• Korean Journal of Mathematics
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• 제16권3호
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• pp.323-334
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• 2008

We define injective and projective representations of quivers with two vertices with n arrows. In the representation of quivers we denote n edges between two vertices as ${\Rightarrow}$ and n maps as $f_1{\sim}f_n$, and $E{\oplus}E{\oplus}{\cdots}{\oplus}E$ (n times) as ${\oplus}_nE$. We show that if E is an injective left R-module, then $${\oplus}_nE{\Longrightarrow[50]^{p_1{\sim}p_n}}E$$ is an injective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $p_i(a_1,a_2,{\cdots},a_n)=a_i,\;i{\in}\{1,2,{\cdots},n\}$. Dually we show that if $M_1{\Longrightarrow[50]^{f_1{\sim}f_n}}M_2$ is an injective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are injective left R-modules. We also show that if P is a projective left R-module, then $$P\Longrightarrow[50]^{i_1{\sim}i_n}{\oplus}_nP$$ is a projective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $i_k$ is the kth injection. And if $M_1\Longrightarrow[50]^{f_1{\sim}f_n}M_2$ is an projective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are projective left R-modules.

• 호남수학학술지
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• 제26권4호
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• pp.379-389
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• 2004

Given operators X and Y acting on a Hilbert space ${\mathcal{H}}$, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for $i=1,2,{\cdots},n$. In this article, we obtained the following : Let ${\mathcal{H}}$ be a Hilbert space and let ${\mathcal{L}}$ be a commutative subspace lattice on ${\mathcal{H}}$. Let X and Y be operators acting on ${\mathcal{H}}$. Then the following statements are equivalent. (1) There exists an operator A in $Alg{\mathcal{L}}$ such that AX = Y, A is positive and every E in ${\mathcal{L}}$ reduces A. (2) sup ${\frac{{\parallel}{\sum}^n_{i=1}\;E_iY\;f_i{\parallel}}{{\parallel}{\sum}^n_{i=1}\;E_iX\;f_i{\parallel}}}:n{\in}{\mathbb{N}},\;E_i{\in}{\mathcal{L}}$ and $f_i{\in}{\mathcal{H}}<{\infty}$ and <${\sum}^n_{i=1}\;E_iY\;f_i$, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$, $n{\in}{\mathbb{N}}$, $E_i{\in}{\mathcal{L}}$ and $f_i{\in}H$.

• 분석과학
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• 제26권1호
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• pp.51-60
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• 2013

본 연구는 c-$C_nF_{2n}$ (n=8, 9)과 $C_{10}F_{18}$ (perfluorodecalin)의 가능한 분자구조를 여러 이론 수준에서 최적화 하였으며, 각 화합물의 가장 안정한 분자구조 (global minimum)를 확인하고 전자 친화도를 계산하여 구조적 특성에 따른 전자 친화도와의 상호 연관성을 고찰하였다. 보다 정확한 전자 친화도를 계산하기 위하여 진동주파수를 계산하여 영점 진동 에너지를 보정하였으며, IR 스펙트럼을 예측하였다. 전자 친화도는 c-$C_8F_{16}$의 경우 ortho 위치에 두 개의 $-CF_3$ 치환기가 붙어있는 구조에 대하여 영점 진동 에너지를 보정한 MP2 이론 수준에서 1.18 eV로 계산되었으며, c-$C_9F_{18}$의 경우 하나의 $-CF_3$와 하나의 $-C_2F_5$ 치환기가 인접하여 붙어있는 구조에 대하여 1.37 eV로, 그리고 $C_{10}F_{18}$인 perfluorodecalin의 경우 1.38 eV로 예측되었다.

