• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1993.11a
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• pp.71-74
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• 1993

In this paper, the permeability(${\mu}$$\sub$r′/, ${\mu}$$\sub$r"/), permittivity($\varepsilon$$\sub$r′/, $\varepsilon$$\sub$r"/) and absorption properties of Ferroxplana/Rubber composites were investigated. The composite specimens were prepared by molding and curing the mixtures of matrix rubber and Ni$_2$Y ferroxplana powders which were synthesized by coprecipitated method. The permeability(${\mu}$$\sub$r′/) of specimen was decreased in the range of 8∼12.5(GHz) and the permeability(${\mu}$$\sub$r"/) and Permittivity($\varepsilon$$\sub$r′/, $\varepsilon$$\sub$r"/) were increased. The optimum thickness of electromagnetic wave absorber (F/R=4, 1,200($^{\circ}C$) ), utilizing the Smith chart, was about 3.0(mm). The Figure of Merit was 93(%).

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1299-1324
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• 2014

We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.93-113
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• 2011

Let $a{\oplus}b$ = max(a, b), $a{\otimes}b$=a+b, a, $b\in\mathbb{R}_{\varepsilon}\;:=\cup\{-\infty\}$. In max-plus algebra we work on the linear algebra structure for the pair of operations (${\oplus},{\otimes}$) extended to matrices and vectors over $\mathbb{R}_{\varepsilon}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $\mathbb{R}_{\varepsilon}$.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.25-33
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• 2002

In this paper we have shown conditions of R for the existence of the solution to the problem of the type $-u''=ue^{{\varepsilon}u}$ on the interval (0, R) with boundary and other conditions as in $(1-{\varepsilon})-(4)$ for various ${\varepsilon}$.

• Journal of Computing Science and Engineering
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• v.3 no.1
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• pp.1-4
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• 2009

In a given text T of size n, we need to search for the information that we are interested. In order to support fast searching, an index must be constructed by preprocessing the text. Suffix array is a kind of index data structure. The compressed suffix array (CSA) is one of the compressed indices based on the regularity of the suffix array, and can be compressed to the $k^{th}$ order empirical entropy. In this paper we improve the lookup time complexity of the compressed suffix array by using the multi-ary wavelet tree at the cost of more space. In our implementation, the lookup time complexity of the compressed suffix array is O(${\log}_{\sigma}^{\varepsilon/(1-{\varepsilon})}\;n\;{\log}_r\;\sigma$), and the space of the compressed suffix array is ${\varepsilon}^{-1}\;nH_k(T)+O(n\;{\log}\;{\log}\;n/{\log}^{\varepsilon}_{\sigma}\;n)$ bits, where a is the size of alphabet, $H_k$ is the kth order empirical entropy r is the branching factor of the multi-ary wavelet tree such that $2{\leq}r{\leq}\sqrt{n}$ and $r{\leq}O({\log}^{1-{\varepsilon}}_{\sigma}\;n)$ and 0 < $\varepsilon$ < 1/2 is a constant.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.9-20
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• 2008

Let ${X_i{\mid}i{\geq}1}$ be a strictly stationary sequence of associated random variables with mean zero and let ${\sigma}^2=EX_1^2+2\sum\limits_{j=2}^\infty{EX_1}{X_j}$ with 0 < ${\sigma}^2$ < ${\infty}$. Set $S_n={\sum\limits^n_{i=1}^\{X_i}$, the precise asymptotics for ${\varepsilon}^{{\frac{2(r-p)}{2-p}}-1}\sum\limits_{n{\geq}1}n^{{\frac{r}{p}}-{\frac{1}{p}}+{\frac{1}{2}}}P({\mid}S_n{\mid}{\geq}{\varepsilon}n^{{\frac{1}{p}}})$,${\varepsilon}^2\sum\limits_{n{\geq}3}{\frac{1}{nlogn}}p({\mid}Sn{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ and ${\varepsilon}^{2{\delta}+2}\sum\limits_{n{\geq}1}{\frac{(loglogn)^{\delta}}{nlogn}}p({\mid}S_n{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ as ${\varepsilon}{\searrow}0$ are established under the suitable conditions.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.111-117
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• 2010

For a based, 1-connected, finite CW-complex X, we denote by $\varepsilon(X)$ the group of homotopy classes of self-homotopy equivalences of X and by $\varepsilon_#\;^{dim+r}(X)$ the subgroup of homotopy classes which induce the identity on the homotopy groups of X in dimensions $\leq$ dim X+r. In this paper, we calculate the subgroups $\varepsilon_#\;^{dim+r}(X)$ when X is a wedge of two Moore spaces determined by cyclic groups and in consecutive dimensions.

