• Journal of the Korean Magnetics Society
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• v.9 no.3
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• pp.154-158
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• 1999

Magnetic properties and microstructure of nanocrystalline $\alpha$-(Fe, Co)-based Nd-(Fe, Co)-B-Nb-Cu alloys have been investigated. $Nd_x(Fe_{0.9}Co_{0.1})_{90-x}B_6Nb_3Cu_1$(x=2, 3, 4, 5, 6) alloys prepared by rapid solidification process show amorphous phase except the one with x=2. By a proper annealing, the amorphous in the alloy is changed to a nanocrystalline phase. It is confirmed that the nanocrystalline alloys are composed of $\alpha$-(Fe, Co) and $Nd_2(Fe, Co)_{14}B_1$ phase. The optimally annealed $Nd_3(Fe_{0.9}Co_{0.1})_87B_6Nb_3Cu_1$ alloy shows the highest remanence of 1.55 T. The coercivity increases with the increase of Nd content The maximum coercivity of 4.6 kOe is obtained from an optimally annealed $Nd_6(Fe_{0.9}Co_{0.1})_84B_6Nb_3Cu_1$ alloy, resulting in the maximum energy product of 10.6 MGOe.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1149-1159
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• 2018

A quadratic polynomial ${\Phi}_{a,b,c}(x,y,z)=x(ax+1)+y(by+1)+z(cz+1)$ is called universal if the diophantine equation ${\Phi}_{a,b,c}(x,y,z)=n$ has an integer solution x, y, z for any nonnegative integer n. In this article, we show that if (a, b, c) = (2, 2, 6), (2, 3, 5) or (2, 3, 7), then ${\Phi}_{a,b,c}(x,y,z)$ is universal. These were conjectured by Sun in [8].

• Journal of the Korean Ceramic Society
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• v.38 no.6
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• pp.558-567
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• 2001

본 연구에서는 알콕사이드를 전구물질로 하는 졸겔공정을 이용하여 Bi 과잉 12 mol%의 조성인 B $i_4$ $Ti_3$ $O_{12}$ 박막과 B $i_4$ $Ti_{3-x}$T $a_{x}$ $O_{12}$(x=0.1, 0.2, 0.3) 박막을 제조하였다. XPS 분석에 따르면 Ta 치환 x=0.2에서 Bi 4f의 photoemission 곡선이 낮은 결합에너지로 이동하였고 피크 강도가 감소하는 현상이 관측되었다. 이는 x=0.1과 0.2 사이에서 Bi-O 결합이 길어져 인장상태 하에 있었음을 나타내었다. B $i_4$ $Ti_3$ $O_{12}$(BIT) 박막의 유전상수와 유전손실은 100 kHz에서 340, 0.05이었고, B $i_4$ $Ti_{3-x}$T $a_{x}$ $O_{12}$ 박막에서 이들 값은 x=0.1에서 가장 높았으며, 각각 480, 0.13이었다. B $i_4$ $Ti_3$ $O_{12}$ 박막의 잔류분극과 항전계는 1.24$\mu$C/$ extrm{cm}^2$, 31.4 kV/cm 이었으나, Ta 치환 x=0.2에서 이들 값은 각각 19.7$\mu$C/$\textrm{cm}^2$, 49.5 kV/cm 에 이르렀다. 또한, B $i_4$ $Ti_3$ $O_{12}$ 박막의 누설전류 밀도는 ~$10^{-6}$ A/$\textrm{cm}^2$ 정도이었으며, Ta 치환은 누설전류를 감소시켜 Ta 치환 x=0.2 이상에서 BIT 박막에 비해 한 차수 정도 낮아졌다. Ta 치환에 따른 B $i_4$ $Ti_3$ $O_{12}$ 전기 물성에서 변화는 Bi-O 결합에서 관측된 인장상태로의 전이와 연관성이 있었으며, 덧붙여 치환에서 생성된 전자에 의한 정공보상이 이에 영향을 끼쳤다. 정공보상이 이에 영향을 끼쳤다.끼쳤다.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.307-314
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• 2005

In this paper we consider positive solutions of the following difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}},{\frac{B}{x_{n-2}}}],\;A,B\;>\;0$$. We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}x_{n-1}{\cdots}x_{n-k}},{\frac{B}{x_{n-(k+2)}{\cdots}x_{n-(2k+2)}}],\;A,B\;>\;0$$.

