• The Transactions of the Korea Information Processing Society
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• v.6 no.8
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• pp.2124-2132
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• 1999

Given a graph G=(V,E), Ld(2,1)-labeling of G is a function f : V(G)$\longrightarrow$[0,$\infty$) such that, if v1,v2$\in$V are adjacent, $\mid$ f(x)-f(y) $\mid$$\geq$2d, and, if the distance between and is two, $\mid$ f(x)-f(y) $\mid$$\geq$d, where dG(,v2) is shortest distance between v1 and in G. The L(2,1)-labeling number (G) is the smallest number m such that G has an L(2,1)-labeling f with maximum m of f(v) for v$\in$V. This problem has been studied by Griggs, Yeh and Sakai for the various classes of graphs. In this paper, we discuss the upper-bound of ${\lambda}$ (G) for a chordal graph G and that of ${\lambda}$(G') for a permutation graph G'.

• Journal of Korean Society of Water and Wastewater
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• v.26 no.6
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• pp.825-831
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• 2012

The retrofitting of a thickening unit process is widely considered in municipal wastewater treatment plants in Korea to enhance the anaerobic digestion efficiency. The authors examined the effect of feed concentration (2-34.1 g VS/L) and feed to microorganism (F/M) ratio (0.50-1.35 g VS/g VS) on anaerobic batch digestion of sewage sludge. Methane yield over 90 mL $CH_4/g$ $VS_{feed}$ was found at a feed concentration in the range of 12-26 g VS/L and a F/M ratio below 0.6 g VS/g VS. A high F/M ratio decreased methane yield and rate with oragnic acid accumulation. As sudden increase of sewage sludge concentration prior to anaerobic digestion would jeopardize the digester performance due to the rasied F/M ratio, gradual increase of the sludge feed concentration or an additional biomass retention in the digester is recommended.

• Membrane Journal
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• v.11 no.4
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• pp.143-151
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• 2001

We have fabricated mixed-ionic conducting membranes, L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ and L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ by the solid state method. Ceramic membranes consisted of perovskite-type structures and exhibited high relative density, >95%. Especially, dense L $a_{0.6}$S $r_{0.4}$Co $O_{3-}$$\delta$/ layer was coated on the L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes by using screen printing technique in order to improve oxygen ion flux. We measured oxygen ion flux on uncoated L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/, uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/, and coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. The L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ membranes showed the highest flux, 0.26 mL/min.$\textrm{cm}^2$ at 90$0^{\circ}C$, after steady state had been reached. The oxygen flux of coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes showed higher value, 0.19 mL/min.$\textrm{cm}^2$ at 95$0^{\circ}C$. This flux was as much as 2 or 3 times higher than those of uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. 3-$\delta$/ membranes.X> 3-$\delta$/ membranes.membranes.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.947-956
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• 1999

We define a crossing point $x_0$ such that f(x)$\geq$g(x) for x$\leq$$x_0$ and f(x)$\leq$g(x) for x>$x_0$ where f and g are probability density functions. We may encounter suchy situation when we compare two histograms from two independent observations. For example two contingency tables where initially admitted students and actually enrolled students are classified according to their high school ranking may show such situation, In this paper we consider maximum likelihood estimation of cell probabilities when a crossing point exists, We first assume a known crossing point and find an estimator. The estimation procedure for the case of unknown crossing point is just a straightforward extension. A real data is analyzed for an illustrative purpose.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.799-808
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• 2011

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_i{\mid}1{\leq}i{\leq}n$} is a conditional associated given $\mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$, $Cov^{\mathcal{F}}$ (f($X_1$, ${\ldots}$, $X_n$), g($X_1$, ${\ldots}$, $X_n$)) ${\geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $\mathcal{F}$-associated random variables.

• Bulletin of the Korean Chemical Society
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• v.24 no.5
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• pp.583-592
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• 2003

The gas phase identity nucleophilic substitution reactions of halide anions (X = F, Cl, Br) with cyclopentadienyl halides (1) are investigated at the B3LYP/6-311+G**, MP2/6-311+G** and G2(+)MP2 levels involving five reaction pathways: σ-attack $S_N2$, β-$S_N$2'-syn, β-$S_N$2'-anti, γ-$S_N$2'-syn and γ-$S_N$2'-anti paths. In addition, the halide exchange reactions at the saturated analogue, cyclopentyl halides (2), and the monohapto circumambulatory halide rearrangements in 1 are also studied at the same three levels of theory. In the σ-attack $S_N2$ transition state for 1 weak positive charge develops in the ring with X = F while negative charge develops with X = Cl and Br leading to a higher energy barrier with X = F but to lower energy barriers with X = Cl and Br than for the corresponding reactions of 2. The π-attack β-$S_N$2' transition states are stabilized by the strong $n_C-{\pi}^{*}_{C=C}$ charge transfer interactions, whereas the π-attack γ-$S_N$2' transition states are stabilized by the strong $n_C-{\sigma}^{*}_{C-X}$ interactions. For all types of reaction paths, the energy barriers are lower with X = F than Cl and Br due to the greater bond energy gain in the partial C-X bond formation with X = F. The β-$S_N$2' paths are favored over the γ-$S_N$2' paths only with X = F and the reverse holds with X = Cl and Br. The σ-attack $S_N2$ reaction provides the lowest energy barrier with X = Cl and Br, but that with X = F is the highest energy barrier path. Activation energies for the circumambulatory rearrangement processes are much higher (by more than 18 kcal $mol^{-1}$) than those for the corresponding $S_N2$ reaction path. Overall the gas-phase halide exchanges are predicted to proceed by the σ-attack $S_N2$ path with X = Cl and Br but by the β-$S_N$2'-anti path with X = F. The barriers to the gas-phase halide exchanges increase in the order X = F < Br < Cl, which is the same as that found for the gas-phase identity methyl transfer reactions.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1829-1839
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• 2014

