• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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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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• v.52 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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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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• v.1 no.1
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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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.30 no.4
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• pp.595-600
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• 1997

The oil content and composition of squid visera were determined to obtain data for utilization of this by-product. There was no significant difference in the glycolipid (GL) and phospholipid (PL) content in Illex argentinus and Todarodes pacificus, but neutral lipid (NL) was different (p<0.05). The viscera oil of I. argentinus contained $30.50\%$ total lipid which consisted of $96.24\%$ NL, $2.63\%$ GL, $2.37\%$ PL, and contained $644mg\%$ cholesterol. The viscera oil of T. pacificus contained $30.20\%$ total lipid which consisted of $94.82\%$ NL, $2.85\%$ GL, $2.34\%$ PL, and contained $1,224\;mg\%$ cholesterol. The NL, GL and PL of viscera oil in I. argentinus mainly consist of triglyceride $(44.01\%)$, esterified steryl glycosides $(58.95\%)$ and phosphatidyl cholines $(32.36\%)$, respertively. Those of viscera oil in T. pacificus mainly consist of triglyceride $(39.63\%)$, monogalactosyl diglycerides $(51.67\%)$ and phosphatidyl cholines $(31.98\%)$, respectively. The major fatty acids of the viscera oil of I. argentinus and T. pacificus were C16 : 0, $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;4\omega6,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$. In Illex argentinus, the fatty acids of NL mainly were $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;4\omega6,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$. PL were $C16\;:\;1\omega7,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$ and GL were $C18\;:\;1\omega9,\;C20\;:\;5\omega3,\;22\;:\;6\omega3$. The major fatty acids of NL in T. pacificus were $C16\;:\;0,\;C18\;:\;1\omega9,\;C20\;:\;4\omega6,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$, PL were $C16\;:\;1\omega7,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$, and GL were $C18\;:\;1\omega9,\;C20\;:\;5\omega3,\;C22\;:\;6\omega3$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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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)

• Communications of the Korean Mathematical Society
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• v.22 no.1
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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 $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• Journal of the Korean Chemical Society
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• v.30 no.3
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• pp.273-281
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• 1986

This study is focused on the correct measurement of the equations for the determination of the impedance parameters-the differential capacity of the double layer $C_d$, solution resistance $R_Q$, transfer resitance $R_i$, and adsorption pseudcapacity $C_{\phi}$/ The application of only an imaginary part of complex function of ${\omega}$ at the sinusoidal steady state indicates the following equations of total impedance: at low frequency $|Z_{LF}|=1/{\omega}_1\;C_{\phi}\;{\sqrt{1+{{\omega}_1}^2/{\omega}^2}$, at high frequency $|Z_{HF}|={\omega}_2/({\omega}_1{\omega}_3C{\phi})({\omega}^2+{{\omega}_2}^2)\;{\sqrt{{({\omega}^2+{\omega}_2{\omega}_3)}^2+{({\omega}_2{\omega}-{\omega_3{\omega})^2}}$. The values of the total impedance of cell, phase angle, and cell current that are necessary for the calculations of impedance parameters were experimentally measured from 200 to 6000Hz for the following supporting electrolytes, 0.5M $Na_2SO_4$, 1M NaCl, 19.373% sea water, 1M HCl, 1M $KNO_3$ and for $10^{-2}M$ KI and 60mM DBNA (Di-iso-Butylnitrosoamine) in these supporting electrolytes. The derived equations in this study shows that the values of impedance parameters of $C_d,\;C_{\phi},\;R_i\;and\;R_Q\;are\;15{\sim}40\;{\mu}F/cm^2,\;162{\sim}758\;{\mu}F/cm^2\;11.5{\sim}57.6\;ohm{\cdot}cm^2\;and\;0.5{\times}10^{-2}{\sim}4.1{\times}10^{-2}\;ohm{\cdot}cm^2$ respectively.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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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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• v.36 no.1
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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.