• Journal of the Korean Magnetics Society
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• v.11 no.2
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• pp.58-62
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• 2001

The L $i_{0.5}$F $e_{2.5-x}$A $l_{x}$ $O_4$ systems (x=0, 0.3, 0.6, 0.9, 1.2, 1.5) were investigated by X-ray diffraction and Mossbauer spectroscopy. The structure of all the samples is cubic spinel type and lattice constant decrease with increasing Al content x. The Moissbauer spectra reveal two sextet for 0$\leq$x$\leq$0.6, two sextet and a doublet for 0.9$\leq$x$\leq$1.2, and a doublet for x=1.5. The cation distribution of the samples is (L $i_{1-a}$$^{+}$F $e_{a}$ $^{3+}$)$^{A}$[L $i_{a-0.5}$$^{+}$A $l_{2.5-a-x}$$^{+}$F $e_{2.5-a-x}$$^{3+}$]$^{B}$ $O_4$$^{2-}$ and substituted $Al^{3+}$ ions decrease the covalency of F $e^{3+}$- $O^{2-}$ bond in B-sites and A-B super-exchange interactions.tions.s.tions.ons.s.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.383-388
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• 2007

A (g, f)-factor F of a graph G is Called a Hamiltonian (g, f)-factor if F contains a Hamiltonian cycle. The binding number of G is defined by $bind(G)\;=\;{min}\;\{\;{\frac{{\mid}N_GX{\mid}}{{\mid}X{\mid}}}\;{\mid}\;{\emptyset}\;{\neq}\;X\;{\subset}\;V(G)},\;{N_G(X)\;{\neq}\;V(G)}\;\}$. Let G be a connected graph, and let a and b be integers such that $4\;{\leq}\;a\;<\;b$. Let g, f be positive integer-valued functions defined on V(G) such that $a\;{\leq}\;g(x)\;<\;f(x)\;{\leq}\;b$ for every $x\;{\in}\;V(G)$. In this paper, it is proved that if $bind(G)\;{\geq}\;{\frac{(a+b-5)(n-1)}{(a-2)n-3(a+b-5)},}\;{\nu}(G)\;{\geq}\;{\frac{(a+b-5)^2}{a-2}}$ and for any nonempty independent subset X of V(G), ${\mid}\;N_{G}(X)\;{\mid}\;{\geq}\;{\frac{(b-3)n+(2a+2b-9){\mid}X{\mid}}{a+b-5}}$, then G has a Hamiltonian (g, f)-factor.

• Journal of the Korean Magnetics Society
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• v.7 no.6
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• pp.293-298
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• 1997

$Fe_5Si_Xb_{5-x}$ (x=0, 1, 2, 3) powders were prepared by mechanical alloying, and their phases and magnetic properties were investigated by using XRD, TEM, Mossbauer spectroscopy and VSM. Starting elements are incorporated into $\alpha$-Fe in the early stage of mechanical alloying, and the stable phases are formed as the milling proceeds. After the annealing at 80$0^{\circ}C$ for 2 hours, it is found that the FeB and $Fe_2B$ phases coexist for the $Fe_5B_5$(x=0) composition. By substituting Si for B, the formation of $Fe_2B$ phase is restricted and the $Fe_5SiB_2$, $Fe_2Si_{0.4}B_{0.6}$ and paramagnetic phase begin to appear. The FeB phase has wide range of hyperfine magnetic field because it is not fully crystallized on the annealing at 800 $^{\circ}C$. On the contrary, others have good crystalline phases and show well-defined hyperfine magnetic field. Magnetic saturation is highest for the $Fe_5B_5$ composition where the amount of the $Fe_2B$ phase in large.

• The Korean Journal of Ceramics
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• v.2 no.2
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• pp.76-82
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• 1996

PLZT ceramics having two nominal compositions, $Pb_{1-3x/2}La_xV_{x/2}(Zr_{03}Ti_{03})O_3$ and $Pb_{1-x}La_x(Zr_{0.2}Ti_{0.5})_{1-x/4}V_{x/4}O_3$ (V: vacancy) with x=0.00~0.30, were prepared. The physical, structural, and dielectric properties were investigated by X-ray diffraction, scanning electron microscopy, Raman spectroscopy, and measurements of bulk density and dielectric constant. The two series with A-stie and B-site vacancies showed different physical, structural, dielectric properties, and, specially, Curie temperature. In comparison to PLZT with B-site vacancies, PLZT with A-site vacancies showed high Curie temperatures and low maxima of dielectric constant. Consequently, it is evident that the properties of PLZT ceramics depend on the vacancy formula adopted as a batch composition in preparation.

• Proceedings of the Korean Ceranic Society Conference
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• 2000.04a
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• pp.117.2-117.2
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• 2000

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.