• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.607-629
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• 2022

In this paper, we give the necessary and sufficient condition for the conformal mapping ϕ : (ℝⁿ, g₀) → (Nⁿ, h) (n ≥ 3) to be triharmonic where we prove that the gradient of its dilation is a solution of a fourth-order elliptic partial differential equation. We construct some examples of triharmonic maps which are not biharmonic and we calculate the trace of the stress-energy tensor associated with the triharmonic maps.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.11
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• pp.1248-1253
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• 2008

The MCS(Micro-Coplanar Strip) line with ground has been analyzed. The conformal mapping method is used to calculate the quasi-static effective dielectric constant and characteristic impedance of this MCS line. The computed results of the present work are found to be in good agreement when compared with the results obtained using commercial S/W, IE3D. And in this paper, the stepped-impedance low pass filter is designed and fabricated with MCS lines for improving the frequency responses. The LPF proposed structure has been also designed and implemented to have the sharp attenuation characteristics in stop band. The agreement between simulation and measurement results verify the implemented LPF.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.821-824
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• 2009

Conformal mapping is useful to solve problems in physics, engineering and so on. This paper is to discuss the numerical conformal mapping from the unit disk onto Jordan region, which can be solved by Theodorsen equation. Wegmann's method has been known as the most efficient one for the Theodorsen equation. However, we found divergence through numerical experiments by the iterative method of Wegmann. The divergence occurs especially when some degree of difficulty is high. We analyze the cause of divergence and propose an improved method by applying a low frequency pass filter to Wegmann's method. By this proposed method we can get a stable convergence for all the problems which was unstable with the Wegmann's method.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1998.10a
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• pp.835-838
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• 1998

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.39-44
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• 2000

In [2], D. Gaier has given an estimate of conformal mappings near the boundary. In this paper, we generalize for the K-quasiconformal mapping the corresponding result.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.988-1000
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• 1999

An experimental study is presented for the effect of number of terms of a pewee series type stress function on stress analysis around a hole in tensile loaded plate. The hybrid method coupling photoelastsic data inputs and complex variable formulations involving conformal mappings and analytical continuity is used to calculate tangential stress on the boundary of the hole in uniaxially loaded, finite width tensile plate. In order to measure isochromatic data accurately, actual photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. For qualitative comparison, actual fringes are compared with calculated ones. For quantitative comparison, percentage errors and standard deviations with respect to percentage errors are caculated for all measured points by changing the number of terms of stress function. The experimental results indicate that stress concentration factors analyzed by the hybrid method are accurate within three percent compared with ones obtained by theoretical and finite element analysis.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.147-156
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• 2007

We introduce the extremal length and examine its properties. And we consider the geometric applications of extremal length to the boundary behavior of analytic functions, conformal mappings. We derive the theorem in connection with the capacity. This theorem applies the extremal length to the analytic function defined on the domain with a number of holes. And we obtain the theorems in connection with the pure geometric problems.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.603-611
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• 2005

We present some geometric applications of extremal length. The method of extremal length leads a simple proofs of theorems. And we consider the applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.281-289
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• 2006

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the cluster sets, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.33-40
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• 2004

Let $E,F{\subset}(R^*)^n$ be non-empty sets and let ${\Gamma}$ be this family of all closed curves which join E to F in $(R^*)^n$. In this paper, we shall study the problems of finding properties for the conductance $C({\Gamma})$. And we obtain the inequalities in connection with capacity of condensers.