• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1753-1757
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• 2015

In this note we obtain a unique continuation result for the differential inequality ${\mid}\bar{\partial}u{\mid}{\leq}{\mid}Vu{\mid}$, where $\bar{\partial}=(i{\partial}_y+{\partial}_x)/2$ denotes the Cauchy-Riemann operator and V (x, y) is a function in $L^2(\mathbb{R}^2)$.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.149-160
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• 2010

Let $W(x)={\prod}_{k=1}^m{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$. Associated with the weight W, upper and lower bounds of the generalized Christoffel functions for generalized nonnegative polynomials are obtained.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.121-125
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• 2000

In this paper, we obtain an algorithm for finding a maximum matching in the line graph L(G) of a graph G. The complexity of our algorithm is O($$\mid$E$\mid$$), where is the edge set of G($$\mid$E$\mid$$ is equal to the number of vertices in L(G)).

• Journal of Korean Society of Forest Science
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• v.58 no.1
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• pp.48-53
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• 1982

This experiment was carried out to distinguish between picea abies (L.) Karsten and Picea koraiensis Nak by the method of discriminant analysis which is used the metrical continuous characteristic on current inorphological plant taxanomy. The results are summarized as follows 1) The discriminant function and discriminant region from the experiment are Z(x)=Z($x_1,\;x_2$)=$0.000379x_1+0.004354x_2-0.311061$ or Z(x)=Z($x_1,\;x_2$=$0.000379(x_1-60.442800)+0.004354(x_2-66.185100)$, $$R_1=(x{\mid}0.000379x_1+0.004354x_2-0.311061{\geq_-}0)$$, $R_2$=($x{\mid}0.000379x_1+0.004354x_2-0.311061$ <0). 2) The probability of misclassification based on the above discriminant region is P($2{\mid}1$)=$P(1{\mid}2)$=0.444 therefore the probability of simultaneous misclassification of P($2{\mid}1$) and $P(1{\mid}2)$ is about 44.4%. 3) the probability of misclassification by the discriminant function resulted from the experiment if recorded as high but it is thought that there is a considerable meaning to perceive the probability of confidence about the discrimination better than its precision.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.55-64
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• 2017

For -2 < ${\alpha}$ < ${\infty}$ and 0 < p < ${\infty}$, the $\mathcal{Q}_K$-type space is the space of all analytic functions on the open unit disk ${\mathbb{D}}$ satisfying $$_{{\sup} \atop a{\in}{\mathbb{D}}}{\large \int_{\mathbb{D}}}{{\mid}f^{\prime}(z){\mid}}^p(1-{{\mid}z{\mid}^2})^{\alpha}K(g(z,a))dA(z)<{\infty}$$, where $g(z,a)=log\frac{1}{{\mid}{\sigma}_a(z){\mid}}$ is the Green's function on ${\mathbb{D}}$ and K : [0, ${\infty}$) [0, ${\infty}$), is a right-continuous and non-decreasing function. For 0 < s < ${\infty}$, the space $\mathcal{Q}_s$ consists of all analytic functions on ${\mathbb{D}}$ for which $$_{sup \atop a{\in}{\mathbb{D}}}{\large \int_{\mathbb{D}}}{{\mid}f^{\prime}(z){\mid}}^2(g(z,a))^sdA(z)<{\infty}$$. Boundedness and compactness of composition operators $C_{\varphi}$ acting on $\mathcal{Q}_K$-type spaces and $\mathcal{Q}_s$ spaces is characterized in terms of the norms of ${\varphi}^n$. Thus the author announces a solution to the problem raised by Wulan, Zheng and Zhou.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.359-366
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• 1996

A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1195-1219
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• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.

• Journal of the Korean Ceramic Society
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• v.33 no.6
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• pp.645-652
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• 1996

The ionic conductivity of NASICON (Na Super Ionic Conductor) solid electrolyte was simulated by using Monte Carlo Method (MCM)based on a hopping model. We assumed that the conduction path of Na ions is Na1→mid-Na→Na2 where the mid-Na sites are shallow potential sites to induce 'a breathing-like movement' of Na ions in the NASICON framework. The minimum of charge correlation factor Fc and the maximum of appeared at nearby x=2.0 The occupancy of mid-Na site affected the depth of potential barrier and the conduc-tivity of the NASICON. At above x=0.3 ln σT vs. 1/T* plots have been shown Arrhenius behavior but in (VWfc)vs. 1/T* have been shown the Arrhenius type tendency at x=1 MCM results accorded with the experi-mental procedure. The role of mid-Na on Na+ ion conduction could be explained by an additional driving force and a breating-like movement model for motions of Na+ ions in the NASICON framework. As we couldn't clearly remarked the model which is the better it seems reasonable to conclude that these hypothesies are suitable to explain the FIC behavior at NASICON.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.173-179
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• 2018

In this paper, we investigate the stability of positive weak solution for the singular p-Laplacian nonlinear system $-div[{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u]+m(x){\mid}u{\mid}^{p-2}u={\lambda}{\mid}x{\mid}^{-(a+1)p+c}b(x)f(u)$ in ${\Omega}$, Bu = 0 on ${\partial}{\Omega}$, where ${\Omega}{\subset}R^n$ is a bounded domain with smooth boundary $Bu={\delta}h(x)u+(1-{\delta})\frac{{\partial}u}{{\partial}n}$ where ${\delta}{\in}[0,1]$, $h:{\partial}{\Omega}{\rightarrow}R^+$ with h = 1 when ${\delta}=1$, $0{\in}{\Omega}$, 1 < p < n, 0 ${\leq}$ a < ${\frac{n-p}{p}}$, m(x) is a weight function, the continuous function $b(x):{\Omega}{\rightarrow}R$ satisfies either b(x) > 0 or b(x) < 0 for all $x{\in}{\Omega}$, ${\lambda}$ is a positive parameter and $f:[0,{\infty}){\rightarrow}R$ is a continuous function. We provide a simple proof to establish that every positive solution is unstable under certain conditions.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.387-395
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• 2004

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{i}\;=\;Y_{i}$, for i = 1,2,...,n. In this article, we showed the following: Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that range(X) is dense in H. Then the following statements are equivalent: (1) There exists an operator A in AlgL such that AX = Y, $A^{*}$ = A and every E in L reduces A. (2) sup ${\frac{$\mid$$\mid${\sum_{i=1}}^n\;E_iYf_i$\mid$$\mid$}{$\mid$$\mid${\sum_{i=1}}^n\;E_iXf_i$\mid$$\mid$}$:n{\epsilon}N,f_i{\epsilon}H\;and\;E_i{\epsilon}L}\;<\;{\infty}$ and = for all E in L and all f, g in H.