• Journal of the Korean Magnetics Society
• /
• v.3 no.3
• /
• pp.185-189
• /
• 1993

급속응고법으로 제작된 비정질 $Fe_{85-x}Co_{x}Zr_{7}B_{7}Cu_{1}$ 합금의 열처리에 따른 구조 및 자기특성이 조사되었다. 비정질 $Fe_{85-x}Co_{x}Zr_{7}B_{7}Cu_{1}$ 합금은 $600^{\circ}C$이하의 열처리온도에서 약 10 nm의 초미세결정립이 형성된다. $600^{\circ}C$이상의 열처리 조건에서는 결정립크기가 급격히 증가하여 자기특성을 열화시킨다. $Fe_{85-x}Co_{x}Zr_{7}B_{7}Cu_{1}$ 합금의 최적열처리온도는 Fe-Zr-B초미세결정립합금에 비하여 낮으며, 결정립크기 또한 감소한다. 이는 Cu의 첨가에 기인하는 것으로 판단된다. 최적열처리조건에서 $Fe_{80}Co_{5}Zr_{7}B_{7}Cu_{1}$ 초미세결정립합금의 포화자화 및 f=50 kHz, $B_{m}=0.2\;T$에서 측정한 투자율 및 철손은 각각 157.3 emu/g(1.5 T), $1.8{\times}10^{4}$ 및 13 W/kg으로 자기특성이 가장 우수하다.

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

• Proceedings of the Korea Association of Crystal Growth Conference
• /
• 1998.06a
• /
• pp.3-5
• /
• 1998

The interest in the use of borate crystals in ultraviolet(UV) nonlinear optics(NLO) has increased because all solid-stste UV lasers obtained with NLO are in highly demand. Much effort has been spent on developing borates series, such as{{{{ { beta -BaB }_{2 } {O }_{4 }(BBO), {LiB }_{ 3}{O }_{5 }(LBO)}}}} and{{{{{ CsKiB}_{6 }{O }_{10 }(CLBO)}}}} in this decade. Recently another new borate crystals, {{{{{ YCa}_{4 }O({BO }_{3 })_{3}}}}} and{{{{{Gd }_{x }{Y }_{1-x }{Ca }_{4 }O({BO }_{ 3})({Gd }_{x }{Y }_{1-x }COB)}}}} have been developed by the present authors. Here, the growth and NLO properties of YCOB and {{{{ {Gd }_{ x} {Y }_{ 1-x} }}}}CO B crystal are reported and their properties discussed in relation to those of other nonlinear optical crystals, such as LBO.

• Korean Journal of Materials Research
• /
• v.11 no.1
• /
• pp.3-7
• /
• 2001

$M\"{o}ssbauer$ spectra of the $Ni_{1+x}Ti_xFe_{2-2x}O_4$ systems ($0{\leqq}x{\leqq}0.7$), which appear as single phase spinel structure, were examined at RT. The $M\"{o}ssbauer$ spectra reveal two sextet for $0{\leqq}x{\leqq}0.3$, two sextet and a doublet for $0.4{\leqq}x{\leqq}0.6$, and a doublet for x=0.7 As x increases, the area ratio of B-site and A-site($A_B/A_A$) of the sextet decreases, and the area ratio of the doublet and the total areas($A_{doublet}/A_{tot.}$) increases. The isomer shift(I.S.) of A-site slightly increases and magnetic hyperfine fields($H_{hf}$) of two sites decrease as the increasing x. From these results, we have obtained the cation distributions of the samples and concluded that the increasing x leads to the decrease of covalency of $Fe^{3+}-O^{2-}$ bond in A-sites and A-B superexchange interactions.eractions.

