• 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 KIISE:Software and Applications
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• v.37 no.3
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• pp.194-204
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• 2010

A space, real or virtual, comprises regions as its parts and physical objects residing in them. A coherent and sophisticated representaion scheme for their spatial relations premises the precision and plausibility in its associated agents' inferencing on the spatial relations and the development of events occurring in such a space. The existing spatial models are not suitable for a comprehensive representation of the general spatial relations in that they have limited expressive powers based on the dichotomy between the large and small scales, or support only a small set of topological relations. The representaion model we propose has the following distinctive chracteristics: firstly, our model provides a comprehensive representation scheme to accommodate large and small scale spaces in an integrated fashion; secondly, our model greatly elaborated the spatial relations among the small-scale objects based on their contact relations and the compositional relations among their respective components objects beyond the basic topological relations like disjoint and touch; thirdly, our model further diversifies the types of supported relations by adding the container property besides the soildness together with considering the gravity direction. The resulting integrated spatial knowledge representation scheme considering the gravity allows the diverse spatial relations in the real world to be simulated in a precise manner in relation to the associated spatial events and provides an expression measure for the agents in such a cyber-world to capture the spatial knowledge to be used for recognizing the situations in the spatial aspects.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.189-200
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• 2020

Let G be a simple connected graph with n vertices and m edges. Denote by d₁ ≥ d₂ ≥ ⋯ ≥ d_n > 0 and d(e₁) ≥ d(e₂) ≥ ⋯ ≥ d(e_m) sequences of vertex and edge degrees, respectively. If vertices v_i and v_j are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳_α(G) = ∑_i~j(d_i + d_j)^α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳_α(G) and 𝒳_α-1(G). Then we use it to obtain some new bounds for 𝒳_α(G).

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.361-378
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• 2020

The most apparent aspect of the present study is to introduce a new sequence space 𝚽^⋆(𝓛_p) derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the α-, β(bp)- and γ-duals of the space 𝚽^⋆(𝓛_p) are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.707-716
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• 2013

The present paper consists of two parts. Since the recent paper [4] proved that an Alexandroff $T_0$-space is a semi-$T_{\frac{1}{2}}$-space, the first part studies semi-open and semi-closed structures of the Khalimsky nD space. The second one focuses on the study of a relation between the LS-property of ($SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$, k) relative to the simple closed $k_i$-curves $SC^{n_i,l_i}_{k_i}$, $i{\in}\{1,2\}$ and its normal k-adjacency. In addition, the present paper points out that the main theorems of Boxer and Karaca's paper [3] such as Theorems 4.4 and 4.7 of [3] cannot be new assertions. Indeed, instead they should be attributed to Theorems 4.3 and 4.5, and Example 4.6 of [10].

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1017-1029
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• 2010

In this paper we obtain a very general theorem of $\rho$-compatibility for three multivalued mappings, one of them from the class $\mathfrak{B}$. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation $\rho$ on $2^Z$ and three mappings P : X $\multimap$ Z, Q : Y $\multimap$ Z and $T\;{\in}\;\mathfrak{B}$(Y,X) satisfying a set of conditions we can find ($\widetilde{x},\;\widetilde{y}$) ${\in}$ $X\;{\times}\;Y$ such that $\widetilde{x}\;{\in}\;T(\widetilde{y})$ and $P(\widetilde{x}){\rho}\;Q(\widetilde{y})$. Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.

• Proceedings of the Korea Contents Association Conference
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• 2017.05a
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• pp.27-28
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• 2017

다양한 위상학적 관계(topological relation)를 분석하는 네트워크 분석은 복잡한 데이터에서 숨어있는 특성과 사실을 발견하는 기술로 최근 빅데이터 분야에서 데이터 분석 핵심 기술로 급부상하고 있다. 본 연구에서는 질병연구에 핵심적인 생물학적 네트워크의 생성 및 사용자 친화적인 네트워크 분석시스템을 개발하였다. 개발한 시스템은 PubMed에서 특정 질병과 관련있는 논문 요약 정보를 자동 수집후 텍스트마이닝을 통해 질병 관련 화합물, 유전자 그리고 상호작용 정보를 추출해 생물학적 네트워크를 생성하는 기능을 제공한다. 또한, 연구자가 손쉽게 생성된 네트워크에 대한 검색 및 다차원 분석을 수행할 수 있는 기능을 제공한다. 마지막으로 개발한 시스템의 우수성을 입증하기 위해 크론병(Crohn's Disease)에 대한 적용사례를 소개한다.

• 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 the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.5
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• pp.359-366
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• 2019

Indoor spatial data has great importance as the demand for representing the complex urban environment in the context of providing LBS (Location-based Services) is increasing. IndoorGML (Indoor Geographic Markup Language) has been established as the data standard for spatial data in providing indoor navigation, but its definitions and relationships must be expanded to increase its applications and to successfully delivering information to users. In this study, we propose an approach to integrate IndoorGML with Indoor POI (Points of Interest) data by extending the IndoorGML notion of space and topological relationships. We consider two cases of representing Indoor POI, by 3D geometry and by point primitive representation. Using the concepts of the NRS (node-relation structure) and multi-layered space representation of IndoorGML, we define layers to separate features that represent the spaces and the Indoor POI into separate, but related layers. The proposed methodology was implemented with real datasets to evaluate its effectiveness for performing indoor spatial analysis.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.41.2-41.2
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• 2018

The Minkowski Functionals of the matter densityeld, as traced by galaxies, contain information regarding the nature of dark energy and the fraction of dark matter in the Universe. In particular, the genus is a statistic that provides a clean measurement of the shape of the linear matter power spectrum. As the genus is a topological quantity, it is insensitive to galaxy bias and gravitational collapse. Furthermore, as it traces the linear matter power spectrum, it is a conserved quantity with redshift. Hence the genus amplitude is a standard population that can be used to test the distance-redshift relation. In this talk, I show how we can extract the genus from galaxy catalogs, and how we can use its properties to constrain the equation of state of dark energy and the energy content of the Universe.