• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.349-355
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• 2016

For any integer $n{\geq}2$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $n{\geq}2$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes ${\sigma}$ with $gcd({\sigma})=1$ to the connected circulant graphs. It was also shown that the number of palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ is the same number of aperiodic palindromes of n. Let $a_n$ (resp. $b_n$) be the number of aperiodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). Let $c_n$ (resp. $d_n$) be the number of periodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). In this paper, we calculate the numbers $a_n$, $b_n$, $c_n$, $d_n$ in two ways. In Theorem 2.3, we $n_d$ recurrence relations for $a_n$, $b_n$, $c_n$, $d_n$ in terms of $a_d$ for $d{\mid}n$ and $d{\neq}n$. Afterwards, we nd formulae for $a_n$, $b_n$, $c_n$, $d_n$ explicitly in Theorem 2.5.

• Bulletin of the Korean Chemical Society
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• v.20 no.10
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• pp.1200-1204
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• 1999

The reactions of Ru(tpy)Cl3 (tpy = 2,2';6',2"-terpyridine) with new N,N,C-terdentate ligands, 3,2'-annulated-6-(2"-pyridyl)-2-phenylpyridines (1, HL) and the properties of their Ru(II) complexes are described. The distribution ratio of the two possible Ru(II) complexes, a pentaaza-coordinated complex [Ru(tpy)(1-N,N')Cl]+ and a cycloruthenated complex [Ru(tpy)(La-N,N',C)]+ are highly dependent on the length of the polymethylene unit. The trimethylene bridge of the N,N,C-terdentate in pentaaza-coordinated complex is rigid enough to induce an asymmetry in the complex.

• Bulletin of the Korean Chemical Society
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• v.18 no.11
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• pp.1158-1161
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• 1997

The potentiometric methods have been used to determined the protonation constants (logKiH) for the synthesized 1,7,13-trioxa-4,10,16-triazacyclooctadecane-N,N',N''-tri(methylacetic acid) [N3O3-tri(methylacetic acid)] and the stability constants (logKML) of the complexes of divalent and trivalent metal ions with the ligand N3O3-tri(methylacetic acid). The protonation constants of N3O3-tri(methylacetic acid) were 9.70 for logK1H, 9.18 for logK2H, 7.27 for logK3H, 3.38 for logK4H, and 2.94 for logK5H. The stability constants for the complexes of divalent metal ions with N3O3-tri(methylacetic acid) were 10.39 for Co2+, 10.68 for Ni2+, 13.45 for Cu2+, and 13.00 for Zn2+. The order of the stability constants for the complexes of the divalent metal ions with N3O3-tri(methylacetic acid) was Co2+ < Ni2+ < Zn2+ < Cu2+. The stability constants for the complexes of trivalent metal ions with N3O3-tri(methylacetic acid) were 16.20 for Ce3+, 16.40 for Eu3+, 16.27 for Gd3+, and 15.80 for Yb3+. The results obtained in this study were compared to those obtained for similar ligands, 1,7-dioxa-4,10,13-triazacyclopentadecane-N,N',N"-tri(methylacetic acid) and 1,7,13-trioxa-4,10,16-triazacyclooctadecane-N,N',N"-triacetic acid, which have been previously reported.

• Korean Journal of Soil Science and Fertilizer
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• v.44 no.6
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• pp.1232-1238
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• 2011

This experiment was conducted to measure concentration of dissolved $N_2O$ in ground-water of 59 wells and to make emission factor for assessment of indirect $N_2O$ emission at agricultural sector in agricultural areas of Gyeongnam province from 2007 to 2010. Concentrations of dissolved $N_2O$ in ground-water of 59 wells were ranged trace to $196.6{\mu}g-N\;L^{-1}$. $N_2O$ concentrations were positively related with $NO_3$-N suggesting that denitrification was the principal reason of $N_2O$ production and $NO_3$-N concentration was the best predictor of indirect $N_2O$ emission. The ratio of dissolved $N_2O$-N to $NO_3$-N in ground-water was very important to make emission factor for assessment of indirect $N_2O$ emission at agricultural sector. The mean ratio of $N_2O$-N to $NO_3$-N was 0.0035. It was greatly lower than 0.015, the default value of currently using in the Intergovernmental Panel on Climate Change (IPCC) methodology for assessing indirect $N_2O$ emission in agro-ecosystems (IPCC, 1996). It means that the IPCC's present nitrogen indirect emission factor ($EF_{5-g}$, 0.015) and indirect $N_2O$ emission estimated with IPCC's emission factor are too high to use adopt in Korea. So we recommend 0.0034 as national specific emission factor ($EF_{5-g}$) for assessment of indirect $N_2O$ emission at agricultural sector. Using the estimated value of 0.0034 as the emission factor ($EF_{5-g}$) revised the indirect $N_2O$ emission from agricultural sector in Korea decreased from 1,801,576 ton ($CO_2$-eq) to 964,645 ton ($CO_2$-eq) in 2008. The results of this study suggest that the indirect Emission of nitrous oxide from upland recommend 0.0034 as national specific emission factor ($EF_{5-g}$) for assessment of indirect $N_2O$ emission at agricultural sector.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.16 no.1
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• pp.106-113
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• 2002

In this paper, breakdown characteristics of pure Kr, Ar and $N_2$gas with gas pressure range were investigated, and the measured values were compared with those in Ar/$N_2$and Kr/$N_2$gas mixtures with pressure varying. Also, various characteristics with gas mixtures in practical incandescent lamps were investigated. Summarizing the experimental results, the breakdown voltages of $N_2$gas were increased than those of Kr and Ar gas with large molecular weight, and the breakdown voltage increased with gas pressure increasing. The breakdown voltages of Ar/$N_2$and Ar/$N_2$gas mixtures were decreased with decreasing the mixtures ratio of $N_2$gas, and corona inception voltage of Kr/$N_2$gas mixtures under non-uniform fields were increased than those of Ar/$N_2$gas mixtures. In case of tactical incandescent lamps, luminous and lifetime of Kr(70%)/$N_2$(30%) gas mixtures were increased about 94[lm] and 380[hr] than those of Ar(70%)/$N_2$(30%) gas mixtures. and injection pressure of gas mixtures with cooling temperature of 20[$^{\circ}C$] in incandescent lamps were increased about 13[%] than those with cooling temperature of 40[$^{\circ}C$].

