• 호남수학학술지
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• 제22권1호
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• pp.31-36
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• 2000

In this paper, we introduce the extremal length and examine its properties and consider the applications of extremal length to conformal mappings. We obtain the theorems in the connection with "the extremal length zero" and "the fundamental sequences".

• 대한수학회논문집
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• 제21권1호
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• pp.135-143
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• 2006

We consider some 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. And we present some geometric applications of extremal length. The method of extremal length lead to simple proofs of theorems.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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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.

• 충청수학회지
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• 제12권1호
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• pp.193-196
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• 1999

In this note, we present some geometric applications of extremal length to analytic functions. We drive an interesting formula by the method of extremal length.

• 충청수학회지
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• 제16권1호
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• pp.49-60
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• 2003

In this note, we introduce the concept of the extremal length of a curve family in the complex plane and apply the extremal length to the boundary behavior of analytic functions. We consider some geometric applications of extremal length and establish applications connected with the logarithmic capacity.

• 충청수학회지
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• 제20권2호
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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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• 제15권1_2호
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• pp.495-502
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• 2004

We consider the applications of extremal length to the boundary behavior of analytic functions and derive a theorem in connection with the capacity. This theorem applies the extremal length to the analytic functions defined on the domain with a number of holes. So it shows us the usefulness of the method of extremal length.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.369-380
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• 2010

We give a criterion for vertex extremal length parabolicity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its immediate finer graphs are circle packing parabolic.

• 대한수학회보
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• 제47권2호
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• pp.423-432
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• 2010

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded $\cal{A}$-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

• 대한수학회보
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• 제54권1호
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• pp.29-42
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• 2017

In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings $R_{k,m}$. Self-dual binary codes are obtained as the Gray images of self-dual QDC codes over $R_{k,m}$. Extremal binary self-dual codes of length 64 are obtained as Gray images of ${\lambda}-four$ circulant codes over $R_{2,1}$ and $R_{2,2}$. Extremal binary self-dual codes of lengths 66 and 68 are constructed by applying extension theorems to the ${\mathbb{F}}_2$ and $R_{2,1}$ images of these codes. More precisely, 10 new codes of length 66 and 39 new codes of length 68 are discovered. The codes with these weight enumerators are constructed for the first time in literature. The results are tabulated.