• 대한수학회보
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• 제55권3호
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• pp.957-965
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• 2018

We study the class $C{\mathcal{V}} ({\Omega})$ of analytic functions f in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}$ : ${\mid}z{\mid}$ < 1} of the form $f(z)=z+{\sum}_{n=2}^{\infty}a_nz^n$ satisfying $$1+\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}{\in}{\Omega},\;z{\in}{\mathbb{D}}$$, where ${\Omega}$ is a convex and proper subdomain of $\mathbb{C}$ with $1{\in}{\Omega}$. Let ${\phi}_{\Omega}$ be the unique conformal mapping of $\mathbb{D}$ onto ${\Omega}$ with ${\phi}_{\Omega}(0)=1$ and ${\phi}^{\prime}_{\Omega}(0)$ > 0 and $$k_{\Omega}(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\exp}\({\displaystyle\smashmargin{2}{\int\nolimits_{0}}^t}{\zeta}^{-1}({\phi}_{\Omega}({\zeta})-1)d{\zeta}\)dt$$. Let $z_0,z_1{\in}{\mathbb{D}}$ with $z_0{\neq}z_1$. As the first result in this paper we show that the region of variability $\{{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0)\;:\;f{\in}C{\mathcal{V}}({\Omega})\}$ coincides wth the set $\{{\log}\;k^{\prime}_{\Omega}(z_1z)-{\log}\;k^{\prime}_{\Omega}(z_0z)\;:\;{\mid}z{\mid}{\leq}1\}$. The second result deals with the case when ${\Omega}$ is the right half plane ${\mathbb{H}}=\{{\omega}{\in}{\mathbb{C}}$ : Re ${\omega}$ > 0}. In this case $CV({\Omega})$ is identical with the usual normalized class of convex univalent functions on $\mathbb{D}$. And we derive the sharp upper bound for ${\mid}{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0){\mid}$, $f{\in}C{\mathcal{V}}(\mathbb{H})$. The third result concerns how far two functions in $C{\mathcal{V}}({\Omega})$ are from each other. Furthermore we determine all extremal functions explicitly.

• Kyungpook Mathematical Journal
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• 제52권3호
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• pp.319-325
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• 2012

The notions of (${\omega}$)compactness and (${\omega}$)paracompactness are studied in product (${\omega}$)topology. The concept of countable (${\omega}$)paracompactness is introduced and some results on this notion are obtained.

• 대한수학회지
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• 제33권3호
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• pp.481-494
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• 1996

We introduced the generalized Sobolev space $H_\omega^s$ in [4]. In this paper, we introduce the space $H_\omega^s(\Omega)$ of the generalized distributions in $H_\omega^s$ with compact supports in $\Omega$ and the local generalized Sobolev spaces $H_{\omega loc}^s(\Omega)$ of the generalized distributions on $\Omega$ which are locally in $H_\omega^s$ and study their properties.

• International Journal of Fluid Machinery and Systems
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• 제1권1호
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• pp.169-180
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• 2008

As a major component of a power plant, a turbine generator must have sufficient reliability. Longer blades have lower natural frequency, thereby requiring that the design of the shaft and blade takes into account the coupling of the blade vibration mode, nodal diameter k=0 and k=1 with vibration of the shaft. The present work analyzes the coupling of the translation motion of the shaft with in-plane vibration of the blades with k=1 modes. At a rotational speed ${\Omega}_1=|{\omega}_s-{\omega}_b|$, the resonance of the blades has a relatively large amplitude. A violent coupled resonance was observed at a rotational speed ${\Omega}_2=|{\omega}_s+{\omega}_b|$. Resonance in blade vibration at ${\Omega}_1=|{\omega}_s-{\omega}_b|$ was experimentally confirmed.

• 한국수산과학회지
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• 제30권4호
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• pp.595-600
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• 1997

오징어 가공부산물인 오징어내장을 효과적으로 사용하기 위한 방법으로 내장에서의 지방 추출 및 추출지방의 특성을 살펴보았다. 그 결과는 다음과 같다. 1) 원양산과 연안산의 총지방량은 각각 $30.50\%,\;30.25\%$였으며 중성지질은 $96.24\%,\;94.82\%$, 당지질은 $2.63\%,\;2.85\%$, 인지질은 $2.37\%,\;2.34\%$으로 나타났으며 콜레스테롤 함량은 $644mg\%,\;1,224mg\%$를 각각 나타내었다. 2) 원양산 및 연안산 오징어의 주요 지방산은 모두 $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;4\omega6,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$으로 나타났으며 중성지방질의 획분조성도 서로 유사하여 품종간의 유의차가 인정되지 않았으나 두군 모두 free fatty acid 함량이 가장 높은 $44.01\%,\;39.63\%$를 각각 나타내었다. 3) 원양산의 분획별 주요지방산은 중성지질획분에서 $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;4\omega6,\;C20\;:\;5\omega3,\;C22\;:\;5\omega3$, 인지질획분에서 $C16\;:\;0,\;C16\;:\;1\omega7,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$ 당지질획분에서 $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$으로 나타났다. 4) 연안산의 분획별 주요지방산은 중성지질획분에서 $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;4\omega6,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$로 나타났으며 인지질획분에서는 $C16\;:\;0,\;C18\;:\;1\omega9,\;C22\;:\;6\omega3$로 당질획분에서 $C16\;:\;0,\;C18\;:\;1\omega9,\;C22\;:\;6\omega3$로 나타났다.

