• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Journal of Korean Society of Water and Wastewater
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• v.23 no.4
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• pp.439-446
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• 2009

This study was performed to evaluate SND(simultaneous nitrification and denitrification)efficiency, nitrogen removal efficiency and filtration function of non-woven fabric by using submerging MBR packed with granular sulfur covered with non-woven fabric filter. Synthetic wastewater was used as influent wastewater. Concentration of $NH_4{^+}-N$ in influent was maintained about 40 mg/L and the experiment was performed in four phases according to the flow rate. Nitrogen loading rate divided four phases ranging from $0.04 kg\;NH_4{^+}-N/m^3-day$ to $0.16 kg\;NH_4{^+}-N/m^3-day$. As a result, the maximum $NH_4{^+}-N$ removal rate was accomplished at $0.142 kg\;NH_4{^+}-N/m^3-day$ in nitrogen loading of $0.147 kg\;NH_4{^+}-N/m^3-day$. Nitrification efficiency was higher than 95% in all phases. $NO_3{^-}-N$ loading rate was adjusted ranging from $0.22 kg\;NO_3{^-}-N/m^3-day$ to $0.89 kg\;NO_3{^-}-N/m^3-day$. The maximum $NO_3{^-}-N$ removal rate was accomplished up to $0.71 kg\;NO_3{^-}-N/m^3-day$ in $NO_3{^-}-N$ loading of $0.89 kg\;NO_3{^-}-N/m^3-day$. The maximum $NO_3{^-}-N$ removal efficiency was 95% in $NO_3{^-}-N$ loading of $0.22 kg\;NO_3{^-}-N/m^3-day$. T-N removal rate was 90% and concentration of T-N in effluent was 3.7 mg/L in T-N loading rate of $0.039 kg\;NO_3{^-}-N/m^3-day$. In this study, TMP in reactor with and without non-woven fabric filter were observed to define fouling of hollow-fiber membrane module. Reaching time to standard washing pressure(22 cm Hg) of two reactors were 29 days with non-woven fabric But the reactor without non-woven fabric reached standard washing pressure only after 4 days. Accordingly, non-woven fabric was demonstrated the superiority as a filtration ability. With high nitrogen removal rate and decreasing of fouling of membrane, MBR packed with granular sulfur covered with non-woven fabric filter submerging in activated sludge aeration tank can be used as an advanced treatment process.

• 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.

• The Korean Journal of Food And Nutrition
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• v.15 no.1
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• pp.58-63
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• 2002

Lipid contents and fatty acid compositions of 16 kind sea algaes in the southern sea coast of Korea were analyzed to evaluate nutrient significance of total polyene, n-3 polyenes and n-6 polyene fatty acids. Total lipid contents were 0.58 ∼ 3.00% in 9 kinds of brown algaes, 0.47 ∼ 2.16% in 5 kinds of red algaes and 0.55 ∼2..99% in 2 kinds of green algeas. N-3 polyenes and n-6 polyenes of the fatty acid compositions were 1.46∼25.67% and 0∼48.51% in the brown algaes, 1.17∼21.91% and 0.28 ∼29.35% in the red algaes, and 3.67%∼ 10.61% and 4.10 ∼ 8.66% in the green algaes, respectirely. The fatty acid contents and compositions of n-3 polyenes and n-6 polyenes, monoenes and saturates were vary different in the algae groups and sepecies.

• Journal of the Korean Chemical Society
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• v.35 no.3
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• pp.240-248
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• 1991

The regioselectivity in the nitrosation of seven N-methyl-N'-substituted phenylureas ($CH_3NHCONHC_6H_4-G$; G = H, p-CH$_3$, m-CH$_3$, m-CH$_3$O, p-F, m-F, m-Br) was examined using NaNO$_2$ and 4 different acids (diluted HCl, HCOOH, CH$_3$COOH, CF$_3$COOH). In all cases, the two regioisomeric products, N-nitroso-N-methyl-N'-substituted phenylureas (A) and N'-nitroso-N-methyl-N'-substituted phenylureas (B) were observed to be formed as major products and product ratios were determined by the integration of their methyl peaks in $^1$H-NMR. Electron donating substitutent(G) on phenyl of the ureas generally led to increase the ratio of B to A. The data have revealed that the relative sensitivity of the nitrosonium species (HONO, HCOONO, CH$_3$COONO, CF$_3$COONO) toward the change of electron density on nitrogen with phenyl substitutents are 1.00 : 0.93 : 0.78 : > ∼ 0.7.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.621-635
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• 2024

