• Journal of the Korean Mathematical Society
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• v.33 no.2
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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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• 2001.11a
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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.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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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 $1 \leq i, j \leq n$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.4
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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.

• Journal of Wetlands Research
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• v.11 no.3
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• pp.37-47
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• 2009

This research was conducted at the constructed wetland in Goheung reclaimed land, and water quality components were measured at the 12 points in 15 March 2008 and 10 January 2009, respectively. Temperature, pH, DO, EC and salinity components were measured at the field, and TOC, Cl-, COD, TSS, T-P and TN components were analyzed laboratory. Concentrations of field measured components at inflow points were higher than in constructed wetland. TOC concentration ratio of inflow water to constructed wetland water was higher in January, and Cl concentration ratio of it was higher in March. And, COD concentration ratio of it were 1.37 for March and 1.49 for January, respectively. T-P and T-N concentration ratios of it at inflow points were higher 3 times than in constructed wetland. Constructed wetland attenuated concentration of contaminated components inflow to it. Removal efficiencies of Cl-, T-P and T-N components in inflow water were high at the constructed wetland. removal efficiencies of Cl component were 83% for 1st monitoring and 76% for 2nd monitoring, this removal efficiency be caused by dilution effect of constructed wetland. removal efficiencies of T-P component were 67% for 1st monitoring and 69% for 2nd monitoring, and they of T-N component were 100% for 1st monitoring and 95% for 2nd monitoring. Abnormal removal efficiency of T-N component is caused that nitrogen in inflow water was a little. Removal efficiency of T-P component was higher in January, and T-N component was higher in March. This is caused by environmental difference between growing season and winter.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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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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• v.28 no.1_2
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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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• v.6 no.2
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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.