• The Korean Journal of Applied Statistics
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• v.18 no.3
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• pp.689-699
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• 2005

We usually use $S^2=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n-1}$ as sample variance. Korean high school text-books use $S^2_n=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n}$as sample variance. We can compare the above two definitions of sample variance through their theoretical relationship and simulation.

• Journal of the Korean Society of Clothing and Textiles
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• v.22 no.1
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• pp.41-48
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• 1998

An investigation made of the easing contraction ratio according to sewing conditions (eased seam angle; 0$^{\circ}$ 20$^{\circ}$ 30$^{\circ}$ 45$^{\circ}$ 60$^{\circ}$ 70$^{\circ}$ 90$^{\circ}$, stitch density; 38 stitches/3 cm(N1.0), 26 stitches/ 3 cm(N1.5), 19 stitches/3 cm(N2.0), 14 stitches/3 cm(N2.5), 12 stitches/3 cm(N3.0), thread; sp 60' s/2) by lockstitch industrial sewing machine with shirring foot. The results abstained were as follows: 1. The lower the stitch density , the higher the easing contraction ratio. 2. The easing contraction ratio at 0$^{\circ}$ and 90$^{\circ}$ were lower than bias angles (20$^{\circ}$, 30$^{\circ}$, 45$^{\circ}$, 60$^{\circ}$, 70$^{\circ}$). 3. As the results of visual test, the maximum easing conditions were Fl -0$^{\circ}$.20$^{\circ}$.30$^{\circ}$.45$^{\circ}$-12 stitches/3 cm(N3.0), 60$^{\circ}$. 70$^{\circ}$. 90$^{\circ}$-14 stitches/3 cm(N2.5), F2 -0$^{\circ}$. 20$^{\circ}$.30$^{\circ}$.60$^{\circ}$.70$^{\circ}$.90$^{\circ}$-19 stitches/ 3 cm(N2.0), 45$^{\circ}$ -14 stitches/3 cm(N2.5), and F3 -0$^{\circ}$.20$^{\circ}$.30$^{\circ}$.45$^{\circ}$.60$^{\circ}$.70$^{\circ}$.90$^{\circ}$-19 stitches/3 cm (N2.0). 4. Approximately easing contraction ratio was obtained as 2.0% (N1.0)~ 10.2% (N3.0) in F1, 6.7% (N1.0)~ 15.7% (N2.0) in F2, and 5.2% (N1.0)~ 12.1% (N2.0) in F3, according to different angles on the sleeve cap curve line. 5. As a resets of SPSS PC) statistics analysis, it confirmed the relations which were observed between easing contration ratio and stitch density, and easing contraction ratio was correlated with bending properties.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.50 no.12
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• pp.599-606
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• 2001

In this paper, the ac breakdown characteristics of pure Ar, Kr and $N_2$ gas with gas pressure range of 58.8-137.3[kPa] under uniform and non-uniform fields were investigated, and the measured values were compared with those In Ar/$N_2$ and Kr/$N_2$ gas mixtures with pressure varying. Summarizing the experimental results, the breakdown voltages of Pure $N_2$gas, under uniform and non-uniform fields, were increased about 4.8 and 1.1 times than those of pure Ar gas, and about 4.4 and 1.2 times than those of pure Kr gas, and the ac breakdown voltage increased with the pressure increasing. The breakdown voltages of Ar/$N_2$ gas mixtures were decreased with decreasing the mixture ratio of Pure $N_2$ gas. In case of Ar(85%)/$N_2$ (15%) and Ar(70%)/$N_2$ (30%) gas mixtures comparing to the pure Ar gas, the breakdown voltages under uniform field were increased about 1.8 and 2.2 times, and under non-uniform field were increased about 1.1 and 1.3 times at the pressure of 101.3[kPa]. Also, in case of Kr(85%)/$N_2$ (15%) and Kr(70%)/$N_2$ (30%) gas mixtures comparing to the pure Kr gas, the breakdown voltages under uniform field were increased about 1.7 and 2.0 times, and under non-uniform field were increased about 1.0 and 1.2 times. Corona inception voltage of Kr(70%)/$N_2$(30%) gas mixtures under non-uniform fields were increased about 1.28 times than those of Ar(70%)/$N_2$ (30%) gas mixtures. In case of practical incandescent lamps, luminous and lifetime of Kr(70%)/$N_2$ (30%) gas mixtures were increased about 1.15 and 1.21 times than those of Ar(70%)/$N_2$ (30%) gas mixtures.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.