Let (${\Omega}$, $\mathcal{S}$, ${\mu}$) be a probabilistic measure space, ${\varepsilon}{\in}\mathbb{R}$, ${\delta}{\geq}0$, p > 0 be given numbers and let $P{\subset}\mathbb{R}$ be an open interval. We consider a class of functions $f:P{\rightarrow}\mathbb{R}$, satisfying the inequality $$f(EX){\leq}E(f{\circ}X)+{\varepsilon}E({\mid}X-EX{\mid}^p)+{\delta}$$ for each $\mathcal{S}$-measurable simple function $X:{\Omega}{\rightarrow}P$. We show that if additionally the set of values of ${\mu}$ is equal to [0, 1] then $f:P{\rightarrow}\mathbb{R}$ satisfies the above condition if and only if $$f(tx+(1-t)y){\leq}tf(x)+(1-t)f(y)+{\varepsilon}[(1-t)^pt+t^p(1-t)]{\mid}x-y{\mid}^p+{\delta}$$ for $x,y{\in}P$, $t{\in}[0,1]$. We also prove some basic properties of such functions, e.g. the existence of subdifferentials, Hermite-Hadamard inequality.

• Journal of Korean Society of Forest Science
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• v.105 no.2
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• pp.177-185
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• 2016

Fertilization is required to keep the balance of tissue nutrients and to produce high quality seedlings at the permanent nursery. This study was conducted to verify the optimum fertilization method for Fraxinus rhynchophylla, F. mandshurica, Pinus koraiensis, and Abies holophylla seedlings with vector diagnosis method. Seven treatments include nitrogen (N, $13.8g{\cdot}m^{-2}$), phosphorus (P, $6.1g{\cdot}m^{-2}$), potassium ($7.5g{\cdot}m^{-2}$) fertilization and 1x (N $6.9g{\cdot}m^{-2}$, P $3.05g{\cdot}m^{-2}$, K $3.65g{\cdot}m^{-2}$), 2x (twice of 1x), 4x (four times of 1x) fertilization and no fertilization. Soil pH decreased as fertilization increased. Nitrogen and NPK fertilization decreased exchangeable $Ca^{2+}$ and $Mg^{2+}$ concentrations. Height and root collar diameter of F. rhynchophylla and F. mandshurica significantly increased with N and NPK fertilization, but those of P. koraiensis and A. holophylla did not. The biomass of F. rhynchophylla and F. mandshurica was about twice higher at NPK fertilization compared to the control. The responses of vector diagnosis were different by tree species and fertilization treatment: F. rhynchophylla was in the status of N "dilution", which means the N concentration decreases with N content. Phosphorus and K were "sufficiency" state with 4x fertilization. F. mandshurica showed "retranslocation" as N content decreased without change of dry weight at N, P, K fertilization, but "dilution" state at NPK fertilization. This result suggested that optimal fertilization was required for F. rhynchophylla and F. mandshurica in seedling production stage, but was not essential for P. koraiensis and A. holophylla.

• The Korean Journal of Ceramics
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• v.5 no.4
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• pp.375-378
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• 1999

In tho XRD study of $56ZrF_4 \cdot34BaF_2 \cdot4AIF_3 \cdot(6-x)LaF_3 \cdotxLnF_3$ glassdLn=Ce, Nd, Gd, Th), halo pattern charactarktic fo an amorphous sample appeared. When the halo peak angle ($\theta_p$) was converted into a wavenumber with $Qp=4\pi sinG\pi/\lambda(\lambda$ is the wavolongth of the radialion used), it was found that the Qp values varied almost liuearly with the concentration 01 $LnF_3$. The emissiou spect1.a of $Ce^{3-}$-containing fluoride glasses nnder 273 nm excitation had a peak maximum at ea. 300 nm $(Ce^{3+}$ 5d-4f- transition). The maximal intensity of the fluorescence was observed when the $CeF_3$, content was extremely low (ca. 1 mol%j. DTA measurement revealed tbat these fluoride glasses had two crystallization temperatures. In $56ZrF_4. 34BaF_2. 4NF_3. (6-x)LaF_3 .xNdF_3$ glasses, the actmation energies of crystallization obtained from a Kssinger plot were 1.7 and 5.0 eV for the glass with x=2, and 1.9 and 5.6 eV for the glass with x=4.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.761-790
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• 2021

For given spaces X and Y, let map(X, Y) and map_*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map_*(X, Y ; g) be the path component of map(X, Y) containing f and map_*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane π^n+m(ΣⁿℂP²) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣⁿℂP², S^m) up to homotopy equivalence. We also determine the generalized Gottlieb groups G_n(ℂP², S^m). Finally, we compute homotopy groups of mapping spaces map(ΣⁿℂP², S^m; f) for all generators [f] of [ΣⁿℂP², S^m], and Gottlieb groups of mapping components containing constant map map(ΣⁿℂP², S^m; *).