• 한국CDE학회논문집
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• 제2권3호
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• pp.150-160
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• 1997

Existing non-manifold data structures which use the ordered topological representation method, are designed based on a "Model" which is the highest topological entity. Their non-manifold information is always included in edges and vertices even if they are in the manifold situation. Thus they require large storage spaces than manifold data structures. The proposed data structure reduces its storage space by removing unnecessary information stored in edges and vertices. Topological information is classified into manifold and non-manifold information. The main non-manifold information is radial cycles and disk cycles. The proposed data structure always stores manifold information. For the non-manifold situation, the edge stores radial cycles, and the vertex stores disk cycles. The storage space can be reduced in the later stage of CAD design when the ratio of non-manifold to manifold entities is small.

• 한국CDE학회논문집
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• 제5권4호
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.951-964
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• 2016

The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.

• 대한수학회지
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• 제44권4호
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• pp.757-766
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• 2007

In this note we construct an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold which is constructed by Thurston and show that the quotient of the Thurston's 4-manifold is not symplectic. Also we construct a non-$K\ddot{a}hler$, symplectic 4-manifold using the Gomph's symplectic sum method and an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold.

• 충청수학회지
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• 제22권4호
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• pp.653-665
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• 2009

We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.

• 충청수학회지
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• 제24권1호
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• pp.91-104
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• 2011

We define a quarter-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection. We also obtain the Gauss, Codazzi and Weingarten equations and the curvature tensor for the submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter-symmetric non-metric connection.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2004년도 추계학술대회 논문집
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• pp.382-387
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• 2004

As the increasing needs in the industrial filed, many studies for the 3D CAD system are carried out. There are two types of 3D CAD system. One is manifold modeler, the other is non-manifold modeler. In the manifold modeler only 3D objects can be modeled. In the non-manifold modeler 3D, 2D, 1D, and 0D objects can be modeled in a unified data structure. Recently there are many studies on the non-manifold modeler. Most of them are focused on finding unknown topological entities and representing all kinds of topological entities found. In this paper, efficient data structure is selected. The boundary information on a face and an edge is included in this data structure. The boundary information on a vertex is excluded considering the frequency of usage. Because the disk cycle information is not required in most case of modeling. It is compact. It stores essential non-manifold information such as loop cycle and radial cycle. A suitable Euler-Poincare equation is studied and selected. Using the efficient data structure and the selected Euler-Poincare equation, 18 basic Euler operators are implemented. Several 3D models are created using the implemented modeler. A non-manifold modeling can be carried out using the implemented 3D CAD system. The results of this paper could be used in the further studies such as an implementation of Boolean operators, and a translation of 2D CAD drawings to 3D models.

• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.507-520
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• 2009

The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.

• 한국CDE학회논문집
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• 제2권4호
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• pp.222-236
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• 1997

Conventional solid or surface modeling systems cannot represent both the complete solid model and the abstract model in a unified framework. Recently, non-manifold modeling systems are proposed to solve this problem. This paper describes FlexDesigner, an open kernel system for modeling non-manifold models. It summarizes the data structure for non-manifold models, system design methodology, system modularization, and the typical characteristics of each module in the system. A data structure based on partial-topological elements is adopted to represent the relationship among topological elements. It is efficient in the usage of memory and has topological completeness compared with other published data structures. It can handle many non-manifold situations such as isolate vertices, dangling edges, dangling faces, a mixed dimensional model, and a cellular model. FlexDesigner is modularized hierarchically and designed by the object-oriented methodology for reusability. FlexDesigner is developed using the C++ and OpenGL on both SGI workstation and IBM PC.

• 한국CDE학회논문집
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• 제3권1호
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• pp.1-14
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• 1998

This paper introduces non-manifold offsetting operations, which add or remove a uniform thickness from a given non-manifold model. Since these operations can be applied to not only solids but also wireframe or sheet objects, they are potentially useful for pipeline modeling, sheet metal and plastic part modeling, tolerance analysis, clearance checking, constant-radius rounding and filleting of solids, converting of abstracted models to solids, HC too1 path generation and so on. This paper describes mathematical properties and algorithms for non-manifold offsetting. In this algorithm, a sufficient set of tentative faces are generated first by offsetting all or a subset of the vertices, edges and faces of the non-manifold model. And then they are merged into a model using the Boolean operations. Finally topological entities which are within offset distance are removed. The partially modified offsetting algorithms for wireframes or sheets are also discussed in order to provide more practical offset models.