• Journal of Mechanical Science and Technology
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• v.15 no.11
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• pp.1463-1471
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• 2001

The Kachanov and Rabotnov (K-R) creep damage model was interpreted and applied to type 316LN and HT-9 stainless steels. Seven creep constants of the model, A, B, $textsc{k}$, m, λ, ${\gamma}$, and q were determine d for type 316LN stainless steel. In order to quantify a damage parameter, the cavity was interruptedly traced during creep for measuring cavity area to be reflected into the damage equation. For type 316LN stainless steel, λ= $\varepsilon$R/$\varepsilon$* and λf=$\varepsilon$/$\varepsilon$R were 3.1 and increased with creep strain. The creep curve with λ=3.1 depleted well the experimental data to the full lifetime and its damage curve showed a good agreement when r=24. However for the HT-9 stainless steel, the values of λ and λf were different as λ=6.2 and λf=8.5, and their K-R creep curves did not agree with the experimental data. This mismatch in the HT-9 steel was due to the ductile fracture by softening of materials rather than the brittle fracture by cavity growth. The differences of the values in the above steels were attributed to creep ductilities at the secondary and the tertiary creep stages.

• The Mathematical Education
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• v.26 no.1
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• pp.41-45
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• 1987

In this paper, we give several fixed point theorems in a complete metric space for two multi-valued mappings commuting with two single-valued mappings. In fact, our main theorems show the existence of solutions of functional equations f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ and $\chi$=f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ under certain conditions. We also answer an open question proposed by Rhoades-Singh-Kulsherestha. Throughout this paper, let (X, d) be a complete metric space. We shall follow the following notations : CL(X) = {A; A is a nonempty closed subset of X}, CB(X)={A; A is a nonempty closed and founded subset of X}, C(X)={A; A is a nonempty compact subset of X}, For each A, B$\in$CL(X) and $\varepsilon$>0, N($\varepsilon$, A) = {$\chi$$\in$X; d($\chi$, ${\alpha}$) < $\varepsilon$ for some ${\alpha}$$\in$A}, E$\sub$A, B/={$\varepsilon$ > 0; A⊂N($\varepsilon$ B) and B⊂N($\varepsilon$, A)}, and (equation omitted). Then H is called the generalized Hausdorff distance function fot CL(X) induced by a metric d and H defined CB(X) is said to be the Hausdorff metric induced by d. D($\chi$, A) will denote the ordinary distance between $\chi$$\in$X and a nonempty subset A of X. Let R$\^$+/ and II$\^$+/ denote the sets of nonnegative real numbers and positive integers, respectively, and G the family of functions ${\Phi}$ from (R$\^$+/)$\^$s/ into R$\^$+/ satisfying the following conditions: (1) ${\Phi}$ is nondecreasing and upper semicontinuous in each coordinate variable, and (2) for each t>0, $\psi$(t)=max{$\psi$(t, 0, 0, t, t), ${\Phi}$(t, t, t, 2t, 0), ${\Phi}$(0, t, 0, 0, t)} $\psi$: R$\^$+/ \longrightarrow R$\^$+/ is a nondecreasing upper semicontinuous function from the right. Before sating and proving our main theorems, we give the following lemmas:

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.635-645
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• 2002

Two examples of $\varepsilon$-famed manifolds are constructed. It is proved that an $\varepsilon$-framed structure on a manifold is not unique. Automorphism groups of r-framed manifolds are studied. Lastly we prove that a connected Lie group G admits a left invariant normal $\varepsilon$-framed structure if and only if the Lie algebra of all left invariant vector fields on G is an $\varepsilon$-framed Lie algebra.