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.331-360
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• 2013

Let ${\sigma}_s(N)$ denote the sum of the sth powers of the positive divisors of a positive integer N and let $\tilde{\sigma}_s(N)={\sum}_{d|N}(-1)^{d-1}d^s$ with $d$, N, and s positive integers. Hahn [12] proved that $$16\sum_{k. In this paper, we give a generalization of Hahn's result. Furthermore, we find the formula ${\sum}_{k=1}^{N-1}\tilde{\sigma}_1(2^{n-m}k)\tilde{\sigma}_3(2^nN-2^nk)$ for $m(0{\leq}m{\leq}n)$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1996.11a
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• pp.75-78
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• 1996

The deposition condition Gf TiN films as electrode was studied by sheet resistance, TiN depositon Thickness X-ray diffraction. TiN was made by reactively DC magnetron sputtering with varying $N_2$/Ar mixture gas and substrate temperature. After finding The deposition condition of TiN films, The samples with the structure of Cu/Ta$_2$O$_{5}$, TiN/Ta$_2$O$_{5}$Si, Cu/TiN/Ta$_2$O$_{5}$ Si were prepared and were measured I-V, C-V. As a results, it was found that when TiN was deposited in an $N_2$a results, it was found that when TiN was deposited in an $N_2$atmosphere its Sheet resistance is lower n than n V$_2$Ar mixtureixture

• Journal of the Korean Vacuum Society
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• v.10 no.2
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• pp.189-193
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• 2001

We have characterized physical and electrical properties of W-TiN stacked gate electrode structure with TiN as a diffusion barrier of fluorine. As the $N_2/Ar$ gas ratio increased during sputter deposition, TiN thin films became N-rich, and the resistivity of the films increased. However, the resistivity of W-TiN stacked gate reduced as a result of the crystallization of tungsten with the increase of $N_2/Ar$ gas ratio. On the other hand, tungsten in W-TiN stacked gate structure have the (100)-oriented crystalline structure although TiN films were subjected to annealing at high temperature (600~$800^{\circ}C$). Leakage currents of W-TiN gate MOS capacitors were less than $10^{-7}\textrm{/Acm}^2$ and also were lowered by the order of 2 compared with those of pure W gate electrode.

• Journal of Industrial Convergence
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• v.19 no.4
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• pp.23-28
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• 2021

This paper finds the regular pattern of n = [3, ∞] for Euler square game related with n = 6(6×6=36) thirty-six officer problem that is still unsolved problem. The solution of this problem is exists for n = [3, 10] without n = 6. Also, previous researchers finds the random assigned solution for specific number using computer programming. Therefore, the solution of n = [11, ∞] Euler squares are unsolved problem because of anything but easy. This paper attempts to find generalized patterns for domains that have been extended to n = [3, ∞], while existing studies have been limited to n = [3, 10]. This paper classify the n = [3, ∞] into n = odd, 4k even, 4k+2 even of three classes. Then we find the simple regular pattern solution for n = odd and 4k even(n/2 = even). But we can't find the regular pattern for 4k+2 even(n/2 = odd).

• Korean Journal of Soil Science and Fertilizer
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• v.46 no.6
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• pp.463-468
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• 2013

The level of nitrous oxide ($N_2O$), a long-lived greenhouse gas, in atmosphere has increased mainly due to anthropogenic source, especially application of nitrogen fertilizers. Quantifying $N_2O$ emission from agricultural field is essential to develop national inventories of greenhouse gases (GHGs) emission. The objective of the study was to develop emission factor to estimate direct $N_2O$ emission from agricultural field in Gangwon-do, Korea by measuring $N_2O$ emissions from potato (Solanum tuberosum), red pepper (Capsicum annum L.), and Chinese cabbage (Brassica campestris L.) cultivation lands from 2009 to 2012. Accumulated $N_2O$ emission was $1.48{\pm}0.25kg$ $N_2O-N\;ha^{-1}$ for red pepper, $1.27{\pm}0.27kg$ $N_2O-N\;ha^{-1}$ for potato, $1.49{\pm}0.06kg$ $N_2O-N\;ha^{-1}$ for Chinese cabbage cultivated in spring, and $1.14{\pm}0.22kg$ $N_2O-N\;ha^{-1}$ for fall Chinese cabbage. Emission factor of $N_2O$ calculated from accumulated $N_2O$ emission, nitrogen fertilization rate, and background $N_2O$ emission was $0.0051{\pm}0.0016kg$ $N_2O-N\;ha^{-1}$ N for cropland in Gangwon province. More extensive study is deserved to be conducted to develop $N_2O$ emission factor for upland crops in Korea through examining the emission factors from various regions and crops because $N_2O$ emission is influenced by many factors including climate characteristics, soil properties, and agricultural practices.