• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.505-521
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• 2011

We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-$C^*$-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in [5] into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.

• Journal of the Korean Data and Information Science Society
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• v.26 no.5
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• pp.1129-1139
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• 2015

Inference process generates additional triples from knowledge represented in RDF triples of semantic web technology. Tens of million of triples as an initial big data and the additionally inferred triples become a knowledge base for applications such as QA(question&answer) system. The inference engine requires more computing resources to process the triples generated while inferencing. The additional computing resources supplied by underlying resource pool in cloud computing can shorten the execution time. This paper addresses an algorithm to allocate the number of computing nodes "elastically" at runtime on Hadoop, depending on the size of knowledge data fed. The model proposed in this paper is composed of the layered architecture: the top layer for applications, the middle layer for distributed parallel inference engine to process the triples, and lower layer for elastic Hadoop and server visualization. System algorithms and test data are analyzed and discussed in this paper. The model hast the benefit that rich legacy Hadoop applications can be run faster on this system without any modification.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.361-366
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• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

• The Mathematical Education
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• v.41 no.2
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• pp.227-231
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• 2002

The Pythagorean theorem and Pythagorean triple are well known. We know some Pythagorean triples, however we don't Cow well that every natural number can belong to some Pythagorean triple. In this paper, we show that every natural number, which is not less than 2, can be a length of a leg(a side opposite the acute angle in a right triangle) in some right triangle, and list some Pythagorean triples.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1243-1253
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• 2008

In this paper, we construct one-factorizations of given complete graphs of even order. These constructions partition the edges of the complete graph into one-factors and triples. Our new constructions of one-factors and triples can be applied to a recursive construction of Steiner triple systems for all possible orders ${\geq}$15.

• International Journal of Knowledge Content Development & Technology
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• v.4 no.1
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• pp.39-51
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• 2014

The paper proposes that the Basic Concepts Classification (BCC) could serve as the controlled vocabulary for the Semantic Web. The BCC uses a synthetic approach among classes of things, relators, and properties. These are precisely the sort of concepts required by RDF triples. The BCC also addresses some of the syntactic needs of the Semantic Web. Others could be added to the BCC in a bottom-up process that carefully evaluates the costs, benefits, and best format for each rule considered.

• Journal of KIISE:Software and Applications
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• v.26 no.8
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• pp.964-973
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• 1999

본 논문에서는 퍼지 트리플을 사용하는 내용 기반 이미지 검색 방법을 제안한다. 이미지 내 객체들 사이의 공간 관계는 내용 기반 이미지 검색을 위해 사용되는 주요한 속성들 중의 하나이다. 그러나, 기존의 트리플을 이용한 이미지 검색 시스템들은 개념 기반 검색 방법을 지원하지 못하고, 방향들 사이의 근사 정합을 처리하지 못하는 문제점을 가지고 있다. 이 문제를 해결하기 위하여 본 논문에서는 개념 기반 정합과 근사 정합을 지원하는 퍼지 트리플을 이용한 이미지 검색 방법을 제안한다. 개념 기반 정합을 위해서는 퍼지 소속성 집합으로 이루어진 시소러스가 사용되며, 근사 정합을 위해서는 방향들 사이의 관계를 정량화 하기 위한 k-weight 함수가 각각 이용된다. 이 두 가지 정합은 퍼지 트리플 간의 퍼지 정합을 통하여 균일하게 지원될 수 있다. 본 논문에서는 또한, 개념 기반 정합과 근사 정합에 대한 검색 효과를 정량적으로 평가하는 작업을 수행한다. Abstract This paper proposes an inexact and a concept-based image match technique based on fuzzy triples. The most general method adopted to index and retrieve images based on this spatial structure may be triple framework. However, there are two significant drawbacks in this framework; one is that it can not support a concept-based image retrieval and the other is that it fails to deal with an inexact match among directions. To compensate these problems, we develope an image retrieval technique based on fuzzy triples to make the inexact and concept-based match possible. For the concept-based match, we employ a set of fuzzy membership functions structured like a thesaurus, whereas for the inexact match, we introduce k-weight functions to quantify the similarity between directions. In fuzzy triples, the two facilities are uniformly supported by fuzzy matching. In addition, we analyze the retrieval effectiveness of our framework regarding the degree of the conceptual matching and the inexact matching.

• ETRI Journal
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• v.15 no.2
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• pp.27-34
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• 1993

Pitman-Intransitive triples of estimators are constructed, based on prior work on equivariant estimators and prior work on shrinkage.

• Journal of Information Technology Services
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• v.6 no.1
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• pp.151-158
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• 2007

D-class computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and search for equivalent $n{\times}n$ Boolean matrices according to a specific equivalence relation. It is easy to see that even multiplying all $n{\times}n$ Boolean matrices with themselves shows exponential time complexity and D-Class computation was left an unsolved problem due to its computational complexity. The vector-based multiplication theory shows that the multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices can be done much more efficiently. However, D-Class computation requires computation of equivalent classes in addition to the efficient multiplication. The paper discusses a theory and an algorithm for efficient D-class computation, and shows execution results of the algorithm.

• Journal of information and communication convergence engineering
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• v.20 no.2
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• pp.113-124
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• 2022

News in the form of web data generates increasingly large amounts of information as unstructured text. The capability of understanding the meaning of news is limited to humans; thus, it causes information overload. This hinders the effective use of embedded knowledge in such texts. Therefore, Automatic Knowledge Extraction (AKE) has now become an integral part of Semantic web and Natural Language Processing (NLP). Although recent literature shows that AKE has progressed, the results are still behind the expectations. This study proposes a method to auto-extract surface knowledge from English news into a machine-interpretable semantic format (triple). The proposed technique was designed using the grammatical structure of the sentence, and 11 original rules were discovered. The initial experiment extracted triples from the Sri Lankan news corpus, of which 83.5% were meaningful. The experiment was extended to the British Broadcasting Corporation (BBC) news dataset to prove its generic nature. This demonstrated a higher meaningful triple extraction rate of 92.6%. These results were validated using the inter-rater agreement method, which guaranteed the high reliability.