• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.19-25
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• 2010

$3{\times}3{\times}3$ is the meaningful smallest product of three chains of each size 2n+1 since $1{\times}1{\times}1$ is a 1-element poset. The linear discrepancy of the product of three chains $2n{\times}2n{\times}2n$ is found as $6n^3-2n^2-1$. But the case of the product of three chains $(2n + 1){\times}(2n + 1){\times}(2n + 1)$ is not known yet. In this paper, we determine ld$(3{\times}3{\times}3)$ as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.

• Korean Journal of Medicinal Crop Science
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• v.3 no.1
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• pp.61-65
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• 1995

Karyotype analysis was carried out in four lines of Bupleurum falcatum L. cultivated in Korea and SDS-PAGE was applied to determine the seed protein profiles among the lines. Chromosomes were classified into two groups, large and small ones. Two kinds of karyotype, 2n=20 and 2n=26, were identified. Chromosome 1 of 2n=20 were all submedian, while that of 2n=26 were median. Chromosomes 2, 3 and 5 of 2n=20 showed polymorphism in size and arm-ratio. Chromosome 2 was submedian, while others were median in the line of 2n=26. Karyotypcs of cultivars native of Korea were similiar each other, while those introduced from Japan showed different patterns. In SDS PAGE gels, qualitative difference s in high molecular weight proteins, more than 45KD, were detected among the lines. The numbers of specific band were three in lines of 2n=20 and two in 2n=26.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.4
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• pp.18-23
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• 1976

We have obtained the solution of van der Pol's equation characterized by an arctangent nonlinearity, using the perturbation method by writing periodicity conditions: $$X^{(n)}(2{\pi})-X^{(n)}(0)=0$$ $$X^{(n)'}(2{\pi})-X^{(n)'}(0)=0 (n=0,1,2......)$$ together with the starting condition: $$X^{(n)}(\frac{\pi}{2})=0,\;X^{(n)}'(\frac{\pi}{2})=-R^{(n)}$$. Our results agree with Liapunov's theorem and our calculated value is more similar to Murata's measured value than Murata's calculated value.

• Korean Journal of Crystallography
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• v.15 no.2
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• pp.83-87
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• 2004

An organometallic complex. $Me_2Pt(PPh_2CH_2C(t-Bu)=N-N=CMe(2-py)-\kappa^2N,P)$ was synthesized from phosphinohydrazone $Ph_2PCH_2C(t-Bu)=NNH_2$, 2-acetylpyridine, and $[PtMe2({\mu}-SMe_2)]_2$. The molecular structure of this complex has been determined by X-ray diffraction. Crystallographic data: monoclinic, space group $P2_1/n,\;a=11.6926(7)\;{\AA},\;b=15.6607(19)\;{\AA},\; c=14.6125(6)\;{\AA},\;\beta=93.018(4)^{\circ},\;Z=4,\;V=2672.0(4)\;{\AA}^3$. The structure was solved by direct methods and refined by full-matrix least-squares methods to give a model with a reliability factor R = 0.0363 for 5238 reflections.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.95-101
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• 2014

An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

• Electrical & Electronic Materials
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• v.7 no.1
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• pp.25-31
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• 1994

Properties of oxynitride films reoxidized by $N_2{O}$ gas after thermal oxidation and $N_2{O}$ oxide films directly oxidized by using $N_2{O}$ gas on the bare silicon wafer have been studied. From the AES analysis, nitrogen pile-up at the interface of Si/oxynitride and Si/$N_2{O}$ oxide has observed. $N_2{O}$ oxide and oxynitride films have the self-limited characteristics. Therefore, it will be possible to obtain ultra-thin films. Nitrogen pile-up at the interfaces of Si/oxynitride and Si/$N_2{O}$ oxide strengthens film structure and improves dielectric reliability. Although fixed charge densities and interface trap densities of N20 oxide and oxynitride films have somewhat higher than those of thermal $SiO_2{O}$, $N_2{O}$ oxide and oxynitride films showed improved I-V characteristics and constant current stress.

• Korean Journal of Materials Research
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• v.2 no.5
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• pp.330-336
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• 1992

Four distinctive hot pressed and heat treated S${i_3}{N_4}$ceramics, S${i_3}{N_4}$-8%${Y_2}{O_3}$, S${i_3}{N_4}$-6% ${Y_2}{O_3}$-2% $A{l_2}{O_3}$, S${i_3}{N_4}$-4% ${Y_2}{O_3}$-3% $A{l_2}{O_3}$, 그리고 S${i_3}{N_4}$-1% MgO-1% Si$O_2$(in wt%), were prepared and characterized by X-ray diffraction, scanning electron microscopy, image analysis and mechanical tests. The fracture toughness of S${i_3}{N_4}$-8% ${Y_2}{O_3}$specimens containing large elongated grains showed the highest value of about 9.8MPa$m^{1/2}$. Two out of four S${i_3}{N_4}$, ceramics(S${i_3}{N_4}$-6% ${Y_2}{O_3}$-2% $A{l_2}{O_3}$and S${i_3}{N_4}$-4% ${Y_2}{O_3}$-3% $A{l_2}{O_3}$) heat treated at 200 $0^{\circ}C$retained the fracture strength of over 900MPa and fracture toughness of over 8.0MPa$m^{1/2}$. Large ${\beta}$-S${i_3}{N_4}$grains having a diameter larger than 1${\mu}$m appeared to contribute to increase in fracture toughness.

