• Communications of Mathematical Education
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• v.15
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• pp.175-180
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• 2003

본 연구에서는 중학교 과정에서 기본이 되는 개념이라 할 수 있는 음수 개념의 이해실태를 중학교 1학년 학생들을 대상으로 분석하고, 예비수학교사들이 음수 개념에 대해 어느 정도의 '교수학적 내용지식'을 갖고있는지 파악하여 분석하고자 하였다. 또 학생들이 겪는 음수개념 학습에서의 어려움을 해결하기 위한 방안을 제시하여 음수 개념 지도에 도움을 주고자 한다.

• Journal of KIISE:Software and Applications
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• v.36 no.5
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• pp.347-352
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• 2009

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering). In this paper we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• School Mathematics
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• v.10 no.4
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• pp.557-571
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• 2008

The objective of this paper is to study De Morgan's thoughts on teaching and learning negative numbers. We studied De Morgan's point of view on negative numbers, and analyzed his didactical approaches for negative numbers. De Morgan make students explore impossible subtractions, investigate the rule of the impossible subtractions, and construct the signification of the impossible subtractions in succession. In De Morgan' approach, teaching and learning negative numbers are connected with that of linear equations, the signs of impossible subtractions are used, and the concept of negative numbers is developed gradually following the historic genesis of negative numbers. Also, we analyzed the strengths and weaknesses of the De Morgan's approaches compared with the mathematics curriculum.

• The Journal of the Acoustical Society of Korea
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• v.31 no.5
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• pp.317-331
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• 2012

In this paper, we develop a multichannel blind source separation algorithm based on a beamspace transform and the multichannel non-negative matrix factorization (NMF) method. The NMF algorithm is a famous algorithm which is used to solve the source separation problems. In this paper, we consider a beamspace-time-frequency domain data model for multichannel NMF method, and enhance the conventional method using a beamspace transform. Our decomposition algorithm is applied to audio source separation, using a dataset from the international Signal Separation Evaluation Campaign 2010 (SiSEC 2010) for evaluation.

• Journal of Educational Research in Mathematics
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• v.17 no.1
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• pp.1-31
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• 2007

Negative numbers have been one of the most difficult mathematical concepts, and it was only 200 years ago that they were recognized as a real object of mathematics by mathematicians. It was because it took more than 1500 years for human beings to overcome the quantitative notion of numbers and recognize the formality in negative numbers. Understanding negative numbers as formal ones resulted from the Copernican conversion in mathematical way of thinking. we first investigated the historic and the genetic process of the concept of negative numbers. Second, we analyzed the conceptual fields of negative numbers in the aspect of the additive and multiplicative structure. Third, we inquired into the levels of thinking on the concept of negative numbers on the basis of the historical and the psychological analysis in order to understand the formal concept of negative numbers. Fourth, we analyzed Korean mathematics textbooks on the basis of the thinking levels of the concept of negative numbers. Fifth, we investigated and analysed the levels of students' understanding of the concept of negative numbers. Sixth, we analyzed the symbolizing process in the development of mathematical concept. Futhermore, we tried to show a concrete way to teach the formality of the negative numbers concepts on the basis of such theoretical analyses.

• Economic and Environmental Geology
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• v.20 no.3
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• pp.197-201
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• 1987

Negative induced polarization (IP) responses are examined for a three-layered earth using a digital linear filter method. The negative IP response can occur when the geoelectric section is of type K or Q. The section of type K creates a more pronounced negative effect than that of type Q. For such sections, IP coefficients are determined as a function of the resistivity distribution and the electrode configuration, and only the IP coefficient of the first layer can be negative. As a result, the negative IP response can occur when the first layer is polarizable in the section of type K or Q. and the polarizabilities of the other layers can act to depress the negative response.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.7
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• pp.397-401
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• 2004

In an edge-weighted(positive, negative, or zero weights are possible) tree, we want to solve the problem of finding a longest path such that the sum of the weights of the edges in the path is non-negative. We present an algorithm to find a longest non-negative path of a degree 3 tree in Ο(n log n) time, where n is the number of nodes in the tree.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.12
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• pp.880-884
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• 2006

In an edge-weighted(positive, negative, or zero weights are possible) tree, we want to solve the problem of finding a longest path such that the sum of the weights of the edges in tile path is non-negative. To find a longest non-negative path of a tree we present a sequential algorithm with O(n logn) time and a CREW PRAM parallel algorithm with $O(log^2n)$ time and O(n) processors. where n is the number of nodes in the tree.

• Journal of KIISE:Computing Practices and Letters
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• v.14 no.3
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• pp.296-300
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• 2008

Nonnegative tensor factorization(NTF) is a recent multiway(multilineal) extension of nonnegative matrix factorization(NMF), where nonnegativity constraints are imposed on the CANDECOMP/PARAFAC model. In this paper we consider the Tucker model with nonnegativity constraints and develop a new tensor factorization method, referred to as nonnegative Tucker decomposition (NTD). We derive multiplicative updating algorithms for various discrepancy measures: least square error function, I-divergence, and $\alpha$-divergence.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.219-223
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• 2007

관측자료 없이 지형인자만으로 미계측 유역의 유출수문해석이 가능한 GIUH(Geomorphologic Instantaneous Unit Hydrograph)의 초기확률을 상안미, 병천, 산계 유역에 대하여 분석하였다. GIUH 이론에서 하천차수가 증가할수록 면적비에 대한 분기비의 영향이 증가하여 대상유역에서의 초기확률이 음수로 발생할 확률이 커진다. 본 연구의 4차하천으로 가정된 모든 대상유역에서의 초기확률 역시 음수로 발생하였다. 뿐만아니라, 3차 하천으로 가정된 경우에도 2차 하천의 합류부에서 유역출구까지의 거리가 짧은 산계유역의 경우에는 면적비에 대한 분기비값이 상대적으로 큰 값을 갖게되어 초기확률이 음수로 발생하였다. 본 연구에서는 초기확률이 음수로 발생하는 문제점을 보완하기 위하여 직접유출면적비를 사용하여 초기확률을 산정하였다. 그 결과, 적절한 초기확률값을 얻을 수 있었으며 순간단위도의 초반부 음수 발생문제를 해결하였다.