• 충청수학회지
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• 제24권1호
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• pp.113-119
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• 2011

Let T be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. An operator T is called class A operator if ${\left|{T^2}\right|}{\geq}{\left|{T^2}\right|}$ and is called class A(k) operator if $({T^*\left|T\right|^{2k}T})^{\frac{1}{k+1}}{\geq}{\left|T\right|}^2$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class A operators and consider the tensor products of class A(k) operators.

• 미생물학회지
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• 제5권1호
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• pp.34-38
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• 1967

Theoretical analysis reported in this paper is on the varities of the growth rate of Chlorella ellipsoidea due to the amount of available phosphorus for the purpose of the continual mass culture. Available phosphorus in the culture media of the Chlorella was also estimated at a limiting factor as this experiment. The equation between the concentration of Chlorella n and growth period t is $\frac{dn}{dt}=Kn$, and the functional relation between the Specific growth rate K and steady state period T is the following: $K=\frac{2.303}{T}$log\frac{n}{no}$ ($n_o$=initial concentration).

• East Asian mathematical journal
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• 제22권2호
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• pp.131-149
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• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• 대한수학회지
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• 제42권3호
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• pp.529-541
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• 2005

An operator T belonging to the algebra B(H) of bounded linear transformations on a Hilbert H into itself is said to be posinormal if there exists a positive operator $P{\in}B(H)$ such that $TT^*\;=\;T^*PT$. A posinormal operator T is said to be conditionally totally posinormal (resp., totally posinormal), shortened to $T{\in}CTP(resp.,\;T{\in}TP)$, if to each complex number, $\lambda$ there corresponds a positive operator $P_\lambda$ such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P_{\lambda}^{\frac{1}{2}}(T-{\lambda}I)|^{2}$ (resp., if there exists a positive operator P such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P^{\frac{1}{2}}(T-{\lambda}I)|^{2}\;for\;all\;\lambda)$. This paper proves Weyl's theorem type results for TP and CTP operators. If $A\;{\in}\;TP$, if $B^*\;{\in}\;CTP$ is isoloid and if $d_{AB}\;{\in}\;B(B(H))$ denotes either of the elementary operators $\delta_{AB}(X)\;=\;AX\;-\;XB\;and\;\Delta_{AB}(X)\;=\;AXB\;-\;X$, then it is proved that $d_{AB}$ satisfies Weyl's theorem and $d^{\ast}_{AB}\;satisfies\;\alpha-Weyl's$ theorem.

• 성인간호학회지
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• 제15권1호
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• pp.33-44
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• 2003

Purpose: The purpose of this study was to identify the patterns and related factors of fatigue in patients with breast cancer undergoing radiotherapy. Method: 31 women with breast cancer receiving radiotherapy were recruited from the out-patient radiologic clinic of the university hospital in Seoul, Korea over a period of 3 months. Data was collected prospectively concerning three points for $5\frac{1}{2}\;-\;6\frac{1}{2}$ weeks : before radiotherapy(T1), 2 weeks after starting radiotherapy(T2) and the completion of radiotherapy(T3). Data were analysed by repeated measure ANOVA, Pearson correlaton, and multiple regression. Result: 1. Score of fatigue increased significantly over the course of radiotherapy. 2. Score of symptom distress and emotional distress increased and functional status scores decreased significantly over time. 3. Fatigue was positively related with symptom distress and emotional distress and negatively related with functional status over the course of radiotherapy. 4. At T2, emotional distress explained 24.7% of the variation in fatigue. At T3, symptom distress(41.9%) and emotional distress(7.2%) explained the variance in fatigue. Conclusion: The results of this study provided evidence that fatigue increased over the course of radiotherapy and symptom distress and emotional distress were influencing factors of fatigue in this group. The results of this study suggest that comprehensive intervention strategy for fatigue should be developed to maintain quality of life during and following radiotherapy considering these factors.

• 대한화학회지
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• 제45권4호
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• pp.293-297
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• 2001

문헌에 보고된 삼중점과 임계점간 기존의 파라수소 증기압 측정값을 이용하여 환원증기압과 환원온도 형태의 아래와 같은 식의 지수와 상수를 구하는데 사용하였다. $lnP_r=2.64-{\frac{2.75}{T_r}}+1.48129lnT_r+0.11T^5_r$ 증기압을 계산하기 위해서 필요한 것은 정상 끓는점($T_b$= 20.268K), 임계압력($P_c$= 1292.81 kPa) 및 임계온도($T_c$= 32.976K)뿐이며 153개 파라수소의 증기압 실험자료에 적용하여 본 결과 전체 평균편차가 0.21% 였다.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.155-163
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• 2004

In this paper, we study oscillation and nonoscillation criteria of solutions for the following nonlinear differential equation $$\[\frac{1}{p(t)}(x^{\prime}(t))^{{\mu}}\]^{\prime}+q(t)x(t)^{{\mu}}=0$$ where ${\mu}$ with ${\mu}{\geq}1$ is a quotient of odd integers.

• 대한수학회보
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• 제49권4호
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• pp.787-797
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• 2012

In this paper the authors study the $L^p$ boundedness for parabolic Littlewood-Paley operator $${\mu}{\Phi},{\Omega}(f)(x)=\({\int}_{0}^{\infty}{\mid}F_{\Phi,t}(x){\mid}^2\frac{dt}{t^3}\)^{1/2}$$, where $$F_{\Phi,t}(x)={\int}_{p(y){\leq}t}\frac{\Omega(y)}{\rho(y)^{{\alpha}-1}}f(x-{\Phi}(y))dy$$ and ${\Omega}$ satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.41-49
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• 2008

We show the existence of a negative solution for the system of the following nonlinear wave equations with critical growth, under Dirichlet boundary condition and periodic condition $$u_{tt}-u_{xx}=au+b{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha-1}{\upsilon}_+^{\beta}+s{\phi}_{00}+f,\\{\upsilon}_{tt}-{\upsilon}_{xx}=cu+d{\upsilon}+\frac{2{\alpha}}{{\alpha}+{\beta}}u_+^{\alpha}{\upsilon}_+^{{\beta}-1}+t{\phi}_{00}+g,$$ where ${\alpha},{\beta}>1$ are real constants, $u_+={\max}\{u,0\},\;s,\;t{\in}R,\;{\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator and f, g are ${\pi}$-periodic, even in x and t and bounded functions.

• 대한수학회보
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• 제44권1호
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• pp.83-86
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• 2007

We determine the largest integer i such that $0 and the coefficient of $t^{i}$ is odd in the polynomial $(1+t+t^{2}+{\cdots}+t^{n})^{n+1}$. We apply this to prove that the co-index of the tangent bundle over $FP^{n}$ is stable if $2^{r}{\leq}n<2^{r}+\frac{1}{3}(2^{r}-2)$ for some integer r.