• 통합자연과학논문집
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• 제13권4호
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• pp.128-131
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• 2020

We studied the structure of symmetric group of rubik's cube with oriented face. In conclusion, we have shown that the symmetric group of rubik's cube with oriented face is isomorphic to C46 / 2 × (C37 ≀ S8) × (C210 ≀ S12).

• 대한수학회보
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• 제60권6호
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• pp.1705-1714
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• 2023

We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.

• 대한수학회지
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• 제53권2호
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• pp.331-346
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• 2016

The primary aim of this paper is to generalize a theorem of Hirzebruch for the complex 2-dimensional Bott manifolds, usually called Hirzebruch surfaces, to more general Bott towers of height n. To do so, we first show that all complex vector bundles of rank 2 over a Bott manifold are classified by their total Chern classes. As a consequence, in this paper we show that two Bott manifolds $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n)$ and $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n^{\prime})$ are isomorphic to each other, as Bott towers if and only if both ${\alpha}_n{\equiv}{\alpha}_n^{\prime}$ mod 2 and ${\alpha}_n^2=({\alpha}_n^{\prime})^2$ hold in the cohomology ring of $B_{n-1}({\alpha}_1,{\ldots},{\alpha}_{n-1})$ over integer coefficients. This result will complete a circle of ideas initiated in [11] by Ishida. We also give some partial affirmative remarks toward the assertion that under certain condition our main result still holds to be true for two Bott manifolds just diffeomorphic, but not necessarily isomorphic, to each other.

• 한국정보과학회논문지:소프트웨어및응용
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• 제33권4호
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• pp.440-448
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• 2006

자기 조직화 신경망 (SOM: Self-Organizing Map)은 자율 학습 신경망으로 사전 지식이 존재하지 않는 자료에 존재하는 구조적 관계성을 보전하는데 이용된다. 자기 조직화 신경망은 벡터 양자화, 조합 최적화, 패턴 인식과 같은 복잡한 문제 해결을 위한 연구에 많이 이용되어 왔다. 이 논문에서는 좀더 효율적인 유전 알고리즘을 얻기 위한 스키마 변환 도구로서 자기 조직화 신경망을 이용하는 새로운 사용법에 대해서 제안한다. 즉, 각 자식해는 탐색 공간에서 좀더 바람직한 모양을 가지는 동질의 인공 신경망으로 변환된다. 이 변환으로 인해 강한 상위(epistasis)를 가지는 유전자들은 염색체 상에서 서로 인접하게 되는 것이다. 실험 결과는 기존 결과에 비해서 주목할만한 성능 개선이 있음을 보여준다.

• Journal of information and communication convergence engineering
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• 제15권2호
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• pp.97-103
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• 2017

Implementation of faster pairing calculation is the basis of efficient pairing-based cryptographic protocol implementation. Generally, pairing is a costly operation carried out over the extension field of degree $k{\geq}12$. But the twist property of the pairing friendly curve allows us to calculate pairing over the sub-field twisted curve, where the extension degree becomes k/d and twist degree d = 2, 3, 4, 6. The calculation cost is reduced substantially by twisting but it makes the discrete logarithm problem easier if the curve parameters are not carefully chosen. Therefore, this paper considers the most recent parameters setting presented by Barbulescu and Duquesne [1] for pairing-based cryptography; that are secure enough for 128-bit security level; to explicitly show the quartic twist (d = 4) and sextic twist (d = 6) mapping between the isomorphic rational point groups for KSS (Kachisa-Schaefer-Scott) curve of embedding degree k = 16 and k = 18, receptively. This paper also evaluates the performance enhancement of the obtained twisted mapping by comparing the elliptic curve scalar multiplications.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.75-96
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• 2006

