• Korean Journal of Logic
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• v.12 no.1
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• pp.1-24
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• 2009

이 논문에서 우리는 집합의 두 점 사이의 관계를 소개하고, '가깝다'와 '충분히 가깝다'의 위상적인 개념을 다양하게 정의할 수 있음을 보인다. 또한 직관주의 논리와 관계가 있는 De Morgan frame을 소개하고 pre-order에 의하여 정의된 동치관계로 만들어진 동치류들의 집합을 기저로 생성된 위상 공간이 extremally disconnected 임을 보인다.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.285-295
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• 2013

In this study I examine the definitions of terms related to ratio and rate from 5, 6, 7th revised elementary school math textbooks to discuss the improvements and the remained problems in 2007 curriculum textbook. Next, I make the alternative definitions of the terms, 'biyoul', the value of 'bi', and 'baekboonyul' by re-establishing the relations between them. Finally, I point out that those problems are intrinsic to the attempt of the textbook to introduce the terms related to ratio with little consideration for the mathematical meaning of ratio as a equivalence class.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.43-49
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• 1979

G를 유한군으로, C를 모든 복소수체로 가정하고, V를 C상에서의 유한차원 벡터공간이라 하자. V상에서의 G의 사영적 표시는, X, $y{\epsilon}G$이고 ${\alpha}:\;G{\times}G{\rightarrow}C$를 Facto set이라 할 때 $T(x)T(y)=T(xy){\alpha}(x,y)$이 되는 함수 $T=\;G{\rightarrow}GL(V)$를 말한다. 본 논문의 목적은 군에 대한 Extension theory를 사용해서, G상의 factor set들의 동치류들은 G의 Second Cohomology group과 동형이라는 것을 증명하는 것이다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.6 no.4
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• pp.97-106
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• 1996

In this paper, we define an equivalence relation on the group of all permutations over the finite field GF($2^n$) and show each equivalence class has common cryptographic properties. And, we classify all exponent permutations over GF($2^7$) and GF($2^8$). Then, three applications of our results are described. We suggest a method for designing $n\;{\times}\;2n$ S(ubstitution)-boxes by the concatenation of two exponent permutations over GF($2^n$) and study the differential and linear resistance of them. And we can easily indicate that the conjecture of Beth in Eurocrypt '93 is wrong, and discuss the security of S-box in LOKI encryption algorithm.

• School Mathematics
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• v.12 no.3
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• pp.337-351
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• 2010

Blackout game on a certain size of the Go table, which looks simple, involves a variety of mathematical modeling. This study uses a research and education method. While the mathematically gifted students were playing blackout game, the author, as the instructor, observed the ways in which they approached various mathematical models. Based on the data, this study examines the effects of blackout game on the children's cognitive processes. This study further discusses the issues of questions.

• Journal of Digital Convergence
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• v.11 no.11
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• pp.343-349
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• 2013

Rough set theory comes to derive optimal rules through the effective selection of features from the redundancy of lots of information in data mining using the concept of equivalence relation and approximation space in rough set. The reduction of attributes is one of the most important parts in its applications of rough set. This paper purports to define a information-theoretic measure for determining the most important attribute within the association of attributes using rough entropy. The proposed method generates the effective reduct set and formulates the core of the attribute set through the elimination of the redundant attributes. Subsequently, the control rules are generated with a subset of feature which retain the accuracy of the original features through the reduction.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.5
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• pp.183-188
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• 2013

A variety of cluster analysis techniques prerequisite to cluster objects having similar characteristics in data mining. But the clustering of those algorithms have lots of difficulties in dealing with categorical data within the databases. The imprecise handling of uncertainty within categorical data in the clustering process stems from the only algebraic logic of rough set, resulting in the degradation of stability and effectiveness. This paper proposes a information-theoretic rough entropy(RE) by taking into account the dependency of attributes and proposes a technique called min-mean-mean roughness(MMMR) for selecting clustering attribute. We analyze and compare the performance of the proposed technique with K-means, fuzzy techniques and other standard deviation roughness methods based on ZOO dataset. The results verify the better performance of the proposed approach.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.199-219
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• 2011

