• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1025-1036
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• 2010

A new class of generalized open sets in a topological space, called e-open sets, is introduced and some properties are obtained by Ekici [6]. This class is contained in the class of $\delta$-semi-preopen (or $\delta-\beta$-open) sets and weaker than both $\delta$-semiopen sets and $\delta$-preopen sets. In order to investigate some different properties we introduce two strong form of e-open sets called e-regular sets and e-$\theta$-open sets. By means of e-$\theta$-open sets we also introduce a new class of functions called strongly $\theta$-e-continuous functions which is a generalization of $\theta$-precontinuous functions. Some characterizations concerning strongly $\theta$-e-continuous functions are obtained.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.817-836
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• 2014

We develop a topological model of site-specific recombination that applies to substrates which are the connected sum of two torus links of the form T(2, n)#T(2, m). Then we use our model to prove that all knots and links that can be produced by site-specific recombination on such substrates are contained in one of two families, which we illustrate.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.429-436
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• 2003

A new linkage framework between elastic shell element with finite rotation and computar-aided geometric design (CAGD) (or surface is developed in the present study. The framework of shell finite element is based on the generalized curved two-parametric coordinate system. To represent free-form surface, cubic B-spline tensor-product functions are used. Thus the present finite element can be directly linked into the geometric modeling produced by surface generation tool in CAD software. The efficiency and accuracy of the Previously developed linear elements hold for the nonlinear element with finite rotations. To handle the finite rotation behavior of shells, exponential mapping in the SO(3) group is employed to allow the large incremental step size. The integrated frameworks of shell geometric design and nonlinear computational analysis can serve as an efficient tool in shape and topological design of surfaces with large deformations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.505-511
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• 2002

In the present study, we visualize the linkage framework between geometric modeling and shell finite element based on B-spline representation. For the development of a consistent shell element, geometrically exact shell elements based on general curvilinear coordinates is provided. The NUBS(Non Uniform B-Spline) is used to generate the general free form shell surfaces. Employment of NUBS makes shell finite element handle the arbitrary geometry of the smooth shell surfaces. The proposed shell finite element .model linked with NUBS surface representation provides efficiency for the integrated design and analysis of shell surface structures. The linkage framework can potentially provide efficient integrated approach to the shape topological design optimizations for shell structures.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2005.10a
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• pp.171-175
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• 2005

The Principle of space composition in modern architecture is thought about functionalism that based on function and program but the present age attempt that escapes form of former space composition. The present age brings fast development than former ages, so we need the space which has correct flexibility on New Age for escaping in existing structural formality. Specially, the space that boundary of existing plate, column and wall is crumbled as becoming possible technological support with social backgrounds. What this study saying is the analysis about the relation between the concept of topology and the consecutive space composition. Therefore, there is the purpose understanding a characteristic of continuity of the plate through the topological concept and understanding the roll in interior space.

• Journal of Korea Multimedia Society
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• v.22 no.1
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• pp.18-26
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• 2019

In this paper we propose how to detect circular objects in the gray scale image and segment them using the discrete Morse theory, which makes it possible to analyze the topology of a digital image, when it is transformed into the data structure of some combinatorial complex. It is possible to get meaningful information about how many connected components and topologically circular shapes are in the image by computing the persistent homology of the filtration using the Morse complex. We obtain a Morse complex by modeling an image as a cubical cellular complex. Each cell in the Morse complex is the critical point at which the topological structure changes in the filtration consisting of the level sets of the image. In this paper, we implement the proposed algorithm of segmenting the circularly shaped objects with a long persistence of homology as well as computing persistent homology along the filtration of the input image and displaying in the form of a persistence diagram.

• KIPS Transactions on Software and Data Engineering
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• v.6 no.2
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• pp.103-116
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• 2017

In this paper, we present the design and implementation of a large-scale qualitative spatial reasoner, which can derive new qualitative spatial knowledge representing both topological and directional relationships between two arbitrary spatial objects in efficient way using Aparch Spark SQL. Apache Spark SQL is well known as a distributed parallel programming environment which provides both efficient join operations and query processing functions over a variety of data in Hadoop cluster computer systems. In our spatial reasoner, the overall reasoning process is divided into 6 jobs such as knowledge encoding, inverse reasoning, equal reasoning, transitive reasoning, relation refining, knowledge decoding, and then the execution order over the reasoning jobs is determined in consideration of both logical causal relationships and computational efficiency. The knowledge encoding job reduces the size of knowledge base to reason over by transforming the input knowledge of XML/RDF form into one of more precise form. Repeat of the transitive reasoning job and the relation refining job usually consumes most of computational time and storage for the overall reasoning process. In order to improve the jobs, our reasoner finds out the minimal disjunctive relations for qualitative spatial reasoning, and then, based upon them, it not only reduces the composition table to be used for the transitive reasoning job, but also optimizes the relation refining job. Through experiments using a large-scale benchmarking spatial knowledge base, the proposed reasoner showed high performance and scalability.

• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.55-66
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• 1998

This paper presents a simple method for relieving the ambiguity problems within the sub-voxel based surface-fitting approach for the surface construction. ECB algorithm is proposed to avoid the ambiguity problem which is the root of the holes within the resulting polygon based approximation. The basic idea of our disambiguation strategy is the use of a set of predefined modeling primitives (we call SMP) which guarantees the topological consistency of resulted surface polygons. 20 SMPs are derived from the extension of the concept of the elementary modeling primitives in the CB algorithm [3], and fit one to five faces of them to the iso-surface crossing a cell with no further processing. A look-up table which has a surface triangle list is pre-calculated using these 20 SMPs. All of surface triangles in the table are from the faces of SMPs and are stored in the form of edge list on which vertices of each surface triangle are located. The resulted polygon based approximation is unique at every threshold value and its validity is guaranteed without considering the complicated problems such as average of density and postprocessing. ECB algorithm could be free from the need for the time consuming post-processing, which eliminates holes by revisiting every boundary cell. Through three experiments of surface construction from volume data, its capability of hole avoidance is showed.

• Korean Institute of Interior Design Journal
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• v.13 no.2
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• pp.29-37
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• 2004

This study analyze the architectural space in the aspect of the 'Raumplan' and 'Plan Libre'. These concepts based on the 'Raumplan versus Plan Libre' exhibition in Delft University, Netherlands. It is generally agreed that the concept of 'Plan Libre' in connection with Le Corbusie architecture and 'Raumplan' related to Adolf Loos's works. that exhibition contents was focused an extent of modem architecture. But, These concepts continually influence contemporary architecture and offer diverse vision in architecture. Therefore, this study focused on the analysis that look for common element in the space through the case study and space element connection in change of the values, technical growth. This Paper reveals that Adolf Loos's Raumplan is similar to Louis I. Kahn's 'Room' concept and Ando Tadao's centrifugal space composition method In the dwelling architecture. And the concept 'Plan Libre': non-definitive formal system and the elements : column, free form screening wall is revived as formal application of 3 dimension composition in architecture. and transfer lots, void, and linear space in Rem Koolhaas's urban design projects. These aspects is so called topology. This topological concept is an attempt in view of the space connection state rather than formative viewpoint.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.