• Honam Mathematical Journal
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• v.26 no.4
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• pp.379-389
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• 2004

Given operators X and Y acting on a Hilbert space ${\mathcal{H}}$, 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 $i=1,2,{\cdots},n$. In this article, we obtained the following : Let ${\mathcal{H}}$ be a Hilbert space and let ${\mathcal{L}}$ be a commutative subspace lattice on ${\mathcal{H}}$. Let X and Y be operators acting on ${\mathcal{H}}$. Then the following statements are equivalent. (1) There exists an operator A in $Alg{\mathcal{L}}$ such that AX = Y, A is positive and every E in ${\mathcal{L}}$ reduces A. (2) sup ${\frac{{\parallel}{\sum}^n_{i=1}\;E_iY\;f_i{\parallel}}{{\parallel}{\sum}^n_{i=1}\;E_iX\;f_i{\parallel}}}:n{\in}{\mathbb{N}},\;E_i{\in}{\mathcal{L}}$ and $f_i{\in}{\mathcal{H}}<{\infty}$ and <${\sum}^n_{i=1}\;E_iY\;f_i$, ${\sum}^n_{i=1}\;E_iX\;f_i>\;{\geq}0$, $n{\in}{\mathbb{N}}$, $E_i{\in}{\mathcal{L}}$ and $f_i{\in}H$.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.377-387
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• 2014

Let G be a (p, q) graph. Let f be a map from V (G) to {1, 2, ${\ldots}$, p}. For each edge uv, assign the label ${\mid}f(u)-f(\nu){\mid}$. f is called a difference cordial labeling if f is a one to one map and ${\mid}e_f(0)-e_f(1){\mid}{\leq}1$ where $e_f(1)$ and $e_f(0)$ denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordial labeling behavior of triangular snake, Quadrilateral snake, double triangular snake, double quadrilateral snake and alternate snakes.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.401-411
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• 2021

A Diophantine m-tuple is a set {a₁, a₂, …, a_m} of positive integers such that a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E_k be the elliptic curve induced by Diophantine triple {F_2k, 5F_2k+2, 3F_2k + 7F_2k+2}. In this paper, we find the structure of a torsion group of E_k, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1 and some further conditions.

• Korean Journal of Microbiology
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• v.33 no.2
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• pp.92-96
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• 1997

The 6.8 kb Xhol fragment of chromosomal ONA of Pseudomonas sp. 0177 contains the phnDEFG genes involved in the degradation of polyaromatic hydrocarbons and chlorinated aromatics. Here, we report the nucleotide sequence of the ORF encoding a polypeptide consisted of 143 amino acids with a Mr of 13,859. The nucleotide sequence of the ORF is 99% and 68.6% identical to the downstream region of catE of Sphingomonas sp. strain HV3 and the ORF between xylE and xylG of Sphingomonas yanoikuyae Bl, respectively. The deduced amino acid sequence of the PhnF has 62.3% identity with the amino acid encoded hy orfY region of Citrobacter freundii DSM30040. We now confirm that the ORF is located between the catechol 2,3-dioxygenase (C230), phnE, and 2-hydroxymuconic semialdehyde dehydrogenase (2HMSO), phnG.

• Journal of Sensor Science and Technology
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• v.3 no.2
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• pp.65-73
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• 1994

TO:F($SnO_{2}:F$) thin films were prepared by RF magnetron sputtering system. The dependence of their structural, electrical, and optical properties on deposition conditions such as substrate temperature, working pressure and power was studied. The optimum conditions of TO:F thin film are $SnF_{2}$ content of 15wt.% in target, RF power of 150W, substrate temperature of $150^{\circ}C$ and working pressure of 2mmTr. The resistivity and transmittance at 550nm in visible spectrum of the TO:F film deposited at optimum condition are $9{\times}10^{-4}{\Omega}{\cdot}cm$ and above 85%, respectively. For the films deposited from the target without $SnF_{2}$ and with 15wt.% $SnF_{2}$, the optical bandgaps calculated from the transmittance curves are 3.84 and 3.9eV, respectively. X-ray diffraction patterns showed that TO and TO:F films had tetragonal rutile structure with (101), (200) direction.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.273-281
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• 2008

