• 대한수학회지
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• 제33권2호
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• pp.413-421
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• 1996

A path g in the plane $R^2$ is the sequence of the points $(t_0, t_1, \ldots, t_n)$, with coordinates in $Z^2$. The point $t_0$ is the starting point and the point $t_n$ is the arriving point. An elementary step of g is a couple $(t_i, t_{i+1}), 0 \leq i \leq n - 1$. We denote the length of the path g by $\mid$g$\mid$ = n.

• 한국생물공학회:학술대회논문집
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• 한국생물공학회 2001년도 추계학술발표대회
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• pp.278-281
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• 2001

A fixed bed biofilm reactor filled with ceramic media were used to remove nitrogen by selective nitrification (ammonium to nitrite). The effects of experimental conditions (nitrogen load, dissolved oxygen, nitrite ratio, C/N ratio) on denitrification were investigated. The reactor showed more than 80% average T-N removal efficiencies at T-N loading in the range of $1.1{\sim}3.3$ kg $T-N/m^3{\cdot}d$ C/N at the C/N ratio of 1. T-N removal efficiencies increased as nitrite ratio.

• 대한수학회논문집
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• 제11권4호
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• pp.997-1002
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• 1996

In this paper we extend the Zemanek's characterization of the Browder spectrum for a commuting n-tuple operators in $L(H)$ and show that if $T = (T_1, \cdots, T_n)$ is Browder then there exists an n-tuple $K = (K_1, \cdots, K_n)$ of compact operators and an invertible commuting n-tuple $(S_1, \cdots, S_n)$ for which $T = S + K$ and $S_i K_j = K_j S_i$ for all $1 \leq i, j \leq n$.

• 대한수학회보
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• 제59권2호
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• pp.345-350
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• 2022

In this work, we confirm a weak version of a conjecture proposed by Hong Wang. The ideal of the work comes from the tree packing conjecture made by Gyárfás and Lehel. Bollobás confirms the tree packing conjecture for many small tree, who showed that one can pack T₁, T₂, …, $T_{n/\sqrt{2}}$ into Kn and that a better bound would follow from a famous conjecture of Erdős. In a similar direction, Hobbs, Bourgeois and Kasiraj made the following conjecture: Any sequence of trees T₁, T₂, …, T_n, with T_i having order i, can be packed into K_n-1,[n/2]. Further Hobbs, Bourgeois and Kasiraj [3] proved that any two trees can be packed into a complete bipartite graph K_n-1,[n/2]. Motivated by the result, Hong Wang propose the conjecture: For each k-partite tree T(𝕏) of order n, there is a restrained packing of two copies of T(𝕏) into a complete k-partite graph B_n+m(𝕐), where $m={\lfloor}{\frac{k}{2}}{\rfloor}$. Hong Wong [4] confirmed this conjecture for k = 2. In this paper, we prove a weak version of this conjecture.

• 한국농공학회지
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• 제41권4호
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• pp.47-56
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• 1999

The concentration and load of T-N and T-P in paddy field areas in Chongwon, Chungbuk , Korea , were investigated during the irrigation period. The concentration of T-N and T-P in ponded water in paddies is higher than that in the irrigation, drainage and percolation waters. For T-N, the average concentration indrainage water was higher than that in irrigation water until end of Jung, But lower thereafter. The average T-N concentration in irrigation water was 2.3 ∼3.2mg/l and therefore the agricultural water quality standard at on-farm level for T-N should be established realistically . The expontial L(load)-Q(discharge) equations have higher coefficients of determination than the linear L-Q equations . Especially, the exponential L-Q equation of T_N showed a coefficient of determinatino of over 0.9 for irrigation water.

