• Honam Mathematical Journal
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• 제34권3호
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• pp.451-465
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• 2012

Since there are several kinds of continuities of maps between digital spaces, the paper compares them, which can play an important role in digital topology and discrete geometry.

• Honam Mathematical Journal
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• 제37권4호
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• pp.577-593
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• 2015

Several kinds of homotopies have been substantially used to study topological properties of digital spaces. The present paper, as a survey article, studies some recent results in the field of homotopy theory associated with Khalimsky topology. In particular, Khalimsky topological properties of digital products related to the establishment of the homotopies are mainly treated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 한국소음진동공학회 2002년도 추계학술대회논문초록집
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• pp.355.1-355
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• 2002

Topology optimization is widely accepted as a conceptual design tool for the product design. Since the resulted layout of the topology optimization is a kind of digital images represented by the density distribution, the seamless process is required to transform digital images to the CAD model for the practical use. In this paper, the general process to construct a CAD model is developed to apply for topology images based on elements. (omitted)

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.523-528
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• 2002

Topology optimization is widely accepted as a conceptual design tool for the product design. Since the resulted layout of the topology optimization is a kind of digital images represented by the density distribution, the seamless process is required to transform digital images to the CAD model for the practical use. In this paper, the general process to construct a CAD model is developed to apply for topology images based on elements. The node density and the morphology technique is adopted to extract boundary contour of the shape and remove the noise of images through erosion and dilation operation. The proposed method automatically generates point data sets of the geometric model. The process is integrated with Pro/Engineer, so that the engineer in practice can directly handle with curves or surface form digital images.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제27권11호
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• pp.1925-1932
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• 2003

Topology optimization is widely accepted as a conceptual design tool for the product design. Since the resulted layout of the topology optimization is a kind of digital images represented by the density distribution, the seamless process is required to transform digital images to the CAD model for the practical use. In this paper, the general process to construct a CAD model is developed to apply for topology images based on elements. The node density and the morphology technique are adopted to extract boundary contour of the shape and remove the noise of images through erosion and dilation operation. The proposed method automatically generates point data sets of the geometric model. The process is integrated with Pro/Engineer, so that the engineer in practice can directly handle with curves or surfaces form digital images.

• Korean Journal of Computational Design and Engineering
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• 제11권4호
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• pp.265-272
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• 2006

For the design and analysis of 3D object featuring complexity and irregularity in shape, sectional digital images measured by an industrial CT scanner are employed to generate a finite element model with uniform voxels. The voxel model plays a key role in developing an integrated reverse engineering system including geometric modeling, simulation and optimization. Design examples applied to topology optimization show that the proposed approach can provide a remarkable reduction in time cost at the conceptual and detail design stages.

• Proceedings of the KIEE Conference
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• 대한전기학회 2003년도 하계학술대회 논문집 B
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• pp.843-845
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• 2003

In this paper, the design of the outer core which is one part of the linear motor is investigated by using the topology optimization and FEM. The object functions are to reduce the outer core area of the linear motor with the maximum magnetic energy in airgap. For topology optimization, the finite element model is made through the result of ANSYS, and the sensitivity calculation is done using ANSTOP(developed general software for topology optimization of electromagnetics). In ANSTOP, the optimization routine is implemented using SLP in DOT and the ANSYS is used as a function solver.

• Honam Mathematical Journal
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• 제27권1호
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• Journal of the Korean Mathematical Society
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• 제47권5호
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• pp.1031-1054
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• 2010

Let $\mathbb{Z}^n$ be the Cartesian product of the set of integers $\mathbb{Z}$ and let ($\mathbb{Z}$, T) and ($\mathbb{Z}^n$, $T^n$) be the Khalimsky line topology on $\mathbb{Z}$ and the Khalimsky product topology on $\mathbb{Z}^n$, respectively. Then for a set $X\;{\subset}\;\mathbb{Z}^n$, consider the subspace (X, $T^n_X$) induced from ($\mathbb{Z}^n$, $T^n$). Considering a k-adjacency on (X, $T^n_X$), we call it a (computer topological) space with k-adjacency and use the notation (X, k, $T^n_X$) := $X_{n,k}$. In this paper we introduce the notions of KD-($k_0$, $k_1$)-homotopy equivalence and KD-k-deformation retract and investigate a classification of (computer topological) spaces $X_{n,k}$ in terms of a KD-($k_0$, $k_1$)-homotopy equivalence.

• Journal of the Korean Mathematical Society
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• 제44권6호
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.