An 𝑙-regular overpartition of n is an overpartition of n with no parts divisible by 𝑙. Recently, the authors introduced a partition statistic called r_𝑙-crank of 𝑙-regular overpartitions. Let M_r𝑙(m, n) denote the number of 𝑙-regular overpartitions of n with r_𝑙-crank m. In this paper, we investigate the monotonicity property and the unimodality of M_r3(m, n). We prove that M_r3(m, n) ≥ M_r3(m, n - 1) for any integers m and n ≥ 6 and the sequence {M_r3(m, n)}_|m|≤n is unimodal for all n ≥ 14.

• Journal of Korean Society on Water Environment
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• v.22 no.5
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• pp.846-850
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• 2006

The biological nutrient removal from domestic wastewater with low C/N ratio is difficult. Therefore, this study was performed to increase influent C/N ratio by ammonia stripping without required carbon source and for improving treatment efficiencies of sewerage by the combination process of ammonia stripping and BNR (StripBNR). The results of this study were summarized as follows. BOD removal efficiencies of BNR and StripBNR were 95.3% and 93.2%, respectively. T-N and T-P removal efficiencies of BNR were 53.3% and 40.8%, respectively. T-N and T-P removal efficiencies of StripBNR were 72.8% and 62.9%, respectively. Concentrations of $NH_3-N$, $NO_2-N$ and $NO_3-N$ at BNR effluent were 0.03 mg/L, 0.08 mg/L and 9.12 mg/L, respectively. On the other hands, concentrations of $NH_3-N$, $NO_2-N$ and $NO_3-N$ at StripBNR effluent were 5.79 mg/L, 0.01 mg/L and 0.14 mg/L, respectively. Consequently, influent C/N ratio of BNR process was increased by ammonia stripping. Removal efficiency of T-N and T-P was improved about 20% by the process of StripBNR.

• Bulletin of the Korean Chemical Society
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• v.30 no.6
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• pp.1293-1296
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• 2009

A new series of N-substituted 2-n-butyl-3-fluoropyrroles were prepared by a simple one-pot reaction designed of retrosynthesis. $\alpha,\alpha-Difluoro-\gamma-iodo-\gamma$-(trimethylsilyl)propyl n-butyl ketone, a component precursor molecule to 2-n-butyl-3-fluoropyrroles, was prepared with Cu(0) catalyst. It reacted with various primary amines to yield N-substituted 2-n-butyl-3-fluoropyrroles. The products were synthesized via a one-pot reaction scheme between $\alpha,\alpha-Difluoro-\gamma-iodo-\gamma$-(trimethylsilyl) propyl n-butyl ketone and primary amines in excess ( $\geq$ 5 molar equivalence), which eliminate the need of KF required in obtaining n-butyl-1H-3-fluoropyrrole. The yield of products depended reversely on spatial bulkness around N-binding carbon.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.25-43
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• 2005

Let F be a finite field of prime power order q(odd) and the multiplicative order of q modulo $2^{n}\;(n>1)\;be\; {\phi}(2^{n})/2$. If n > 3, then q is odd number(prime or prime power) of the form $8m{\pm}3$. If q = 8m - 3, then the ring $R_{2^n} = F[x]/ < x^{2^n}-1 >$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length $2^{n}$ generated by these idempotents are completely described. If q = 8m + 3 then the expressions for the 2n - 1 primitive idempotents of $R_{2^n}$ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n-1 idempotents are also obtained. The case n = 2,3 is dealt separately.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.1003-1016
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• 2016

In this paper, we introduce a new kind of slant helix for null curves called null $W_n$-slant helix and we give a definition of new harmonic curvature functions of a null curve in terms of $W_n$ in (n + 2)-dimensional Lorentzian space $M^{n+2}_1$ (for n > 3). Also, we obtain a characterization such as: "The curve ${\alpha}$ s a null $W_n$-slant helix ${\Leftrightarrow}H^{\prime}_n-k_1H_{n-1}-k_2H_{n-3}=0$" where $H_n,H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $k_1,k_2$ are the Cartan curvature functions of the null curve ${\alpha}$.