• 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.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2015년도 학술발표회
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• pp.94-94
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• 2015

기후변화와 변동으로 인한 기상이변이 갈수록 심각해지고 발생 빈도도 잦아짐에 따라 현재의 배수관련 사회기반시설(Drainage Infrastructure)이 이런 문제에 대처할 준비가 잘되어 있는지에 대해 의문점이 제기되고 있다. 현재의 배수관련 사회기반시설의 설계는 이른바 정상성(stationarity)이라는 가정 하에 강우의 강도(Intensity), 지속기간(Duration), 빈도(Frequency)의 관계를 나타내는 I-D-F 곡선을 주로 이용하기 때문에 기후변화로 인한 극치사상(extremes)의 유의한 변화를 나타낼 수가 없다는 한계점을 가지고 있다. 그러나 기후변화는 극한기후(climatic extremes)의 특성을 비정상성(nonstationarity)이라 일컫는 개념으로 바꾸고 있기 때문에 배수관련 기반구조 설계(Drainage Infrastructuredesign)의 기본 가정의 하나인 강우 통계 매개변수의 정상성은 기후변화의 시대에는 더는 유효하지 않을 수 있다. 본 논문에서는 이러한 비정상성을 고려하여 조건부 GEV 분포를 이용하여 지속시간별 확률강우량 과비정상성 I-D-F 곡선식을 유도하였다. 또한, 분포형 홍수유출모형인 S-RAT(Spatial Runoff Assessment Tool)을 이용하여 강우강도의 증가가 설계 최대유량(design peak flows)에 미치는 영향을 분석하였다. 분석결과 지속기간별 차이는 있었지만 고빈도로 갈수록 전반적으로 현행 I-D-F 곡선이 실질적으로 극한강수를 과소평가하고 있으며 정상성 I-D-F 곡선 작성 방법이 기후변화의 배수관련 기반구조물의 능력설계에 적합지 않을 수도 있음을 제시하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.327-344
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• 2009

In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale $\mathbb{T}$ $$\{{{{{{x^{\bigtriangleup\bigtriangleup}(t)+f(t,\;y(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}\atop{y^{\bigtriangleup\bigtriangleup}(t)+g(t,\;x(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}}\atop{\alpha_1x(a)-\beta_1x^{\bigtriangleup}(a)=\gamma_1x(\sigma(b))+\delta_1x^{\bigtriangleup}(\sigma(b))=0,}}\atop{\alpha_2y(a)-\beta_2y^{\bigtriangleup}(a)=\gamma_2y(\sigma(b))+\delta_2y^{\bigtriangleup}(\sigma(b))=0,}}$$ where $\alpha_i$, $\beta_i$, $\gamma_i\;{\geq}\;0$ and $\rho_i=\alpha_i\gamma_i(\sigma(b)-a)+\alpha_i\delta_i+\gamma_i\beta_i$ > 0(i = 1, 2), f(t, y) may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems $x^{\bigtriangledown\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangledown}(t)$ + g(t, x(t)) = 0, $x^{\bigtriangleup\bigtriangledown}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangleup\bigtriangledown}(t)$ + g(t, x(t)) = 0, and $x^{\bigtriangledown\bigtriangleup}(t)$ + f(t, y(t)) = 0, $y^{\bigtriangledown\bigtriangleup}(t)$ + g(t, x(t)) = 0 satisfying similar boundary conditions.

• 대한수학회논문집
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• 제12권2호
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1289-1295
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• 2008

We find the generalized characteristic polynomial of graphs G($F_{1},F_{2},{\cdots},F_{v}$) the semi-zigzag product of G and ${\{F_{i}\}^{v}_{i=1}$ obtained from G by replacing vertices by circulant graphs of vertices and joining $F_{i}$'s along the edges of G. These graphs contain discrete tori and are key examples in the study of network model.

• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.139-149
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• 1997

For split plot designs exact univariate F tests of the within-subjects main effect are based on the assumption of multisample sphericity. Type I error rates and power are reported for the F test and two tests designed for use when multisample sphericity is violated: the $\widetilde{\xi}$-adjusted test and the Corrected Improved General Approximation(CIGA) test.The results indicate that even though the F test and the $\widetilde{\xi}$-adjusted test have better power than the CIGA test in some conditions, the F test and the $\widetilde{\xi}$-adjusted test do not control Type I error rates when the design is unbalanced and the F test dose not have a good control of Type I error rates when sphericity assumption is severely violated.

• 호남수학학술지
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• 제30권4호
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• pp.685-691
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• 2008

Given operators $X_i$ and $Y_i$ (i = 1, 2, ${\cdots}$, n) acting on a Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A acting on $\mathcal{H}$ such that $AX_i$ = $Y_i$ for i= 1, 2, ${\cdots}$, n. In this article, if the range of $X_k$ is dense in H for a certain k in {1, 2, ${\cdots}$, n), then the following are equivalent: (1) There exists a self-adjoint operator A in $\mathcal{B}(\mathcal{H})$ stich that $AX_i$ = $Y_i$ for I = 1, 2, ${\cdots}$, n. (2) $sup\{{\frac{{\parallel}{\sum}^n_{i=1}Y_if_i{\parallel}}{{\parallel}{\sum}^n_{i=1}X_if_i{\parallel}}:f_i{\in}H}\}$ < ${\infty}$ and < $X_kf,Y_kg$ >=< $Y_kf,X_kg$> for all f, g in $\mathcal{H}$.

• Journal of Microbiology
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• 제41권1호
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• pp.1-6
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• 2003

The genetic relatedness of multidrug-resistant pneumococcal isolates of serotypes 19F and 23F was investigated. The DNA fragments digested with Sma I were resolved by pulsed-field gel electrophoresis (PFGE). PFGE analysis of 365. pneumoniae isolates showed 13 different patterns. Among 22 isolates of serotype 19F, 9 different PFGE patterns were present and 14 isolates of serotype 23F isolates represented 5 distinct PFGE patterns. Two isolates of serotype 19F and six isolates of serotype 23F shared the same PFGE pattern (Pattern I). Based on the genetic relatedness within the strains (one genetic cluster was defined as having more than 85% homology), we divided the pneumococcal strains into genefic clusters (Ⅰ, II, III, IV, V, and VI). The 22 strains of serotype 19F belonged to five distinct genetic clusters (I, II, III, IV, V and VI) and 14 strains of serotype 23F represented two genetic clusters (I and II ). These results showed that strains of serotype 19F are genetically more diverse than those of serotype 23F, Serotype 19F isolates with PFGE patterns H and I appeared to be less related to those of the remaining PFCE patterns (A to G) (less than 60% genetic relatedness), but those strains were genetically closely related with serotype 23f. These results suggest that the latter isolates originated from horizontal transfer of the capsular type 19F gene locus to 23F pneumococcal genotypes. In conclusion, the multidrug-resistant pneumococcal isolates of serotype 19f and 23F isolated in Korea are the result of the spread of a limited number of resistant clones.

• 대한수학회보
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• 제46권2호
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• pp.235-243
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• 2009

In this paper we will investigate the superstability of the generalized d'Alembert type functional equations ${\sum}^m_{i=1}f(x+{{\sigma}^i}(y))$ = kg(x)f(y) and ${\sum}^m_{i=1}f(x+{{\sigma}^i}(y))$ = kf(x)g(y).

• 충청수학회지
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• 제27권3호
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• pp.455-467
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• 2014

In this paper, we consider the additive set-valued functional equation $nf(\sum_{i=1}^{n}x_i)=\sum_{i=1}^{n}f(x_i){\oplus}\sum_{1{\leq}i&lt;j{\leq}n}f(x_i+x_j)$ where $n{\geq}2$ is an integer, and prove the Hyers-Ulam stability of the functional equation.