• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.573-580
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• 2006

In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.

• Korean Journal of Mathematics
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• v.11 no.2
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• pp.117-125
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• 2003

Let $x(t)$ satisty $$(p(t)x^{\prime}(t))^{\prime}+q(t)x^{{\alpha}}(t)+r(t)x^{{\beta}-1}x^{\prime}(t){\leq}0({\geq}0)$$. Then the zeros of $x(t)$ or $x^{\prime}(t)$ are simple.

• Proceedings of the KAIS Fall Conference
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• 2008.11a
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• pp.90-92
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• 2008

본 논문에서는$xAg_2O$-(5-x)$Na_2O$-36CaO-$10TiO_2$-$19.5P_2O_5$ (mol ratio)의 유리조성으로부터 $Ag_2O$의 함량을 변화시켜 유리의 제조 및 특성평가를 하였다. 제조된 유리는 TG-DSC를 통하여 열적특성을 관찰하였으며, 항균특성은 staphylococcus aureus균주에 대하여 항균특성을 평가하였다. 평가결과 열적특성은 $Ag_2O$함량이 증가할수록 결정화온도가 낮아짐이 관찰되었고, 항균특성 역시 $Ag_2O$성분의 함량이 증가 할수록 항균특성이 증가하는 것으로 관찰되었다.

• Journal of the Korean Society of Industry Convergence
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• v.7 no.1
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• pp.107-113
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• 2004

Several transition metal complexes, [$M(L)X_2$](M=Pd(II), Ni(II); X=CI, Br) are prepared with aminophosphine ligands such as 1,2-bis{(diphenylphosphino)amino}ethane{$Ph_2PNHCH_2CH_2NHPPh_2$}($L_1$), 1,2-bis{(diphenylphosphino)amino}propane{$Ph_2PNHCH(CH_3)CH_2NHPPh_2$}($L_2$), trans-1,2-bis{(diphenylphosphino)amino}cyclohexane{$Ph_2PNHC_6H_{10}NHPPh_2$}($L_3$) and 1,2-bis{(diphenylphosphino)amino}benzene{$Ph_2PNHC_6H_4NHPPh_2$}($L_4$). The properties of these complexes are characterized by optical spectroscopic methods including UV/vis spectroscopy, CD, IR, $^1H$- and $^{31}P-NMR$ together with conductometer and elemental analysis. All complexes are stable under atmospheric environment. Catalytic reactivity for C-C coupling between [$M(L)X_2$] and Grignard reagents(RMgX; R=phenyl, propyl, buthyl) by thermolysis were investigated utilizing GC/mass, $^1H$- and $^{13}C-NMR$. When mol scale is 1:20 at [$Pd(L)Cl_2$] and Grignard reagents, the high catalytic activity for C-C coupling is apparent. The [$M(L)X_2$](X=Cl, Br) complexes which have strong bond at M-P exhibit high yields for C-C coupling reactions. When the central metal ion is Pd(II), the high catalytic activity for C-C coupling is apparent. The complex coordinated with Br shows higher catalytic activity for C-C coupling reactions compared to Cl.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2004.11a
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• pp.451-452
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• 2004

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• The Korean Journal of Ecology
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• v.13 no.4
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• pp.297-309
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• 1990