• Journal of the Korean Ceramic Society
• /
• v.40 no.4
• /
• pp.323-327
• /
• 2003

Microwave dielectric properties of (P $b_{0.4}$C $a_{0.6}$)[($Fe_{\frac{1}{2}}$N $b_{\frac{1}{2}}$)$_{1-x}$ (M $g_{1}$ 3/N $b_{2}$ 3/)x] $O_3$ (PCFMN) ceramics were investigated as a function of (M $g_{1}$ 3/N $b_{2}$ 3/)$^{4+}$ content (0.1$\leq$x$\leq$0.8). A single perovskite phase with the cubic structure was obtained through the given composition range. The unit cell volume was increased with (M $g_{1}$ 3/N $b_{2}$ 3/)$^{4+}$, due to the larger average ionic size of (M $g_{1}$ 3/N $b_{2}$ 3/)$^{4+}$ than that of ($Fe_{\frac{1}{2}}$N $b_{\frac{1}{2}}$)$^{4+}$ for B-site ion. Dielectric constant (K) and Temperature Coefficient of Resonant Frequency(TCF) of PCFMN ceramics were dependent on (M $g_{1}$ 3/N $b_{2}$ 3/)$^{4+}$ content due to the decrease of ionic polarizability and B-site bond valence, respectively. Qf value was decreased with (M $g_{1}$ 3/N $b_{2}$ 3/)$^{4+}$ content due to the decrease of grain size. Typically, K of 73.56, Qf of 5,074 GHz and TCF of -6.45 ppm/$^{\circ}C$ were obtained for the specimens with x=0.4 sintered at 125$0^{\circ}C$ for 3 h.125$0^{\circ}C$ for 3 h.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.21 no.2
• /
• pp.3-11
• /
• 2011

Evaluation of cube roots in characteristic three finite fields is required for Tate (or modified Tate) pairing computation. The Hamming weights (the number of nonzero coefficients) in the polynomial representations of $x^{1/3}$ and $x^{2/3}$ determine the efficiency of cube roots computation, where $F_{3^m}$is represented as $F_3[x]/(f)$ and $f(x)=x^m+ax^k+b{\in}F_3[x]$ (a, $b{\in}F_3$) is an irreducible trinomial. O. Ahmadi et al. determined the Hamming weights of $x^{1/3}$ and $x^{2/3}$ for all irreducible trinomials. In this paper, we present formulas for cube roots in $F_{3^m}$ using the shifted polynomial basis(SPB). Moreover, we provide the suitable shifted polynomial basis bring no further modular reduction process.

• Korean Journal of Materials Research
• /
• v.8 no.2
• /
• pp.141-146
• /
• 1998

Ball mill을 이용하여 Ar 분위기에서 기계적 합금법으로 $Fe_{ 5}$$Si_{x}$ $B_{5-x}$ 분말을 제조하고, 제조된 분말을 연속 진공 열처리 시킨 후 Si첨가에 따른 결정구조 및 자기적성질을 조사하였다. 250시간 볼밀처리한 Fe$_{5}$ $B_{5}$ 합금에서 전체적으로 비정질 구조가 형성되었으나 일부분에 결정질이 존재하고 있었으며, $800^{\circ}C$에서 2시간 열처리하면 FeB와 $Fe_{2}$B 상이 혼재된 구조를 얻었다. 250시간 볼밀처리한 $Fe_{5}$ $Si_{2}$$B_{3}$합금에서 전체적으로 비정질 구조를 얻을 수 있었고, 이 시료를 2시간, $800^{\circ}C$로 열처리 하였을 때 $Fe_{2}$B상은 사라지고, 대부분 FeB의 균질한 상을 나타내었다. $Fe_{5}$ $B_{5}$ /조성에서는 분말 입자크기가 약 $1\mu\textrm{m}$이었으나, Si이 첨가되면 분말 입자크기가 약 $10\mu\textrm{m}$로 커졌다. Si의 첨가에 의해서 비정질상의 형성을 촉진시켜 단일 FeB상의 합성시간을 단축시킬 수 있었다.

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.567-579
• /
• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

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

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