We define the Lie-admissible algebra NW$({\mathbb{F}}[e^{A[s]},x_1,{\cdots},x_n])$ in this work. We show that the algebra and its antisymmetrized (i.e., Lie) algebra are simple. We also find all the derivations of the algebra NW$(F[e^{{\pm}x^r},x])$ and its antisymmetrized algebra W$(F[e^{{\pm}x^r},x])$ in the paper.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.437-449
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• 2009

In this paper, we calculate the number of points on elliptic curves $E^{a^3}_0:y^2=x^3+a^3$ over ${\mathbb{F}}_p$ mod 24 and $E^b_0:y^2=x^3+b$ over ${\mathbb{F}}_p$ mod 6, where b is cubic non-residue in ${\mathbb{F}}^*_p$. For example, if p ${\equiv}$ 1 (mod 12) is a prime, and a and a(2t - 3) are quadratic residues modulo p with $3t^2{\equiv}1$ (mod p), then the number of points in $E^{a^3}_0:y^2=x^3+a^3$ is congruent to 0 modulo 24.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.37-43
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• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

• Journal of the Korean Magnetics Society
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• v.3 no.1
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• pp.48-55
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• 1993

We report the photoemission (PES) studies for the Co/Pd multilayter. The Co 3d PES spectrum of Co/Pd exhibits two interesting features, one near the Fermi energy, $E_{F}$, and another at ~2.5 eV below $E_{F}$. The Co 3d peak near $E_{F}$ of Co/Pd is much narrower than that of the bulk Co, consistent with the enhanced Co magnetic moment in Co/Pd compared to that in the bulk Co. The Co 3d feature at ~-2.5 eV resembles the Pd valence band structures, which suggests a substantial hybridization between the Co and Pd sublayers. The Co 3d PES spectrum of Co/Pd is compared with the existing band structures, obtained using the local spin density functional calculations. A reasonable agreement is found concerning the bandwidth of the occupied part of the Co 3d band, whereas a narrow Co 3d peak near $E_{F}$ seems not to be described by the band structure calculations.

• Journal of the Korean Magnetics Society
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• v.2 no.2
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• pp.114-118
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• 1992

아크로를 이용하여 제작한 NdF $e_{12-x}$ $Ti_{x}$ (1 .leq. x .leq. 2) 합금의 상분석 결과 이들 합금은 ThM $n_{12}$ 구조의 경자성상(1-12상) 과 반강자성의 F $e_{2}$Ti 및 연자성의 .alpha. -Fe 등으로 구성되며, x=1.3 인 NdF $e_{10.7}$ $Ti_{1.3}$ 조성에서 단상에 가까운 ThM $n_{2}$ 구조가 얻어짐이 밝혀졌다. 한편, 합금중의 1-12 상은 50 .mu. m - 100 .mu. m 의 사각주 형태로 생성되며, FeTi은 1-12상의 결정립계에 고립된 입자의 형태로 존재한다. NdF $e_{10.7}$ $Ti_{1.3}$ 합금을 질화처리할 경우 단위포의 체적, 자화, 이방성자장 및 큐리온도가 증가하며, 이합금을 500 .deg. C 에서 15분간 질화처리한 NdF $e_{10.7}$ $Ti_{1.3}$ $N_{x}$ 의 비포화자화, 이방성자장 및 큐리온 도는 각각, .sigma. $_{s}$ =128 A $m^{2}$/kg $H_{A}$=6400 kA/m (80 kOe) 및 Tc=470 .deg. C로 질화처리 전에 비하여 크게 증가한다.크게 증가한다. 증가한다.