• 한국습지학회지
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• 제11권3호
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• pp.37-47
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• 2009

본 연구지역은 전라남도에 위치한 고흥만 간척지 내 인공습지이며, 인공습지수와 주변 유입수의 수질특성을 파악하기 위해 2008년 3월 15일 및 2009년 1월 10일에 12개 지점에서 현장조사를 수행하였다. 수온, pH, DO, EC 및 salinity 항목은 현장측정 되었으며, 채수된 시료는 실내에서 TOC, Cl-, COD, TSS, T-P 및 T-N 성분을 분석하였다. 현장 관측된 5개 항목은 인공습지에 비해 유입지점들에서 높게 나타났으며, 이는 주변 농경 작지에서 유입되는 오염물질에 의한 것이다. 인공습지수와 유입수 내 농도비는 TOC 성분은 1월에, Cl 성분은 3 월에 더욱 높은 값을 보였다. COD 성분은 인공습지수에 대한 유입수의 농도비가 1.37배와 1.49배로서 유사하였다. 유입지점들에서 T-P와 T-N 성분의 평균값은 인공습지 내에서보다 3배 이상 높았으며, 인공습지의 자정능력에 의해 농도가 저감되었다. 본 연구지역의 인공습지에서는 유입수 내 Cl, T-P, T-N 성분의 정화효율이 높은 것으로 나타났다. Cl- 성분의 정화효율은 1차 관측 시 83%, 2차 관측 시 76% 이었으며, 이는 인공습지수에 의한 희석효과에 의한 것이다. T-P 성분의 정화효율은 67%(1차 관측)와 69%(2차 관측), T-N 성분은 100%(1차 관측)와 95%(2차 관측) 로서 매우 높았다. 본 연구에서 T-N의 정화효율이 비현실적으로 높은 것은 유입수의 양이 소량이어서 인공습지수 내에서는 질소 농도가 분석한계 이하로 나타났기 때문이다. 본 연구에서는 T-P 성분의 정화효율이 1월에, T-N 성분은 3월에 높게 나타나 생장기와 동절기의 영향에 의한 것으로 판단된다.

• 대한수학회논문집
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• 제20권4호
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• pp.671-683
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• 2005

The set of all $m\;{\times}\;n$ matrices with entries in $\mathbb{Z}_+$ is de­noted by $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$. We say that a linear operator T on $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ is a (U, V)-operator if there exist invertible matrices $U\;{\in}\; \mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ and $V\;{\in}\;\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ such that either T(X) = UXV for all X in $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$, or m = n and T(X) = $UX^{t}V$ for all X in $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$. In this paper we show that a linear operator T preserves the rank of matrices over the nonnegative integers if and only if T is a (U, V)­operator. We also obtain other characterizations of the linear operator that preserves rank of matrices over the nonnegative integers.

• 대한수학회보
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• 제56권5호
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.175-192
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• 2010

In this paper, we introduced the notion of T-vague n-ary subgroups on n-ary subgroups (G, f) and have studied their related properties.

• Journal of Photoscience
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• 제6권2호
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• pp.61-65
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• 1999

The fluorescence properties and photoisomerization behavior of 1-(9-anthryl)-2-(n-quinolinyl)ethene (n-AQE, n=2-4) have been investigated in various solvents. t-3-AQE is strongly fluorescent, but does not accomplish photoisomerization, similar to parent hydrocarbon compound, t-1-(9-anthryl)-2-phenylethene (t-9-APE) or t-1-(9-anthryl)-2-(1-naphthyl)ethene (t-1-ANE). Fluorescence and photoisomerization oft-2-AQE and t-4-AQE are strongly affected by solvent polarity. Dependence of fluorescence quantum yield on the solvent polarity is moderate for t-2-AQE and large for t-4-AQE. In nonpolar solvent (in n-hexane), they exhibit relatively strong fluorescence, but do not isomerize to cis isomer on irradiation, even if inefficient isomerization is observed for t-4-AQE. However, as solvent polarity increases, their fluorescences become weak with efficient photoisomerization to corresponding cis isomer. Intramolecular charge-transfer excited state is presumed to contribute to photoisomerization. The S$_1$ decay parameters were found to be solvent-dependent due to the charge-transfer character of lowest S$_1$ state. In polar solvents, the activation barrier to twisting is reduced enhancing the isomerization of r-2-AQE and t-4-AQE in the singlet manifold.