• Journal of Astronomy and Space Sciences
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• 제30권4호
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• pp.223-230
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• 2013

Sudden enhancements of daytime NmF2 appeared in Anyang ionosonde data during summer seasons in 2006-2007. In order to investigate the causes of this unusual enhancement, we compared Anyang NmF2's with the total electron contents (GPS TECs) observed at Daejeon, and also with ionosonde data at at mid-latitude stations. First, we found no similar increase in Daejeon GPS TEC when the sudden enhancements of Anyang NmF2 occurred. Second, we investigated NmF2's observed at other ionosonde stations that use the same ionosonde model and auto-scaling program as the Anyang ionosonde. We found similar enhancements of NmF2 at these ionosonde stations. Moreover, the analysis of ionograms from Athens and Rome showed that there were sporadic-E layers with high electron density during the enhancements in NmF2. The auto-scaling program (ARTIST 4.5) used seems to recognize sporadic-E layer echoes as a F2 layer trace, resulting in the erroneous critical frequency of F2 layer (foF2). Other versions of the ARTIST scaling program also seem to produce similar erroneous results. Therefore we conclude that the sudden enhancements of NmF2 in Anyang data were due to the misrecognition of sporadic-E echoes as a F-layer by the auto-scaling program. We also noticed that although the scaling program flagged confidence level (C-level) of an ionogram as uncertain when a sporadic-E layer occurs, it still automatically computed erroneous foF2's. Therefore one should check the confidence level before using long term ionosonde data that were produced by an auto-scaling program.

• 자연과학논문집
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• 제10권1호
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• pp.9-12
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• 1998

본 논문에서는 $\psi : E \to F$가 섬유 화이버 함수일 때 후합성 $\psi :C_B(Y, E) \to C_B(Y, F)$도 섬유 화이버 함수이고, (X, A)가 닫힌 섬유 화이버 함수일 때 전합성 $\upsilon : C_B(X, E) \to C_B(A, E)$ 도 섬유 화이버 함수임을 보인다.

• 대한수학회논문집
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• 제21권2호
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• 한국자기학회지
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• 제10권3호
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• pp.106-111
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• 2000

페라이트 도금 방법으로 M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08)와 N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$(x=0.00~0.15)의 스피넬 페라이트 박막을 제작하였다. 반응용액의 조성비 변화에 따라 형성된 박막의 조성비와 성장속도를 조사하였다. 제조한 시료들의 결정성과 미세구조는 x-선 회절분석과 전자현미경으로 조사하고, 시료의 자기적 성질을 진동 시료형 자력계를 사용하여 조사했다. 조성비 x가 증가함에 따라 격자상수는 M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08) 박막에서 증가하지만, N $i_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.15) 박막에서 감소한다. M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x = 0.00~0.08) 박막의 포화자화는 419 emu/㎤에서 394 emu/㎤ 의 값을 가져 N $i_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.15)의 $M_{s}$ 보다 높게 나타났다. 보다 높게 나타났다. 보다 높게 나타났다.

• 대한수학회지
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• 제36권5호
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• pp.945-958
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• 1999

Let E be an elliptic curve over with complex multiplication. Suppose that E is defined over F= (j(E)). We study possible degrees of F-isogenies of E.

• 대한수학회논문집
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• 제9권4호
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• pp.837-846
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• 1994

Let A denote a unital normed algebra over a field K = R or C and let e be the identity of A. Given $a \in A$ and $x \in A$ with $\Vert x \Vert = 1$, let $$ V(A, a, x) = {f(ax) : f \in A', f(x) = 1 = \Vert f \Vert}. $$ Then the (Bonsall and Duncan) numerical range of an element $a \in A$ is defined by $$ V(a) = \cup{V(A, a, x) : x \in A, \Vert x \Vert = 1}, $$ where A' denotes the dual of A. In [2], $V(a) = {f(a) : f \in A', f(e) = 1 = \Vert f \Vert}$.

• 대한수학회보
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• 제57권5호
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• pp.1095-1113
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• 2020

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fⁿf^(k) + Q_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z), where $Q_{d_*}(z,f)$ and Q_d(z, f) are differential polynomials in f with small functions as coefficients, of degree d_* (≤ n - 1) and d (≤ n - 2) respectively, R, p₁, p₂ are non-vanishing small functions of f, and α, α₁, α₂ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.