• International Journal of CAD/CAM
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• 제5권1호
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• pp.59-68
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• 2005

Euclidean Voronoi diagram of spheres in 3-dimensional space has not been explored as much as it deserves even though it has significant potential impacts on diverse applications in both science and engineering. In addition, studies on the data structure for its topology have not been reported yet. Presented in this, paper is the topological representation for Euclidean Voronoi diagram of spheres which is a typical non-manifold model. The proposed representation is a variation of radial edge data structure capable of dealing with the topological characteristics of Euclidean Voronoi diagram of spheres distinguished from those of a general non-manifold model and Euclidean Voronoi diagram of points. Various topological queries for the spatial reasoning on the representation are also presented as a sequence of adjacency relationships among topological entities. The time and storage complexities of the proposed representation are analyzed.

• 한국생산제조학회지
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• 제6권1호
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• pp.51-58
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• 1997

The verification of the STL file is essential to build the confident parts using a RP machine, because the STL file obtained from the CAD software has many errors-the orientation of triangle does not coincide with adjacent triangles or some triangles are omitted, overlpped and so forth. Especially, the STL file translated from the surface model has more errors than those translated from the solid model. In this study, all possible errors were classified with the most general from and the causes of errors were analyzed to verify and correct errors. Using the triangle based non-manifold geometric modeling, these errors were corrected. Especially, this study took the notice of the problem about the intersected triangles and non-manifold properties overlooked in the previous studies. But this study has a penalty on computing time of $O(n^2)$.

• 대한수학회논문집
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• 제12권1호
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• pp.193-201
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• 1997

The paper presens results on the perturbation problem of invariant manifolds of differential equations. It is well-known that if there is a pseudohyperbollic structure on an invariant manifold then one is strongly indestructible. The set of strongly inderstructible invariant manifolds is wider than the set of persistent (normally hyperbolic) manifolds. The following theorem is main result of the paper: if the condition of transversality holds on an invariant manifold, except, possibly, for the non-degenerate strong sources and non-degenerate strong sinks, then there is the pseudohyperbolic structure on the invariant manifold. From this it follows the conditions for the indestructibility of locally non-unique invariant manifolds. An example is considered.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2002년도 춘계학술대회 논문집
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• pp.833-835
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• 2002

In this paper, we propose multi-resolutional representation of B-rep solid models using the selective Boolean operations on non-manifold geometric models. Since the union and subtraction operations of the selective Boolean operations are commutative, the integrity of the model is guaranteed for reordering design features. A multi-resolution representation is established using a non-manifold merged set model and a feature modeling tree reordered according to some criterion of level of detail (LOD). Then, a solid model for a specified LOD can be extracted from this multi-resolution model using the selective Boolean operations.

• 대한수학회보
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• 제50권3호
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• pp.705-717
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• 2013

In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold $\tilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $\tilde{M}$ is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.

• Journal of Mechanical Science and Technology
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• 제19권2호
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• pp.558-566
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• 2005

We propose a feature-based multi-resolution representation of B-rep solid models using history-based Boolean operations based on the merge-and-select algorithm. Because union and subtraction are commutative in the history-based Boolean operations, the integrity of the models at various levels of detail (LOD) is guaranteed for the reordered features regardless of whether the features are subtractive or additive. The multi-resolution solid representation proposed in this paper includes a non-manifold topological merged-set model of all feature primitives as well as a feature-modeling tree reordered consistently with a given LOD criterion. As a result, a B-rep solid model for a given LOD can be provided quickly, because the boundary of the model is evaluated without any geometric calculation and extracted from the merged set by selecting the entities contributing to the LOD model shape.

• 한국정밀공학회지
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• 제12권11호
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• pp.74-81
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• 1995

Several non-manifold data structures have been compared, which are radial-edge data structure, partial-face data structure, vertex-based data structure, and Yamaguchi's data structrue. All the entities in the data structures are classified into common entities and special entities. The entities are also classified as model entities, primitive entities bounding entities, and coupling entities. The four data structures for nonmanifold solid modelers are compared in terms of accessing efficiency, storage requirements, and inclusion of circulation. The results of comparison will serve as the basis to develope a nonmanifold modeler.

• 대한수학회논문집
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• 제35권2호
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• pp.591-602
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• 2020

There is a well-known class of compact, complex, non-Kählerian manifolds constructed by Bosio, called the LVMB manifolds, which properly includes the Hopf manifold, the Calabi-Eckmann manifold, and the LVM manifolds. As in the case of LVM manifolds, these LVMB manifolds can admit a regular holomorphic foliation 𝓕. Moreover, later Meersseman showed that if an LVMB manifold is actually an LVM manifold, then the regular holomorphic foliation 𝓕 is actually transverse Kähler. The aim of this paper is to deal with a converse question and to give a simple and new proof of a well-known result of Cupit-Foutou and Zaffran. That is, we show that, when the holomorphic foliation 𝓕 on an LVMB manifold N is transverse Kähler with respect to a basic and transverse Kähler form and the leaf space N/𝓕 is an orbifold, N/𝓕 is projective, and thus N is actually an LVM manifold.

• 대한수학회논문집
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• 제39권2호
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• pp.479-492
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• 2024

In this paper, we study Riemannian submersions whose total manifold admits h-almost Ricci-Yamabe soliton. We characterize the fibers of the submersion and see under what conditions the fibers form h-almost Ricci-Yamabe soliton. Moreover, we find the necessary condition for the base manifold to be an h-almost Ricci-Yamabe soliton and Einstein manifold. Later, we compute scalar curvature of the total manifold and using this we find the necessary condition for h-almost Yamabe solition to be shrinking, expanding and steady. At the end, we give a non-trivial example.

• 대한수학회논문집
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• 제11권4호
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• pp.1077-1085
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• 1996

This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.