• Journal of Korean Society of Environmental Engineers
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• v.32 no.1
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• pp.33-46
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• 2010

We investigated and estimated at the characteristics of decomposition and by-products of N-Nitrosodimethylamine (NDMA) using a design of experiment (DOE) based on the Box-Behken design in an UV process, and also the main factors (variables) with UV intensity($X_2$) (range: $1.5{\sim}4.5\;mW/cm^2$), NDMA concentration ($X_2$) (range: 100~300 uM) and pH ($X_2$) (rang: 3~9) which consisted of 3 levels in each factor and 4 responses ($Y_1$ (% of NDMA removal), $Y_2$ (dimethylamine (DMA) reformation (uM)), $Y_3$ (dimethylformamide (DMF) reformation (uM), $Y_4$ ($NO_2$-N reformation (uM)) were set up to estimate the prediction model and the optimization conditions. The results of prediction model and optimization point using the canonical analysis in order to obtain the optimal operation conditions were $Y_1$ [% of NDMA removal] = $117+21X_1-0.3X_2-17.2X_3+{2.43X_1}^2+{0.001X_2}^2+{3.2X_3}^2-0.08X_1X_2-1.6X_1X_3-0.05X_2X_3$ ($R^2$= 96%, Adjusted $R^2$ = 88%) and 99.3% ($X_1:\;4.5\;mW/cm^2$, $X_2:\;190\;uM$, $X_3:\;3.2$), $Y_2$ [DMA conc] = $-101+18.5X_1+0.4X_2+21X_3-{3.3X_1}^2-{0.01X_2}^2-{1.5X_3}^2-0.01X_1X_2+0.07X_1X_3-0.01X_2X_3$ ($R^2$= 99.4%, 수정 $R^2$ = 95.7%) and 35.2 uM ($X_1$: 3 $mW/cm^2$, $X_2$: 220 uM, $X_3$: 6.3), $Y_3$ [DMF conc] = $-6.2+0.2X_1+0.02X_2+2X_3-0.26X_1^2-0.01X_2^2-0.2X_3^2-0.004X_1X_2+0.1X_1X_3-0.02X_2X_3$ ($R^2$= 98%, Adjusted $R^2$ = 94.4%) and 3.7 uM ($X_1:\;4.5\;$mW/cm^2$, $X_2:\;290\;uM$, $X_3:\;6.2$) and $Y_4$ [$NO_2$-N conc] = $-25+12.2X_1+0.15X_2+7.8X_3+{1.1X_1}^2+{0.001X_2}^2-{0.34X_3}^2+0.01X_1X_2+0.08X_1X_3-3.4X_2X_3$ ($R^2$= 98.5%, Adjusted $R^2$ = 95.7%) and 74.5 uM ($X_1:\;4.5\;mW/cm^2$, $X_2:\;220\;uM$, $X_3:\;3.1$). This study has demonstrated that the response surface methodology and the Box-Behnken statistical experiment design can provide statistically reliable results for decomposition and by-products of NDMA by the UV photolysis and also for determination of optimum conditions. Predictions obtained from the response functions were in good agreement with the experimental results indicating the reliability of the methodology used.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.307-314
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• 2012

Let M be a left R-module and R be a ring with unity, and $S=\{0,2,3,4,{\ldots}\}$ be a submonoid. Then $M[x^{-s}]=\{a_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ is an $R[x^s]$-module. In this paper we show some properties of $M[x^{-s}]$ as an $R[x^s]$-module. Let $f:M{\rightarrow}N$ be an R-linear map and $\overline{M}[x^{-s}]=\{a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ and define $N+\overline{M}[x^{-s}]=\{b_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}b_0{\in}N,\;a_i{\in}M}$. Then $N+\overline{M}[x^{-s}]$ is an $R[x^s]$-module. We show that given a short exact sequence $0{\rightarrow}L{\rightarrow}M{\rightarrow}N{\rightarrow}0$ of R-modules, $0{\rightarrow}L{\rightarrow}M[x^{-s}]{\rightarrow}N+\overline{M}[x^{-s}]{\rightarrow}0$ is a short exact sequence of $R[x^s]$-module. Then we show $E_1+\overline{E_0}[x^{-s}]$ is not an injective left $R[x^s]$-module, in general.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.127-131
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• 2003

