• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.487-501
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• 2003

The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in \mathbb{C}^n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in \mathbb{C}^n does not exceed n.

• Communications of the Korean Mathematical Society
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• v.1 no.1
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• pp.43-54
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• 1986

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.299-305
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• 2007

We prove that the bounded attracting basin of the origin for a complex homogeneous polynomial of degree larger than two is Carath$\'{e}$odory finitely compact.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.17-30
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• 2012

Let D be an arbitrary domain in $\mathbb{C}^n$, n > 1, and $M{\subset}{\partial}D$ be an open piece of the boundary. Suppose that M is connected and ${\partial}D$ is smooth real-analytic of finite type (in the sense of D'Angelo) in a neighborhood of $\bar{M}$. Let f : $D{\rightarrow}\mathbb{C}^n$ be a holomorphic correspondence such that the cluster set $cl_f$(M) is contained in a smooth closed real-algebraic hypersurface M' in $\mathbb{C}^n$ of finite type. It is shown that if f extends continuously to some open peace of M, then f extends as a holomorphic correspondence across M. As an application, we prove that any proper holomorphic correspondence from a bounded domain D in $\mathbb{C}^n$ with smooth real-analytic boundary onto a bounded domain D' in $\mathbb{C}^n$ with smooth real-algebraic boundary extends as a holomorphic correspondence to a neighborhood of $\bar{D}$.

• Journal of the Korean Graphic Arts Communication Society
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• v.28 no.2
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• pp.45-56
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• 2010

The computer simulation is presented of gravure ink transferring behavior and penetration to the paper when an gravure roller is used to transfer a printing ink onto a substrate. The three dimensional unsteady ink motion is simulated by Polyflow package software and experimented by IGT gravure printing test machine. The simulation is performed where the flow domain is bounded above by a stress free surface and bounded below by a moving substrate. Specific predictions are made for particular pattern of cells and substrates. Cell size and ink rheological properties are found to be the principal determination of transferring behavior. Simulation is currently restricted to the flow domain beneath the receding meniscus. Both Newtonian and shear thinning inks are considered.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.245-251
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• 2019

Assume that ${\Omega}$ is a bounded domain in ${\mathbb{R}}^n$ with $n{\geq}2$. We study positive solutions to the problem, ${\Delta}u=u^p$ in ${\Omega}$, $u(x){\rightarrow}{\infty}$ as $x{\rightarrow}{\partial}{\Omega}$, where p > 1. Such solutions are called boundary blow-up solutions of ${\Delta}u=u^p$. We show that a boundary blow-up solution exists in any bounded domain if 1 < p < ${\frac{n}{n-2}}$. In particular, when n = 2, there exists a boundary blow-up solution to ${\Delta}u=u^p$ for all $p{\in}(1,{\infty})$. We also prove the uniqueness under the additional assumption that the domain satisfies the condition ${\partial}{\Omega}={\partial}{\bar{\Omega}}$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.419-424
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• 2006

In this paper we extend the study of ascend and descend of factorization properties (for atomic domains, domains satisfying ACCP, bounded factorization domains, half-factorial domains, pre-Schreier and semirigid domains) to the finite factorization domains and idf-domains for domain extension $A\;{\subseteq}\;B$.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.651-662
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• 2014

The main goal of this study is to extend the domain of influence result to cover the micropolar thermoelastic diffusion. So, we prove that for a finite time t>0 the displacement field $u_i$, the microrotation vector ${\varphi}_i$, the temperature ${\theta}$ and the chemical potential P generate no disturbance outside a bounded domain $B_t$.