• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권1호
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• pp.91-110
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• 2015

본 연구는 초등수학 영재교육 대상자들이 원주율 개념에 대해서 어떻게 이해하고 있는지를 살펴보고자 하였다. 이를 위해 원주율 계산 방법의 역사 발달 단계를 토대로 세 가지 과제를 개발한 후 6학년 영재교육 대상자 12명을 대상으로 적용하여 그 반응을 분석하였다. 연구결과, 학생들은 '원주율 = 3.14'라는 사고의 고착화로 인하여 원주율의 개념, 근사성, 무한성을 제대로 이해하지 못하였으며, 원주율과 원주율의 근삿값을 혼동하는 오류를 보였다. 또한 학생들은 원주율을 '(원주) ${\div}$ (지름)'의 대수적인 식으로 이해하려는 성향이 강하였으며, 원주율의 상수성과 무한성을 깊이 있게 이해하고 있는 학생은 극히 적었다. 반면에 과제에 대한 토론 활동은 학생들이 원주율의 근사성에 대한 아이디어를 발견할 수 있는 기회를 제공하였다. 이상의 결과를 종합하여, 초등학교에서의 원주율 지도와 관련하여 원주율을 원의 지름을 단위길이로 원의 둘레를 측정하여 얻을 수 있는 값으로 도입할 것과 공학적 도구 등을 이용하여 직관적인 방법을 통해 이해하도록 할 것, 원주율 개념이 가지는 본질적인 의미를 이해할 수 있도록 다양한 상황을 통해 도입할 것을 제안하였다.

• 대한수학회보
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• 제52권2호
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• pp.439-452
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• 2015

In this paper we introduce and study the new properties ($W_{\Pi}$), ($UW_{{\Pi}_a}$), ($UW_E$) and ($UW_{\Pi}$). The main goal of this paper is to study relationship between these new properties and other Weyl type theorems. Moreover, we reconsider several earlier results obtained respectively in [11], [18], [14], [1] and [13] for which we give stronger versions.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.391-401
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• 2019

A module is said to be ${\pi}$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this article, we focus on the class of modules having the ${\pi}$-extending property by looking at the singularity of quotient submodules. By doing so, we provide counterexamples, using hypersurfaces in projective spaces over complex numbers, to show that being generalized ${\pi}$-extending is not inherited by direct summands. Moreover, it is shown that the direct sums of generalized ${\pi}$-extending modules are generalized ${\pi}$-extending.

• 폴리머
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• 제38권5호
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• pp.632-639
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• 2014

Trimellitic anhydride chloride와 2,7-dihydroxynaphthalene을 이용하여 2,7-dihydroxynaphthalene bis(trimellitate anhydride) (2,7-TA)의 무수물 단량체를 합성하였다. 합성된 2,7-TA와 p-xylylenediamine 및 2,2'-bis(trifluoromethyl) benzidine(TFB)을 다양한 몰 비로 반응하여 얻은 폴리아믹산(polyamic acid, PAA)을 유리판에서 열처리하여 에스터기를 가지는 폴리이미드 공중합체(copolyimide, Co-PI)를 합성하였다. 합성된 Co-PI는 TFB의 몰 비 조성에 따라 열적 성질, 가스 투과도, 및 광학 성질 등을 조사하였다. 용액 캐스팅으로 합성된 Co-PI 필름은 유연하고 질긴 성질을 보였다. Co-PI 필름은 모두 투명하였으며, 각 필름의 cut-off wavelength은 370~395 nm이었고, 노란색 지수는 3.55~7.63의 비교적 낮은 값을 보여주었다. Co-PI 필름의 열적 성질들은 TFB의 몰 비가 증가할수록 증가하였지만, 산소 차단성과 광학 투명성에서는 반대의 결과를 보여주었다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권1호
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• pp.1-29
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• 2014

When taught the precise definition of ${\pi}$, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that ${\pi}$ has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant nor formally proves that it is a constant. In this study, we aim to investigate prospective teachers' conceptual understanding of ${\pi}$, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of ${\pi}$, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation.

• 대한수학회보
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• 제49권5호
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• pp.1027-1040
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• 2012

The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.

• ETRI Journal
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• 제29권6호
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• pp.838-840
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• 2007

The relation between the allowed range of variation of polarization controller wave-plates angles and the respective polarization scattering properties is investigated. It is demonstrated that a nearly uniform polarization scattering over the Poincare sphere is obtained using a concatenation of three polarization controllers with angles randomly changed between $-{\pi}$/4 and ${\pi}$/4. It is also shown that an improvement of the scattering properties is obtained if the configuration angles are allowed to change between $-{\pi}$/2 and ${\pi}$/2.

• 대한수학회지
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• 제41권1호
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• pp.39-50
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• 2004

In [25] Taskinen shows that if $\{E_n\}_n\;and\;\{F_n\}_n$ are two sequences of Frechet spaces such that ($E_m,\;F_n$) has the BB-property for all m and n then (${\Pi}_m\;E_m,\;{\Pi}_n\;F_n$) also has the ΒΒ-property. Here we investigate when this result extends to (i) arbitrary products of Frechet spaces, (ii) countable products of DFN spaces, (iii) countable direct sums of Frechet nuclear spaces. We also look at topologies properties of ($H(U),\;\tau$) for U balanced open in a product of Frechet spaces and $\tau\;=\;{\tau}_o,\;{\tau}_{\omega}\;or\;{\tau}_{\delta}$.

• 대한수학회보
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• 제53권3호
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• pp.925-942
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• 2016

We study the structure of rings whose principal right ideals contain a sort of two-sided ideals, introducing right ${\pi}$-duo as a generalization of (weakly) right duo rings. Abelian ${\pi}$-regular rings are ${\pi}$-duo, which is compared with the fact that Abelian regular rings are duo. For a right ${\pi}$-duo ring R, it is shown that every prime ideal of R is maximal if and only if R is a (strongly) ${\pi}$-regular ring with $J(R)=N_*(R)$. This result may be helpful to develop several well-known results related to pm rings (i.e., rings whose prime ideals are maximal). We also extend the right ${\pi}$-duo property to several kinds of ring which have roles in ring theory.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 춘계학술대회 학술발표 논문집
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• pp.252-255
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• 1997

In this paper, we will propose the methodology of data analysis using the fuzzy property set model. In real world, the data can be represented with the object. $\theta$. and the property, $\pi$, and its has-property relation, P. Then, the conceptual space can be defined with the chosen properties. Each object has a unique location in the conceptual space. In Fuzzy mode, the fuzzy property, and fuzzy conceptual space can be redefined. To analyze data using the fuzzy property set model, the rough set need to be defined in the fuzzy conceptual space.