• 대한수학회논문집
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• 제9권2호
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• pp.467-489
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• 1994

Let $\Omega$ be a closed and bounded polygonal domain in R$^2$, or a closed line segment in R$^1$ with boundary $\Gamma$, such that there exists an invertible mapping T : $\Omega$ \longrightarrow $\Omega$ with the following correspondence: x$\in$$\Omega$ ↔ x = T(x) $\in$$\Omega$, (1.1) and (1.2) t $\in$ U$\sub$p/($\Omega$) ↔ t = to T$\^$-1/ $\in$ U$\sub$p/($\Omega$), where $\Omega$ denotes the corresponding reference elements I = [-1,1] and I ${\times}$ I in R$^1$ and R$^2$ respectively, (1.3) U$\sub$p/($\Omega$) = {t : t is a polynomial of degree $\leq$ p in each variable on $\Omega$}, and (1.4) U$\sub$p/($\Omega$) = {t : t = to T $\in$ U$\sub$p/($\Omega$)}.(omitted)

• 대한수학회논문집
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• 제22권1호
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• 대한화학회지
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• 제30권3호
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• pp.273-281
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• 1986

본 연구는 임피던스 파라미터(전기이중층 내의 미분용량 $C_d$, 용핵저향 $R_Q$, 전하이동저항 $R_t$,및 흡착유사용량 $C{\phi}$)를 결정하기 위해 정확한 측정식을 얻는데 주력하낟. 정현파가 정상상태에 있을 때 복소수함수 ${\omega}$중의 허수부분만을 으용하여 구한 전체임피던스식은 낮은 주파수에서 $|Z_{LF}|=1/{\omega}_{1C\phi}{\sqrt{1+{{\omega}_1}^2/{\omega}^2}$에, 높은 주파수에서는 $|Z_{HF}|={\omega}_2/({\omega}_1{\omega}_3C{\phi})({\omega}^2+{{\omega}_2}^2){\sqrt{{({\omega}^2+{\omega}_2{\omega}_3)}^2+{({\omega}_2{\omega}-{\omega_3{\omega})^2}}$에 따름을 나타낸다. 이들 임피던스 파라미터의 계산에 필요한 전체임피던수, 위상각 및 쎌전류값을 .5M $NA_2SO_4$ 또는 1M NaCl, 19.373% 해수, 1M HCl, 1M $KNO_3$ 지지전해질과 이들의 지지전해질내에 각각 $10^{-2}M Kl$ 또는 6mM DBNA를 첨가하여 20~60Hz 범위에서 실험적으로 측정하였다. 본 연구에서 유도한 식은 임피던스 파라미터 $C_d,\;C_{\phi},\;R_t$ 및 $R_Q$의 값들이 각각 $15{\sim}4{\mu}F/cm^2,\;162{\sim}758{\mu}F/cm^2,\;11.5{\sim}57.6ohm{\cdot}cm^2$ 및 $0.5{\times}10^{-2}{\sim}4.1{\sim}10^{-2}\;ohm{\cdot}cm^2$임을 보여준다.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.483-488
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• 2007

Given a set ${\Omega}$, the notion of ${\Omega}-fuzzy$ ideals in a near-ring is introduced, and related properties are investigated. Using fuzzy ideals, ${\Omega}-fuzzy$ ideals are described. Conversely, fuzzy ideals are constructed by using ${\Omega}-fuzzy$ ideals.

• Journal of Dairy Science and Biotechnology
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• 제36권1호
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• pp.32-38
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• 2018

The objective of this research was to determine the grain oil most suitable for the production of omega-3 fatty acids (FAs) in China, in order to supply dietary omega-3 FAs. This study focused on the nutritional significance of omega-3 FAs and the wide search of sources of dietary omega-3 FA from oil grains produced in China. Five oil grains produced in the Yanbian region, namely sesame, flax, peanut, soybean, and corn, were selected and analyzed for their fat content and FA composition. Results showed that the lipid content in sesame, flax, and peanut, which was more than 30%, was higher than that in soybean and corn. The polyunsaturated FA content was found to be directly proportional to omega-3 FA content. Flax showed a considerably higher omega-3 FA content (53.43%) than other samples, suggesting its potential as a source of dietary omega-3 FA. The optimal daily intake of flax for males and females was determined to be 2.99 g (over one table spoon) and 2.06 g (nearly one table spoon), respectively. Flax showed the lowest ratio of omega-6 and omega-3 FA (0.32%), which can help reduce this ratio in the human body; the intake of equal amounts of flax and corn could achieve an optimum ratio of 1:1. These results can prove to be valuable in the preparation of various functional dairy foods in the future.