• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.69-73
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• 1997

We show that if T is an $\varepsilon$-approximate Jordan functional such that T(a) = 0 implies $T(a^2) = 0 (a \in A)$ then T is continuous and $\Vert T \Vert \leq 1 + \varepsilon$. Also we prove that every $\varepsilon$-near Jordan mapping is an $g(\varepsilon)$-approximate Jordan mapping where $g(\varepsilon) \to 0$ as $\varepsilon \to 0$ and for every $\varepsilon > 0$ there is an integer m such that if T is an $\frac {\varepsilon}{m}$-approximate Jordan mapping on a finite dimensional Banach algebra then T is an $\varepsilon$-near Jordan mapping.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.2
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• pp.81-91
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• 1991

A k-$\varepsilon$ equation model was established to investigate the behaviours of two-dimensional surface buoyant jets. Its computational results were compared with experimental data on the mean flow and the turbulent transport. The model was proved to predict the flow characteristics reasonably. The influence of the values of k and $\varepsilon$ given in the inlet on the evaluation of surface buoyant jets was examined to determine them quantitatively. Computations for several values of buoyancy production coefficient $C\varepsilon$$_3$ in the $\varepsilon$ equation, which has been neglected by many researchers. were carried out to evaluate its effect on the flow development. Computational results of the two-dimensional surface buoyant jets were presented and briefly discussed.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.8
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• pp.69-74
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• 2008

The propagation constant, which is defined for a double-positive (DPS) material of positive permittivity (${\varepsilon}'$) and permeability (${\mu}'$), is extended and derived for an epsilon-negative (ENG) material (${\varepsilon}'<0,\;{\mu}'>0$), a mu-negative (MNG) material (${\varepsilon}'>0,\;{\mu}'<0$), and a double-negative (DNG) material (${\varepsilon}'<0,\;{\mu}'<0$). By investigating how the permittivity loss (${\varepsilon}"$) and permeability loss (${\mu}"$) terms affect the propagation constant, we determine that the wave in the materials propagates as a right-handed (RH) triad or a left-handed (LH) triad. Regardless of the magnitudes of ${\varepsilon}"$ and ${\mu}"$, DPS and DNG materials become RH and LH media, respectively. However, ENG and MNG materials possess unusual characteristics that both materials become a RH medium when the sign of (${\varepsilon}'{\mu}"+{\varepsilon}"{\mu}'$) is positive and they become a LH medium when the sign is negative.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.773-789
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• 2014

We consider linear operators on square matrices over antinegative semirings. Let ${\varepsilon}_k$ denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set ${\varepsilon}_1$ and the set ${\varepsilon}_2$, and those that preserve the set ${\varepsilon}_{n^2-2n+2}$ and the set ${\varepsilon}_{n^2-2n+1}$. We also characterize those linear operators that strongly preserve ${\varepsilon}_2$, ${\varepsilon}_{n^2-2n+2}$ or ${\varepsilon}_{n^2-2n+1}$.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1047-1063
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• 2006

Let $\varepsilon_#(X)$ be the subgroups of $\varepsilon(X)$ consisting of homotopy classes of self-homotopy equivalences that fix homotopy groups through the dimension of X and $\varepsilon_*(X) $ be the subgroup of $\varepsilon(X)$ that fix homology groups for all dimension. In this paper, we establish some connections between the homotopy group of X and the subgroup $\varepsilon_#(X)\cap\varepsilon_*(X)\;of\;\varepsilon(X)$. We also give some relations between $\pi_n(W)$, as well as a generalized Gottlieb group $G_n^f(W,X)$, and a subset $M_{#N}^f(X,W)$ of [X, W]. Finally we establish a connection between the coGottlieb group of X and the subgroup of $\varepsilon(X)$ consisting of homotopy classes of self-homotopy equivalences that fix cohomology groups.

• Journal of Life Science
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• v.17 no.11
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• pp.1511-1516
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• 2007

Basophils and mast cells play an important role in $Fc{\varepsilon}RI-mediated$ allergic reaction as effector cells. We studied the effects of Acanthopanax chiisanensis on $Fc{\varepsilon}RI\;{\alpha}$ chain expression in human basophilic KU812F cells. Ethanol extracts from root and stem of A. chiisanensis were tested for inhibitory effects of $Fc{\varepsilon}RI\;{\alpha}$ chain expression. The cell surface $Fc{\varepsilon}RI\;{\alpha}$ chain expression was examined by flow cytometric analysis. All of the extracts of A. chiisanensis reduced the cell surface $Fc{\varepsilon}RI\;{\alpha}$ chain expression. Furthermore, A. chiisanensis extracts caused a decrease in the level of $Fc{\varepsilon}RI\;{\alpha}$ chain mRNA level and $Fc{\varepsilon}RI-mediated$ histamine release. These results suggest that root and stem extracts of A. chiisanensis play an important role in anti-allergic activity via down-regulation of $Fc{\varepsilon}RI\;{\alpha}$ chain expression and decrease in release of inflammatory mediator such as histamine.

