• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.103-113
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• 1995

Let $S^{n+p}$(c) be the (n + p)-dimensional Euclidean sphere of constant curva ture c and let M be an n-dimensional compact minimal submanifold isometric ally immersed in $S^{n+p}$(c). Let $A_\xi$ be the second fundamental form of M in the direction of a normal $\xi$ and T the tensor defined by $T(\xi, \eta) = traceA_\xi A_\eta$.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.1 s.190
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• pp.64-70
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• 2007

A long-exposing technique (LET) has been conducted to create nanoscale patterns applicable to diverse micro-devices using two-photon polymerization (TPP). By the weakly-polymerized region via the LET, double-layered embossing patterns can be fabricated simply in a single step. The LET makes possible a voxel and its surrounding to be fully grown into more than 500 nm in lateral size and weakly-polymerized region (WPR), respectively. In the WPR. interconnecting ribs between voxels are generated, and they lead to the creation of double-layered dot patterns. Moreover, by controlling the distance between voxels, various shapes of interconnecting rib can be fabricated when the LET is applied. Various embossing patterns were fabricated to evaluate the usefulness of the proposed technique as a novel nanopatterning technique in TPP.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.45-51
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• 2010

Let A be an abelian variety defined over a number field K and let L be a cyclic extension of K with Galois group G = <${\sigma}$> of order n. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and of A over L. Assume III(A/L) is finite. Let M(x) be a companion matrix of 1+x+${\cdots}$+$x^{n-1}$ and let $A^x$ be the twist of $A^{n-1}$ defined by $f^{-1}{\circ}f^{\sigma}$ = M(x) where $f:A^{n-1}{\rightarrow}A^x$ is an isomorphism defined over L. In this paper we compute [III(A/K)][III($A^x$/K)]/[III(A/L)] in terms of cohomology, where [X] is the order of an finite abelian group X.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.137-141
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• 2017

Let A be an abelian variety defined over a number field K and let L be a finite Galois extension of K. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Let $Res_{L/K}(A)$ be the restriction of scalars of A from L to K and let B be an abelian subvariety of $Res_{L/K}(A)$ defined over K. Assuming that III(A/L) is finite, we compute [III(B/K)][III(C/K)]/[III(A/L)], where [X] is the order of a finite abelian group X and the abelian variety C is defined by the exact sequence defined over K $0{\longrightarrow}B{\longrightarrow}Res_{L/K}(A){\longrightarrow}C{\longrightarrow}0$.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• Proceedings of the Membrane Society of Korea Conference
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• 1991.10a
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• pp.29-33
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• 1991

Alumina UF membranes were prepared by sol-gel process and their gas permeabilities were characterized. Alumina MF membrane with average pore diameter about 0.12$\mu$m and tubular shape was used as a support. Gas permeation measurements of helium and nitrogen gas exhibited the permeabilities of 1.58 $\times$ 10E-6 and $0.63 \times 10E-6 cc\cdot cm(STP)/cm^2\cdot sec \cdot cmHg$, respectively. The permeability ratio was 2.5. This means the gas permeation is fully governed by knudsen diffusion mechanism.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.10a
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• pp.225-230
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• 2002

Machine of textiles let off is equipment supplying constantly fabrics. Nowdays, as it is replaced band - brake type with hydraulic motor driven type, we looked into characteristic of hydraulic solenoid pilot direction valve(SPDV) for controlling acceleration performance of hydraulic motor. This study deals with controlling the initial speed of textiles let off machine. Finally, to control the initial speed of hydraulic motor, we controlled the adjustment screw of SPDV by a hand. Test which was carried out in the laboratory shows that initial speed of textiles let off could be improved by controlling adjustment screw of SPDV. Also, the results of experiment work were compared with dynamic characteristic of other on/off solenoid direction valve(SDV).

• Journal of Sensor Science and Technology
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• v.25 no.1
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• pp.41-45
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• 2016

In this study, LET (Linear Energy Transfer) calibration of CR-39 SSNTD (Solid State Nuclear Track Detector) was performed using 500 MeV/u Fe heavy ions in HIMAC (Heavy Ion Medical Accelerator) for high LET radiation dosimetry. The irradiated CR-39 SSNDT were etched according JAXA (Japan Aerospace Exploration Agency) etching conditions. And the etched SSNTD were analyzed by using Image J. Determined dose-mean lineal energy ($\overline{y_D}$) of 500 MeV/u Fe is about 283.3 keV/um by using the CR-39 SSNTD. This value is very similar result compare to the results calculated by GEANT4 Monte Carlo simulation and measured with TEPC active radiation detector. We confirmed that the CR-39 SSNTD was useful for high LET radiation dosimetry such as heavy iron ions.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.35-42
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• 1989

Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A$a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.