Let X$_1$, X$_2$,... be a sequence of independent and identically distributed random variables with continuous cumulative distribution function F(x). X$_j$ is an upper record value of this sequence if X$_j$ > max {X$_1$,X$_2$,...,X$_{j-1}$}. We define u(n)=min{j$\mid$j> u(n-1), X$_j$ > X$_{u(n-1)}$, n $\geq$ 2} with u(1)=1. Then F(x) = 1-x$^{\theta}$, x > 1, ${\theta}$ < -1 if and only if (${\theta}$+1)E[X$_{u(n+1)}$$\mid$X$_{u(m)}$=y] = ${\theta}E[X_{u(n)}$\mid$X_{u(m)}=y], (\theta+1)^2E[X_{u(n+2)}$\mid$X_{u(m)}=y] = \theta^2E[X_{u(n)}$\mid$X_{u(m)}=y], or (\theta+1)^3E[X_{u(n+3)}$\mid$X_{u(m)}=y] = \theta^3E[X_{u(n)}$\mid$X_{u(m)}=y], n $\geq$ M+1$.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.24 no.2
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• pp.27-34
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• 1979

Dormant rice seeds were treated with different levels of ethyl methanesulfonate(EMS) and sown directely on the well managed seed beds and the ontogenetically different tillers of $_{x}\textrm{M}_1 plants were marked as they are developed. The biological effects of $_{x}\textrm{M}_1 plant and mutation frequency of $_{x}\textrm{M}_2 were investigated. utation frequency evaluated with tiller groups and $_{x}\textrm{M}_1 sterility, differs from the results reported with radiation treatment. Hence, selection of $_{x}\textrm{M}_1 panicle of primary or secondary tillers could be recommended for increase mutation frequency in $_{x}\textrm{M}_2 generation.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.399-404
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• 2005

Let M be a finite commutative nilpotent algebra over a perfect field k of prime characteristic p and let $M^p$ be the sub-algebra of M generated by $x^p$, $x{\in}M$. Eggert[3] conjectures that $dim_kM{\geq}pdim_kM^p$. In this paper, we show that the conjecture holds for $M=R^+/I$, where $R=k[X_1,\;X_2,\;{\cdots},\;X_t]$ is a polynomial ring with indeterminates $X_1,\;X_2,\;{\cdots},\;X_t$ over k and $R^+$ is the maximal ideal of R generated by $X_1,\;X_2,{\cdots},\;X_t$ and I is a monomial ideal of R containing $X_1^{n_1+1},\;X_2^{n_2+1},\;{\cdots},\;X_t^{n_t+1}$ ($n_i{\geq}0$ for all i).

• Korean Journal of Medicinal Crop Science
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• v.13 no.3
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• pp.118-121
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• 2005

Karyotypes were established in seven Angelica species cultivated in Korea. The somatic chromosome numbers were 2n = 2x = 22 with the basic number of x = 11 in all Angelica plants examined. Their metaphase chromosomes ranged from 3.56 ${\mu}M$. to 8.91 x. in length. Distinctive Karyotypes were found in two species, A. tenuissima with all metacentries, K(2n) = 2x = 22m, and A. genuflexa with all subtelocentrics, K(2n) = 2x = 22st. Karyotype formulas of A. gigas, A. acutiloha, A. sinensis, A. decursiva and A. dahurica were K(2n) = 2x = 20m + 2sm, K(2n) = 2x = 12m + 10sm, K(2n) = 2x = 16m + 6sm, K(2n) = 2x = 18m + 4sm and K(2n) = 2x = 10m + 10sm + 2st, respectively. Cytological data showed that chromosomal polymorphisms within species were observed in Angelica plants compare to other regions.

• Journal of the Korean Magnetics Society
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• v.10 no.3
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• pp.106-111
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• 2000

The magnetic thin films can be prepared without vacuum process and under the low temperature (<100 $^{\circ}C$) by ferrite plating. We have performed ferrite plating of M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$(x=0.00~0.08) films and N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$(x=0.00~0.15) films on cover glass at the substrate temperature 90 $^{\circ}C$. The crystal structure of the samples has been identified as a single phase of polycrystal spinel structure by x-ray diffraction technique. The lattice constant in the M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$films increases but in the N $i_{x}$Z $n_{0.22}$F $e_{*}$2.78-x/ $O_4$films decrease with the composition parameter, x. The saturation magnetization in the M $n_{x}$Z $n_{0.22}$F $e_{2.78-x}$ $O_4$films does not greatly change, in agreement with observations on bulk samples.k samples.k samples.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.31-38
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• 2018

In [4], the authors show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type ($d_1$, ${\ldots}$, $d_s$) with $d_s$ > $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(md_s-1)$ is the number of lines containing exactly $d_s-points$ of ${\mathbb{X}}$ for $m{\geq}2$. They also show that if ${\mathbb{X}}$ is a ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)$ is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}s+1$. In this paper, we explore a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ and find that if ${\mathbb{X}}$ is a standard ${\mathbb{k}}-configuration$ in ${\mathbb{P}}^2$ of type (1, 2, ${\ldots}$, s) with $s{\geq}2$, then ${\Delta}H_{m{\mathbb{X}}}(m{\mathbb{X}}-1)=3$, which is the number of lines containing exactly s-points in ${\mathbb{X}}$ for $m{\geq}2$ instead of $m{\geq}s+1$.