedom that can connect two regions of vastly different levels of discretisation.

• Interaction and multiscale mechanics
• /
• v.6 no.2
• /
• pp.173-195
• /
• 2013

Meshfree methods are known to have the capability to overcome the strict regularization requirements and numerical instabilities that encumber the finite element method (FEM) in large deformation problems. They are also more naturally suited for problems involving material perforation and fragmentation. To take advantage of the high efficiency of FEM and high accuracy of meshfree methods, a coupled finite element (FE) and reproducing kernel (RK, one of the meshfree approximations) formulation is described in this paper. The coupling of FE and RK approximation is implemented in an evolutionary fashion, where the extent and location of the evolution is dependent on a triggering criteria provided by the material constitutive laws. To enhance computational efficiency, Gauss quadrature is applied to integrate both FE and RK domains so that no state variable transfer is required when mesh conversion is performed. To control the hourglassing that might occur with 1-point integrated hexahedral grids, viscous type hourglass control is implemented. Meanwhile, the FEM version of the K&C concrete (KCC) model was modified to make it applicable in both FE and RK formulations. Results using this code and the KCC model are shown for the modeling of concrete responses under quasi-static, blast and impact loadings. These analyses demonstrate that fragmentation phenomena of the sort commonly observed under blast and impact loadings of concrete structures was able to be realistically captured by the coupled formulation.

• Proceedings of the Korean Vacuum Society Conference
• /
• 2013.08a
• /
• pp.99-99
• /
• 2013

In this talk, I will present two research works in progress, which are: i) mapping of piezoelectric polarization and associated charge density distribution in the heteroepitaxial InGaN/GaN multi-quantum well (MQW) structure of a light emitting diode (LED) by using inline electron holography and ii) in-situ observation of the polarization switching process of an ferroelectric Pb(Zr1-x,Tix)O3 (PZT) thin film capacitor under an applied electric field in transmission electron microscope (TEM). In the first part, I will show that strain as well as total charge density distributions can be mapped quantitatively across all the functional layers constituting a LED, including n-type GaN, InGaN/GaN MQWs, and p-type GaN with sub-nm spatial resolution (~0.8 nm) by using inline electron holography. The experimentally obtained strain maps were verified by comparison with finite element method simulations and confirmed that not only InGaN QWs (2.5 nm in thickness) but also GaN QBs (10 nm in thickness) in the MQW structure are strained complementary to accommodate the lattice misfit strain. Because of this complementary strain of GaN QBs, the strain gradient and also (piezoelectric) polarization gradient across the MQW changes more steeply than expected, resulting in more polarization charge density at the MQW interfaces than the typically expected value from the spontaneous polarization mismatch alone. By quantitative and comparative analysis of the total charge density map with the polarization charge map, we can clarify what extent of the polarization charges are compensated by the electrons supplied from the n-doped GaN QBs. Comparison with the simulated energy band diagrams with various screening parameters show that only 60% of the net polarization charges are compensated by the electrons from the GaN QBs, which results in the internal field of ~2.0 MV cm-1 across each pair of GaN/InGaN of the MQW structure. In the second part of my talk, I will present in-situ observations of the polarization switching process of a planar Ni/PZT/SrRuO3 capacitor using TEM. We observed the preferential, but asymmetric, nucleation and forward growth of switched c-domains at the PZT/electrode interfaces arising from the built-in electric field beneath each interface. The subsequent sideways growth was inhibited by the depolarization field due to the imperfect charge compensation at the counter electrode and preexisting a-domain walls, leading to asymmetric switching. It was found that the preexisting a-domains split into fine a- and c-domains constituting a $90^{\circ}$ stripe domain pattern during the $180^{\circ}$ polarization switching process, revealing that these domains also actively participated in the out-of-plane polarization switching. The real-time observations uncovered the origin of the switching asymmetry and further clarified the importance of charged domain walls and the interfaces with electrodes in the ferroelectric switching processes.