The distribution of aquatic macrophytes in TanChon basin, a stream of the Han River, were investigated in terms of environmental gradient from June 1989 to March 1990. In the basin, 12 species of aquatic macrophytes were listed and four communities of Potamogeton crispus community. $P. octandrus$ community, $Hydrilla verticillata$ community and $Vallisneria$ asiatica community were recongized by character species. $P. crispus, P. octandrus$ and $V. asiatica$ were found in rapids while $H. verticillata , Ceratophyllum demersum$ and $Trapa japonica$ were done in pools. The depth of sediment $TanCh\u{o}n$ was showed as a exponential function of water velocity, Bd=exp (-K Wv). The values of Biochemical Oxygen Demand(BOD), Chemical Oxygen Demand(COD) and Suspendid Solid(SS) were recorded as range of 3.2~121.0mg/1, 4.2~54.5mg/1 and 4.1~114.0mg/1, respectively. And the linear positive correlation between BOD(X) and COD(Y) were expressed as Y=3.904+0.4308 X with $R^2$=0.9808 and also the correlation between BOD value(X) and SS value(Y) were done as Y=5.333+0.9606X with $R^2$=0.9700. In two dimensional analysis of BOD and water velocity, their clusters were showed similar types matching to communities classified by character species. However, no aquatic macrophyes were found at the site with BOD$\geq$50mg/l or DO$\leq$0.2mg/l.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.185-220
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• 2016

We study the Gauss and Poisson semigroups connected with the Riemann-Liouville operator defined on the half plane. Next, we establish a principle of maximum for the singular partial differential operator $${\Delta}_{\alpha}={\frac{{\partial}^2}{{\partial}r^2}+{\frac{2{\alpha}+1}{r}{\frac{\partial}{{\partial}r}}+{\frac{{\partial}^2}{{\partial}x^2}}+{\frac{{\partial}^2}{{\partial}t^2}}};\;(r,x,t){\in}]0,+{\infty}[{\times}{\mathbb{R}}{\times}]0,+{\infty}[$$. Later, we define the Littlewood-Paley g-function and using the principle of maximum, we prove that for every $p{\in}]1,+{\infty}[$, there exists a positive constant $C_p$ such that for every $f{\in}L^p(d{\nu}_{\alpha})$, $${\frac{1}{C_p}}{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}{\leqslant}{\parallel}g(f){\parallel}_{p,{\nu}_{\alpha}}{\leqslant}C_p{\parallel}f{\parallel}_{p,{\nu}_{\alpha}}$$.

• Journal of Korean Ophthalmic Optics Society
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• v.13 no.1
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• pp.107-112
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• 2008

urpose: This thesis is a study the Night myopia was surveyed by Subjective refraction and Objective refraction (Dark retinoscopy), and analyzed the relationship between them. It also looked at the relation between Night myopia and pupil size. Methods: 82 adult subjects (ages of 19 to 44, 44 males and 38 females) were examined by Subjective refraction and Objective refraction in the light place. Then Night myopia and pupil size were examined by Subjective refraction and Objective refraction in the dark again. The Statistics were analyzed by SPSS (Statistical Package for Social Science). Results: As the subjects became younger, the observed Night myopia was getting higher in both Subjective refraction, $x^2$=219.48 (p<0.01) and Objective refraction, $x^2$=241.98 (p<0.01). The relationship was statistically significant by showing large pupil size, $x^2$=151.74 (p<0.01). In Objective refraction, as pupil size became larger in the dark place, so did Night myopia, $x^2$=84.27 (p<0.01), reaching a statistically significant correlation, however, the correlation was low in Subjective refraction. In Subjective refraction, observed Night myopia was 73%, 64 examples of 88 examples, a standard of 0.96${\pm}$0.4584D in ${\pm}$0.25D, in male examples, and it was 64%, 49 examples of 76 examples, a standard of 1.01${\pm}$0.4509D in ${\pm}$0.25D, in female examples. In Objective refraction, it was 48%, 42 examples of 88 examples, in standard of 0.85${\pm}$0.4651D in ${\pm}$0.25D, in male examples. And it was 71%, 54 examples of 76 examples, in standard of 0.96${\pm}$0.4133D in ${\pm}$0.25D, in female examples. Conclusions: Night myopia which is measured by both methods, observed as $x^2$=265.35 (p<0.01) and showed a large relationship. The correlation between the two refractions suggests that observed night myopia diopter by Subjective refraction could be used as correction of night myopia.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.465-490
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• 1998

In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)＋$\delta$│ $u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)＋$\delta$ │ $v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.