• Asian-Australasian Journal of Animal Sciences
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• v.27 no.11
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• pp.1608-1614
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• 2014

The objective of this study was to investigate the different dietary ratios of n-6 to n-3 (n-6/n-3) fatty acid (FA) on performance and n-6/n-3 FA in muscles of broiler chickens. A total of 300 one-day-old Cobb chicks were randomly assigned to 3 treatments of 10 replicates in each (10 birds/replicate). Birds were fed on a corn-soybean meal-based diet containing 1% oil during starter (day 1 to 21) and 2% oil during finisher (day 22 to 39) phases, respectively. Treatments of high, medium and low dietary n-6/n-3 FA were formulated by replacing rice bran oil with linseed oil to achieve n-6/n-3 FA close to >20:1, 10:1 and 5:1, respectively. Average daily gain, average daily feed intake, and feed conversion ratio were similar (p>0.05) among the treatments. Serum glucose, cholesterol and triglycerides concentrations were not affected (p>0.05) by dietary treatments. In breast, concentration of C18:3n-3 was significantly greater (p = 0.001) for medium and low vs high n-6/n-3 FA, while concentrations of C20:5n-3, C22:6n-3, total n-3 FA, and n-6/n-3 FA were significantly higher for low vs medium, and medium vs high dietary n-6/n-3 FA. In contrast, concentrations of C18:2 and mono-unsaturated FA (MUFA) were lower for low vs high dietary n-6/n-3 FA. In thigh muscles, concentrations of C20:5n-3 were higher (p<0.05) for medium and low vs high dietary n-6/n-3 FA, and concentrations of C18:3n-3, C22:6, and n-3 FA were greater (p<0.05) for medium vs high, low vs medium dietary n-6/n-3 FA. However, concentrations of C18:1, MUFA, n-6/n-3 were lower (p<0.05) for low and medium vs high dietary n-6/n-3 FA. In conclusion, lowering the dietary n-6/n-3 FA did not affect the performance of chickens, but enhanced beneficial long-chain n-3 FA and decreased n-6/n-3 FA in chicken breast and thigh, which could be advantageous for obtaining healthy chicken products.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1071-1085
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• 2016

For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.

• Journal of Adhesion and Interface
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• v.14 no.2
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• pp.57-67
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• 2013

The incompletion of TIR (Total Internal Reflection) in FTIR (Frustrated Total Internal Reflection) touch screen has been investigated as follows. Assuming a 3 layer thin film of medium1 ($n_1$)-medium2 ($n_2$)-medium3 ($n_3$) with refraction indices of $n_1=n_3{\neq}n_2$, it was theoretically proven that FTIR or OT (ordinary transmission) phenomena might happen through medium2 from medium1 to medium3 relying on relative difference in $n_1(=n_3)$ and $n_2$, and that the formulae for FTIR and OT could be transformed into each other depending on the number state (imaginary or real) of the light wave phase. In parallel to the theoretical analysis, the incompletion of TIR in acrylate due to external contacts was also elucidated from the experimental and phenomenological viewpoints. On the basis of this considerate work, we explained how to improve the touching performance for better FTIR touch screen.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.6
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• pp.1115-1121
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• 2007

[ $Bi_2Sr_2Ca{_{n-1}}Cu_nO_x$ ](n=0,1,2) thin fans have been fabricated by co-deposition at an ultra-low growth rate using ion beam sputtering(IBS) method. Bi 2212 phase appeared in the temperature range of 750 and $795^{\circ}C$ and single phase of Bi 2201 existed in the lower region than $785^{\circ}C$. Whereas, $PO_3$ dependance on structural formation was scarcely observed regardless of the pressure variation. And high quality of c-axis oriented Bi 2212 thin film with $T_c$(onset) of about 90 K and $T_c$(zero) of about 45 K is obtained. Only a small amount of CuO in some films was observed as impurity, and no impurity phase such as $CaCuO_2$ was observed in all of the obtained films.

• East Asian mathematical journal
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• v.19 no.1
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• pp.73-80
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• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.1-37
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• 2004

We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.