In this thesis, we designed a experimental learning-teaching plan of 'decimal fraction concept' at the 4-th grade level. We rest our plan on two basic premises. One is the fact that a essential concept of decimal fraction is 'polynomial of which indeterminate is 10', and another is the fact that the origin of decimal fraction is successive measurement activities which improving accuracy through decimal partition of measuring unit. The main features of our experimental learning-teaching plan is as follows. Firstly, students can experience a operation which generate decimal unit system through decimal partitioning of measuring unit. Secondly, the decimal fraction expansion will be initially introduced and the complete representation of decimal fraction according to positional notation will follow. Thirdly, such various interpretations of decimal fraction as 3.751m, 3m+7dm+5cm+1mm, $(3+\frac{7}{10}+\frac{5}{100}+\frac{1}{1000})m$ and $\frac{3751}{1000}m$ will be handled. Fourthly, decimal fraction will not be introduced with 'unit decimal fraction' such as 0.1, 0.01, 0.001, ${\cdots}$ but with 'natural number+decimal fraction' such as 2.345. Fifthly, we arranged a numeration activity ruled by random unit system previous to formal representation ruled by decimal positional notation. A experimental learning-teaching plan which presented in this thesis must be examined through teaching experiment. It is necessary to successive research for this task.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.2
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• pp.124-136
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• 1990

This paper presents a catalog of AND-EXOR expressions for representative function of four-variable NP-equivalence classes. Minimality is defined as minimizing first the number of product terms and then the total number of literal in the expression. Also, the propoerties of minimum expressions are discussed. Using this as a base, We compare minimum expressions of AND-OR type two-variable circuit with minimum expressions of AND-EXOR type two-variable circuit which used algorithm in this paper. As a results it was found that in the case of AND-OR type minimum expressions, number of product terms is under 8, and in the case of AND-EXOR type minimum expressions all functions are formed in which number of product terms is under 6, and generally number of product term is considerably small to realize four-vaiable function toward ADN-EXOR type minimum expression circuit. Algorithm suggested in this paper are realized on Sun 3/50, and through this, logic function under four-variable can get minimum immedately by a catalog suggested in this paper. As for five-variale function, we can do shanon-development a part of the function with suitable variable, and by applying four-variable minimum of this paper on this, it can be possible to get minimum in a short time and it can be said that it is possible to apply this method to functions over 6 variable.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.30 no.6
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• pp.509-515
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• 2004

Photodynamic therapy(PDT) has advanced to clinical trials for the treatment of a variety of solid tumors and presents an alternative treatment option for tumors resistant to chemo-and/or radio-therapy. PDT is based on the combination of laser light of appropriate wavelength and energy to activate a systemically or locally applied photosensitizer that concentrates preferentially in malignant tissues. In this study, phototoxicity of laser EIT 21 was analysed in human osteosarcoma cell(HOS) and the second objective of this study was to determine the ability of laser EIT 21 to induce apoptosis. This study demonstrated that laser EIT 21 had a phototoxicity to HOS cells. In order to examinate whether cell death was induced by necrosis or apoptosis, variety of techniques which assess apoptosis were used. TUNEL assay showed only a few the positive reaction on condensed nuclei. It is hard to find condensed or fragmented nuclei on HOS cells irradiated with laser EIT 21 in Hemastat and AO/EB stain. By DNA electrophoresis, cells also did not show DNA degradation characteristic of apoptosis with a ladder pattern of DNA fragments. Apoptosis-related factors were analyzed by western blotting. The expression of p53 was constant and cells irradiated with laser did not show the caspase-3 and PARP degradation, therefore we suggest that p53 and caspase-3 are not involved in laserinduced cell death.