Let m, n be positive integers. We denote by R(m,n) (respectively P(m,n)) the class of all groups G such that, for every n subsets $X_1,X_2\ldots,X_n$, of size m of G there exits a non-identity permutation $\sigma$ such that $X_1X_2{\cdots}X_n{\cap}X_{\sigma(1)}X_{/sigma(2)}{\cdots}X_{/sigma(n)}\neq\phi$ (respectively $X_1X_2{\cdots}X_n=X_{/sigma(1)}X_{\sigma(2)}{\cdots}X_{\sigma(n)}$). Let G be a non-abelian group. In this paper we prove that (i) $G{\in}P$(2,3) if and only if G isomorphic to $S_3$, where $S_n$ is the symmetric group on n letters. (ii) $G{\in}R$(2, 2) if and only if ${\mid}G{\mid}\geq8$. (iii) If G is finite, then $G{\in}R$(3, 2) if and only if ${\mid}G{\mid}\geq14$ or G is isomorphic to one of the following: SmallGroup(16, i), $i\in$ {3, 4, 6, 11, 12, 13}, SmallGroup(32, 49), SmallGroup(32, 50), where SmallGroup(m, n) is the nth group of order m in the GAP [13] library.

• 대한수학회보
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• 제47권5호
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• pp.997-1000
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• 2010

We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras. It is shown that the reduced group $C^*$-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian $C^*$-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian $C^*$-algebras is not isomorphic to the tensor product of a nuclear $C^*$-algebra and a reduced free product of abelian $C^*$-algebra. We discuss the freeness of free product $II_1$-factors and solidity of free product $II_1$-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product $II_1$-factors. Finally, we give a free product factor which is not solid in the weak sense.

• 대한두경부종양학회지
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• 제3권1호
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• pp.91-96
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• 1987

이하선의 기저세포선종은 pleomorphic adenoma와는 달리 종양구성세포에서 myoepithelial cell을 볼수없는 아주 희귀한 isomorphic epithelial tumor 이다. 병리학적으로 pleomorphic adenoma 와 adenoid cystic carcinoma 와 감별이 어려운 점이 문제이며, 임상 경과는 pleomorphic adenoma 에 준하는 수술로 양호한 결과를 얻을 수 있다. 저자는 최근에 63세와 71세된 남자환자에서 좌측 이하선 심부엽에 발생한 기저세포선종 2 예를 치험하였기에 이를 문헌고찰과 함께 보고하였다.

• 논리연구
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• 제17권1호
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• pp.71-109
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• 2014

셔어는 타르스키의 논리적 귀결 정의가 개념적으로나 외연적으로 적합한 설명이라고 믿는다. 셔어는 모스토프스키의 동형 구조 내의 불변적인 것으로서 일반화된 양화사 개념, 그리고 자신의 모형 이론에 근거해서 그 믿음을 정당화하려 하였다. 이 글에서 나는 타르스키의 정의를 정당화하려는 셔어의 시도는 반만 성공한 것임을 보이려 한다. 나는 논리적인 것이 동형 구조 내의 불변적인 것이라는 셔어의 생각은 논리적 귀결의 형식적 특징을 보이기에 충분하다는 점을 인정한다. 반면 나는 용어의 의미에 대한 셔어의 생각은 외연이 빈 술어의 문제를 제대로 다루기에는 아주 부적합해서, 결국 셔어는 논리적으로 필연적인 진리들과 그 밖의 진리들을 구별하는 데 실패하였다고 생각한다.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.503-507
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• 2006

Let X be a Tychonoff space and ${\sum}(X)$ the set of all the subrings of C(X) that contain $C^*(X)$. For any A(X) in ${\sum}(X)$ suppose $_{{\upsilon}A}X$ is the largest subspace of ${\beta}X$ containing X to which each function in A(X) can be extended continuously. Let us write A(X) ~ B(X) if and only if $_{{\upsilon}A}X=_{{\upsilon}B}X$, thereby defining an equivalence relation on ${\sum}(X)$. We have shown that an A(X) in ${\sum}(X)$ is isomorphic to C(Y ) for some space Y if and only if A(X) is the largest member of its equivalence class if and only if there exists a subspace T of ${\beta}X$ with the property that A(X)={$f{\in}C(X):f^*(p)$ is real for each $p$ in T}, $f^*$ being the unique continuous extension of $f$ in C(X) from ${\beta}X$ to $\mathbb{R}^*$, the one point compactification of $\mathbb{R}$. As a consequence it follows that if X is a realcompact space in which every $C^*$-embedded subset is closed, then C(X) is never isomorphic to any A(X) in ${\sum}(X)$ without being equal to it.