• Journal of computational fluids engineering
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• v.15 no.4
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• pp.1-8
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• 2010

This article describes the numerical investigation of turbulent blood flow in the stenosed artery bifurcation under periodic acceleration of the human body. Numerical analyses for turbulent blood flow were performed with different magnitude of periodic accelerations using a modified turbulence model which was considering drag reduction of non-Newtonian fluid. The blood was considered to be a non-Newtonian fluid which was based on the power-law viscosity. In order to validate the modified $k-{\varepsilon}$ model, numerical simulations were compared with the standard $k-{\varepsilon}$ model and the Malin's low Reynolds number turbulence model for power-law fluid. As results, the modified $k-{\varepsilon}$ model represents intermediate characteristics between laminar and standard $k-{\varepsilon}$ model, and the modified $k-{\varepsilon}$ model showed good agreements with Malin's verified power law model. Moreover, the computing time and computer resource of the modified $k-{\varepsilon}$ model were reduced about one third than low Reynolds number model including Malin's model.

• Journal of the Korean Chemical Society
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• v.20 no.2
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• pp.158-165
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• 1976

The anionic polymerization of ${\varepsilon}$-caprolactam with N,N'-adipyl-bis-${\varepsilon}$-caprolactam as an initiator and potassium hydroxide as a catalyst was studied under various conditions.It was found that concentration of catalyst and initiator was 4.2 and 1.6 mole %, and polymerization temperature of 130$^{\circ}C$C, polymerization time of 1.5 hours was the optimum condition. The intrinsic viscosity and molecular weight of the obtained polymer was over 0.9 dl/g and 12,000. The polymerization was carried out in the presence of N-acyl-${\varepsilon}$-caprolactam as an initiator, it was observed that the reactivity of N,N'-adipyl-bis-${\varepsilon}$-caprolactam was greater than both of the N-benzoyl-${\varepsilon}$-caprolactam and N-acetyl-${\varepsilon}$-caprolactam. In general it was also observed that the intrinsic viscosity and yield of conversion was increased as an increasing of concentration of catalyst and initiator and also highly depend on temperature.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.141-151
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• 2002

Let X and Y be real Banach spaces and $\varepsilon$, p $\geq$ 0. A mapping T between X and Y is called an ($\varepsilon$, p)-isometry if ｜∥T(x)-T(y)∥-∥x-y∥｜$\leq$ $\varepsilon$∥x-y∥$^{p}$ for x, y$\in$X. Let H be a real Hilbert space and T : H longrightarrow H an ($\varepsilon$, p)-isometry with T(0) = 0. If p$\neq$1 is a nonnegative number, then there exists a unique isometry I : H longrightarrow H such that ∥T(x)-I(y)∥$\leq$ C($\varepsilon$)(∥x∥$^{ 1+p)/2}$+∥x∥$^{p}$ ) for all x$\in$H, where C($\varepsilon$) longrightarrow 0 as $\varepsilon$ longrightarrow 0.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.399-415
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• 2017

Given a topological space X and a non-negative integer k, we study the self-homotopy equivalences of X that do not change maps from X to n-sphere $S^n$ homotopically by the composition for all $n{\geq}k$. We denote by ${\varepsilon}^{\sharp}_k(X)$ the set of all homotopy classes of such self-homotopy equivalences. This set is a dual concept of ${\varepsilon}^{\sharp}_k(X)$, which has been studied by several authors. We prove that if X is a finite CW complex, there are at most a finite number of distinguishing homotopy classes ${\varepsilon}^{\sharp}_k(X)$, whereas ${\varepsilon}^{\sharp}_k(X)$ may not be finite. Moreover, we obtain concrete computations of ${\varepsilon}^{\sharp}_k(X)$ to show that the cardinal of ${\varepsilon}^{\sharp}_k(X)$ is finite when X is either a Moore space or co-Moore space by using the self-closeness numbers.