• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1051-1063
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• 2018

The real moment-angle complex (or, more generally, real polyhedral product) and its real toric space have recently attracted much attention in toric topology. The aim of this paper is to give two interesting remarks regarding real polyhedral products and real toric spaces. That is, we first show that Moore's conjecture holds to be true for certain real polyhedral products. In general, real polyhedral products show some drastic difference between the rational and torsion homotopy groups. Our result shows that at least in terms of the homotopy exponent at a prime this is not the case for real polyhedral products associated to a simplicial complex whose minimal missing faces are all k-simplices with $k{\geq}2$. Moreover, we also show a structural theorem for a finite group G acting simplicially on the real toric space. In other words, we show that G always contains an element of order 2, and so the order of G should be even.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1621-1626
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• 2003

This study deals with the heat transfer analysis on phase change optical disc with land/groove recording by means of numerical method. Finite difference time domain(FDTD) method was used to obtain the amount of absorption of light propagating inside disc and finite difference element(FEM) method was used to calculate the temperature distribution. The calculated results present the detailed information of recording characteristics on the phase change optical disc. The temperature profiles are quite different between the land track and the groove track. The recorded mark shape on land track is smaller and more elliptic than that on groove track. It is shown that the thermal problem to the neighboring track takes place due to secondary peaks. It is found that the different write strategy should be applied to land and groove recording, respectively.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.101-113
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• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.461-486
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• 2003

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2843-2853
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• 1996

The multi-point procedure is developed to predict the shape change of a semi-elliptical surface crack during stable fatigue crack growth. 3-D stress intensity factors along a crack front are calculated using the simplified 3-D J-intergral. Crack growth rate coefficient in the Paris law is assumed to be constant along the crack growth. Crack growth rate is set to be the distance between the two parallel tangent lines on the two semi-elliptic crack fronts before and after crack growth.

• The Journal of the Korea Contents Association
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• v.15 no.6
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• pp.539-546
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• 2015

In this study, we develop numerical model using the elliptic mild-slope equation for waves propagating around axis-symmetric topographies where the water depth varies arbitrarily having zero at the coastline. The entire region is divided into three regions. In the both of inner and outer regions, an existing analytical solutions are used. In the middle region, the finite element technique is applied to the governing equation. To get the solution, the methods of separation of variables, Frobenius series are used. Developed solution is validated by comparing with previously developed analytical solution. We also investigate various cases with different bottom topographies.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.469-484
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• 1996

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1140-1149
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• 2004

The absorption characteristics of water vapor into a LiBr-H$_2$O solution flowing down on finned inclined surfaces are numerically investigated in order to study the absorbing performances of different surface shapes of finned tubes as an absorber element. A three-dimensional numerical model is developed. The momentum, energy, and diffusion equations are solved simultaneously using a finite difference method. In order to obtain the temperature and concentration distributions, the Runge-Kutta and the Successive over relaxation methods are used. The flat, circular, elliptic, and parabolic shapes of the tube surfaces are considered in order to find the optimal surface shapes for absorption. In addition, the effects of the fin intervals and Reynolds numbers are studied. The results show that the absorption mainly happens near the fin tip due to the temperature and concentration gradient, and the absorbing performance of the parabolic surface is better than those of the other surfaces.

• Steel and Composite Structures
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• v.30 no.4
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• pp.305-313
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• 2019

Creating different cutout shapes in order to make doors and windows, reduce the structural weight or implement various mechanisms increases the likelihood of buckling in thin-walled structures. In this study, the effect of cutout shape and geometric imperfection (GI) is simultaneously investigated on the critical buckling load and knock-down factor (KDF) of composite cylindrical shells. The GI is modeled using single perturbation load approach (SPLA). First, in order to assess the finite element model, the critical buckling load of a composite shell without cutout obtained by SPLA is compared with the experimental results available in the literature. Then, the effect of different shapes of cutout such as circular, elliptic and square, and perturbation load imperfection (PLI) is investigated on the buckling behavior of cylindrical shells. Results show that the critical buckling load of a shell without cutout decreases by increasing the PLI, whereas increasing the PLI does not have a great impact on the critical buckling load in the presence of cutout imperfection. Increasing the cutout area reduces the effect of the PLI, which results in an increase in the KDF.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.4
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• pp.275-282
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• 2017

In this paper, using a pattern transformation triggered by deformation, we propose a porous structure that exhibits the characteristic of negative Poisson's ratio in both tension and compression. Due to the lack of torque for rotational motion of ligaments, the existing porous structure of circular holes shows positive Poisson's ratio under tension loading. Also, the porous structure of elliptic holes has a drawback of low durability due to stress concentration. Thus, we design curved ligaments to increase the rotational torque under tension and to alleviate the stress concentration such that strain energy is uniformly distributed in the whole structure. The developed structure possesses better stiffness and durability than the existing structures. It also exhibits the negative Poisson ratio in both compression and tension of 10% nominal strain. Through nonlinear finite element analysis, the performance of developed structure is compared with the existing structure of elliptic holes. The developed structure turns out to be significantly improved in terms of stiffness and durability.