• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.276-279
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• 1996

This paper deals with the method providing an exact solution to the 3-dimensional guillotine cutting stock problem. We suggest a 3-stage sutting method using the property that cubic material has to be cut into 2-dimensional planes firstly. This method requires more stocks that the general guillotine cutting methods but can save work force. By using the 1-dimensional dynamic programming, we reduce the computational time and the memory requirement in the 3-stage guillotine cutting method.

• International Journal of Precision Engineering and Manufacturing
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• v.1 no.2
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• pp.14-23
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• 2000

A numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three dimensional mixed mode crack. The method is based on the path independence of J and M integral and mutual or two-state conservation integral , which involves two elastic fields. Some numerical example are presented to investigate the effectiveness and applicability of the method for and axisymmetric crack and a three dimensional penny shaped crack problem under mixed mode.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.23-42
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• 1997

A 6-dimensional sphere considered as a homogeneous space $G_2/SU(3)$ where $G_2$ is the group of automorphism of the octonians O. From this representation, we can define an almost comlex structure on a 6-dimensional sphere by making use of the vector cross product of the octonians. Also it is known that a homogeneous space $G_2/U(2)$ coincides with the Grassmann manifold of oriented 2-planes of a 7-dimensional Euclidean space.

• Proceedings of the KSR Conference
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• 2009.05a
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• pp.1083-1087
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• 2009

We present an 1-dimensional annular disk element with which natural vibration of a circular plate can be analyzed accurately and facilely. The natural vibration characteristics of a circular plate with free outer boundary are analyzed by using the presented I-dimensional element. Its results are compared with the results obtained by utilizing 2-dimensional 8-node quadrilateral plane element and cyclic symmetry of the circular plate. And also, by comparing with the theoretical results of previous researchers, the accuracy and facility of the presented I-dimensional element are verified.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.55-63
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• 1998

A Gauss map of m-dimensional distribution on a Riemannian manifold M is called a harmonic Gauss map if it is a harmonic map from the manifold into its Grassmann bundle $G_m$(TM) of m-dimensional tangent subspace. We calculate the tension field of the Gauss map of m-dimensional distribution and especially show that the Hopf fibrations on $S^{4n＋3}$ are the harmonic Gauss map of 3-dimensional distribution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.55-64
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• 2005

In this paper, generalized difference methods(GDM) for one-dimensional viscoelastic problems are proposed and analyzed. The new initial values are given in the generalized difference scheme, so we obtain optimal error estimates in $L^p$ and $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ as well as some superconvergence estimates in $W^{1,p}(2\;{\leq}\;p\;{\leq}\;{\infty})$ between the GDM solution and the generalized Ritz-Volterra projection of the exact solution.

• Journal of electromagnetic engineering and science
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• v.12 no.1
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• pp.13-19
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• 2012

In this paper, we investigate cooperative transmission in one-dimensional random wireless networks. In this scheme, a stationary source communicates with a stationary destination with the help of N relays, which are randomly placed in a one-dimensional network. We derive exact and approximate expressions of the average outage probability over Rayleigh fading channels. Various Monte-Carlo simulations are presented to verify the accuracy of our analyses.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.205-214
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• 2016

Any open Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we will prove that, given any open Riemann surface, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. This result along with [5] now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension ${\geq}3$.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.493-506
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• 2017

In this paper, we define the modulus of n-dimensional U-flatness as the determinant of an $(n+1){\times}(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1481-1494
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• 2013

The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras the criterium of nilpotency is established in terms of the properties of corresponding matrices. Moreover, it is proved that for nilpotent $n$-dimensional complex evolution algebras the possible maximal nilpotency index is $1+2^{n-1}$.