• Korean Journal of Plant Tissue Culture
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• v.25 no.2
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• pp.135-139
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• 1998

Reciprocal interspecific hybrids between N. glauca(2n=24) and N. langsdorffii(2n=18) were obtained by intercrossing. One hundred percent of F$_1$ seeds was produced from intercrossing of N. glauca $\times$ N. langsdorffii, whereas the frequency of F$_1$ hybrid seed formation from N. langsdorffii $\times$ N. glauca was very low. However, all the hybrid seeds were germinated well and then grown to normal plantlets. All the plants of F$_1$ hybrids have chromosome number of interspecific hybrids (2n=21). From observation of morphological characteristic, the structure of petrol, leaf, flower, and the morphology of pollen have characteristics of F1 hybrid. Spontaneous tumors (genetic tumor) were formed from each F$_1$ hybrid; the genetic tumor arose at the reproductive phase when the maternal type of F$_1$ hybrid came from N. glauca, while the genetic tumor arose only after reproductive phase when the maternal type of F$_1$ hybrid came from N. langsdorffii. The genetic tumor actively proliferated on hormone-free medium and produced numerous teratoma shoots. In addition, normal leaf or stem explants of F$_1$ hybrid produced calli on hormone-free medium after 15 days of culture, the calli produced new numerous teratoma shoots after 30 days. The frequency of teratoma shoot formation from rnterspecific hybrid was higher in the N. glauca $\times$ N. langsdorffii than in the N. langsdorffii $\times$ N. glauca. Root development from the teratoma shoots was hardly obtained. Teratoma shoots without roots in vitro can form genetic tumor at the vegetative growth phase after tissue culture.

• Korean Journal of Metals and Materials
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• v.48 no.5
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• pp.456-461
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• 2010

We investigated the In-based ohmic contacts on Nitrogen-face (N-face) n-type GaN, as well as Ga-face n-type GaN, for InGaN-based vertical Light Emitting Diodes (LEDs). For this purpose, we fabricated Circular Transfer Length Method (CTLM) patterns on the N-face n-GaN that were prepared by using a laser-lift off method, as well as on the Ga-face n-GaN that were prepared by using a dry etching method. Then, In/transparent conducting oxide (TCO) and In/TiW schemes were deposited on the CTLM in order for low resistance ohmic contacts to form. The In/TCO scheme on the Ga-face n-GaN showed high specific contact resistance, while the minimum specific contact resistance was only 3${\times}$10$^{-2}$ $\Omega$-cm$^{2}$ after annealing at 300${^{\circ}C}$, which can be attributed to the high sheet resistance of the TCO layer. In contrast, the In/TiW scheme on the Ga-face n-GaN produced low specific contact resistance of 2.1${\times}$10$^{5}$ $\Omega$-cm$^{2}$ after annealing at 500${^{\circ}C}$ for 1 min. In addition, the In/TiW scheme on the N-face n-GaN also resulted in a low specific contact resistance of 2.2${\times}$10$^{-4}$ $\Omega$-cm$^{2}$ after annealing at 300${^{\circ}C}$. These results suggest that both the Ga-face n-GaN and N-face n-GaN.

• Korean Journal of Soil Science and Fertilizer
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• v.45 no.4
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• pp.544-550
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• 2012

This study was conducted to investigate the characteristic factors which have been influenced on nitrous oxide ($N_2O$) emissions related to the environment change of nitrogen application level, rainfall and temperature during the potato cultivation at black volcanic ash soil from 2010 to 2011. During the potato cultivation, the more amount of nitrogen fertilizer applied, $N_2O$ emissions amounts were released much. $N_2O$ emissions with the cultivation time were released much at the first and middle of cultivation with heavy rainfall, but it was released very low until the end of cultivation and drought season. $N_2O$ emissions mainly were influenced by the rainfall and soil water content. The correlation (r) with $N_2O$ emissions, soil wate, soil temperature in 2010 were very significant at $0.6251^{**}$ and $0.6082^{**}$ respectively, but soil EC was not significant to 0.10824. In 2011, soil temperature was very significant at $0.4879^{**}$, but soil water and soil EC were not significant at 0.0468 and 0.0400 respectively. Also, $NH_4$-N was very significant at $0.7476^{**}$, but $NO_3$-N and soil nitrogen ($NO_3-N+NH_4-N$) were not significant at 0.0843 and 0.1797, respectively. During the potato cultivation period, the average emissions factor of 2 years released by the nitrogen fertilizer application was presumed to be 0.0040 ($N_2O-N\;kg\;N^{-1}\;kg^{-1}$). This factor was lower about 2.5 times than the IPCC guideline default value (0.0100 $N_2O-N\;kg\;N^{-1}\;kg^{-1}$).