• 충청수학회지
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• 제34권3호
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• pp.209-219
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• 2021

A set {a₁, a₂, ⋯ , a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. Let F_n be the nth Fibonacci number which is defined by F₀ = 0, F₁ = 1 and F_n+2 = F_n+1 + F_n. In this paper, we find the extendibility of Diophantine pairs {F_2k, b} with some conditions.

• 대한수학회논문집
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• 제32권3호
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• pp.653-659
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• 2017

Let $p{\geq}1$ be a real number. A tuple $T=(T_1,{\ldots},T_n)$ of commuting bounded linear operators on a Banach space X is called an ${\ell}^p$-spherical isometry if ${\sum_{i=1}^{n}}{\parallel}T_ix{\parallel}^p={\parallel}x{\parallel}^p$ for all $x{\in}X$. The tuple T is called a toral isometry if each Ti is an isometry. By a result of Ansari, Hedayatian, Khani-Robati and Moradi, for every $n{\geq}1$, there is a supercyclic ${\ell}^2$-spherical isometric n-tuple on ${\mathbb{C}}^n$ but there is no supercyclic ${\ell}^2$-spherical isometry on an infinite-dimensional Hilbert space. In this article, we investigate the supercyclicity of ${\ell}^p$-spherical isometries and toral isometries on Banach spaces. Also, we introduce the notion of semicommutative tuples and we show that the Banach spaces ${\ell}^p$ ($1{\leq}p$ < ${\infty}$) support supercyclic ${\ell}^p$-spherical isometric semi-commutative tuples. As a result, all separable infinite-dimensional complex Hilbert spaces support supercyclic spherical isometric semi-commutative tuples.

• 대한수학회지
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• 제55권2호
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• pp.425-445
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• 2018

A set {$a_1,\;a_2,{\ldots},\;a_m$} of positive integers is called a Diophantine m-tuple if $a_ia_j+1$ is a perfect square for all $1{\leq}i$ < $j{\leq}m$. In this paper, we show that the form of third element in Diophantine pairs and develop some results which are needed to prove the extendibility of the Diophantine pair {a, b} with some conditions. By using this result, we prove the extendibility of Diophantine pairs {$F_{k-2}F_{k+1},\;F_{k-1}F_{k+2}$} and {$F_{k-2}F_{k-1},\;F_{k+1}F_{k+2}$}, where $F_n$ is the n-th Fibonacci number.

• 대한산업공학회지
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• 제22권4호
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• pp.567-578
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• 1996

In relational databases the number of disk accesses depends on the amount of data transferred from disk to main memory for processing the transactions. N-ary vertical partitioning of the relation can often result in a decrease in the number of disk accesses, since not all attributes in a tuple are required by each transactions. In this paper, a 0-1 integer programming model for solving n-ary vertical partitioning problem minimizing the number of disk accesses is formulated and a branch-and-bound method is used to solve it. A preprocessing procedure reducing the number of variables is presented. The algorithm is illustrated with numerical examples and is shown to be computationally efficient. Numerical experiments reveal that the proposed method is more effective in reducing access costs than the existing algorithms.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제8권2호
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• pp.107-114
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• 2004

University teachers of linear algebra often feel annoyed and disarmed when faced with the inability of their students to cope with concepts that they consider to be very simple. Usually, they lay the blame on the impossibility for the students to use geometrical intuition or the lack of practice in basic logic and set theory. J.-L. Dorier [(2002): Teaching Linear Algebra at University. In: T. Li (Ed.), Proceedings of the International Congress of Mathematicians (Beijing: August 20-28, 2002), Vol. III: Invited Lectures (pp. 875-884). Beijing: Higher Education Press] mentioned that the situation could not be improved substantially with the teaching of Cartesian geometry or/and logic and set theory prior to the linear algebra. In East Asian countries, science-orientated mathematics curricula of the high schools consist of calculus with many other materials. To understand differential and integral calculus efficiently or for other reasons, students have to learn a lot of content (and concepts) in linear algebra, such as ordered pairs, n-tuple numbers, planar and spatial coordinates, vectors, polynomials, matrices, etc., from an early age. The content of linear algebra is spread out from grades 7 to 12. When the high school teachers teach the content of linear algebra, however, they do not concern much about the concepts of content. With small effort, teachers can help the students to build concepts of vocabularies and languages of linear algebra.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.573-581
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• 2018

In this paper we consider all orientation-preserving ${\mathbb{Z}}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0 for p an odd prime. To do so, we examine particular graphs of groups (${\Gamma}(v)$, G(v)) in canonical form for some 5-tuple v = (r, s, t, m, n) with r + s + t + m > 0. These graphs of groups correspond to the handlebody orbifolds V (${\Gamma}(v)$, G(v)) that are homeomorphic to the quotient spaces $V_g/{\mathbb{Z}}_{p^2}$ of genus less than or equal to g. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_{p^2}$-actions on such handlebodies, up to equivalence.

• 한국산학기술학회논문지
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• 제21권11호
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• pp.728-739
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• 2020

이 연구는 웹보메트릭 빅데이터를 활용하여 코로나바이러스 확진 국가(지역)들의 온라인 정보원의 다양성을 조사했다. 구체적으로 2020년 2월에 코로나바이러스 확진자가 발생한 28개국을 대상으로 웹 데이터를 수집한 결과, 호주, 캐나다, 이탈리아 등의 온라인 가시성이 높게 나타나면서 관련 정보를 가장 많이 생산하고 있었다. 국가별 검색건수(hit counts)와 정보채널의 역할을 하는 도메인(domain) 빈도와는 통계적으로 유의한 상관성이 있었다. 한편 데이터 수집도구인 bing.com의 점유률이 평소에도 높은 국가들을 제외하고 다시 검토한 결과, 당시 확진자 수가 많았던 일본, 중국, 싱가포르 등이 코로나바이러스와 관련된 웹데이터를 주도적으로 올리고 있었다. 온라인 정보원은 n-헬릭스를 활용하여 분류되었다. n-헬릭스는 대학-기업-정부의 3주체간 상호작용과 혁신을 강조하는 트리플헬릭스모델(Triple Helix Model)에 기반한 확장된 분석틀이다. 그 결과, 정부기관이 18.1%를 차지하면서 코로나바이러스 정보의 최대 공급자로 나타났다. 2원성 네트워크 분석결과를 보면 언론사, 대학병원, 공중보건에 특화된 조직 등도 코로나바이러스 연구와 방역 정보의 온라인 유통에 적극적이었다. 웹페이지에 포함된 단어들을 중심으로 내용분석을 해 보니 건강, 학교, 가족, 공공, 방안 등의 단어가 중심성이 높게 나타나 코로나바이러스로 인한 개인별 예방수칙뿐만 아니라 생활 불편과 업무장애로 인한 대처방안 등에 관심이 높다는 것을 알 수 있었다.