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

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.61-65
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• 2008

In this paper we prove that every positive solution of the third order rational difference equation $$x_{n+1}\;=\;\frac{{\beta}x_n\;+\;x_{n-2}}{A\;+\;Bx_n\;+\;x_{n-2}}$ converges to the positive equilibrium point $$\bar{x}\;=\;\frac{{\beta}\;+\;1\;-\;A}{B\;+\;1}$, where $0\;<\;{\beta}\;{\leq}\;B$, $1\;<\;A\;<\;{\beta}\;+\;1$

• 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.

• Transactions on Electrical and Electronic Materials
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• v.12 no.1
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• pp.28-31
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• 2011

Transformation behavior and shape memory characteristics of Ti-(45-x)Ni-5Cu-xCr (x=0.5-2.0) alloys have been investigated by means of electrical resistivity measurements, differential scanning calorimetry, X-ray diffraction and thermal cycling tests under constant load. Two-stage B2-B19-B19' transformation occurred in Ti-(45-x)Ni-5Cu-xCr alloys. The B2-B19 transformation was separated clearly from the B19-B19' transformation in Ti-44.0Ni-5Cu-1.0Cr and Ti-43.5Ni-5Cu-1.5Cr alloys. A temperature range where the B19 martensite exists was expanded with increasing Cr content because decreasing rate of Ms (85 K / % Cr) was larger than that of Ms' (17 K / % Cr). Ti-(45-x)Ni-5Cu-xCr alloys were deformed in plastic manner with a fracture strain of 68% ~ 43% depending on Cr content. Substitution of Cr for Ni improves the critical stress for slip deformation in a Ti-45Ni-5Cu alloy due to solid solution hardening.

• 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

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.919-920
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• 2011

For two even unimodular positive definite integral quadratic forms A[X], B[X] in n-variables, J. K. Koo [1, Theorem 1] showed that ${\theta}_A(\tau)/{\theta}_B(\tau)$ is a rational function of J, satisfying a certain condition. Where ${\theta}_A(\tau)$ and ${\theta}_B(\tau)$ are theta series related to A[X] and B[X], respectively, and J is the classical modular invariant. In this paper we give a simple proof of Theorem 1 of [1].

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.100-109
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• 1983

Let ${X_i}$ be a process with stationary and independent increments whose log characteristic function is expressed as $ibut-2^{-1}\sigma^2u^2t+t\int_{{0 }^c}{(exp(iux)-1-iux(i+x^2)^{-1})dv(x)}$. Our main result is taht $x^2(\int_{\y\>x}{dv(y)})/(\int_{$\mid$y$\mid$\leqx}{y^2dv(y)+\sigma^2}) \to 1$ as $x \to 0 (resp. x \to \infty)$ is necessary, and sufficient for ${X-i}$ to have ${A_t}$ and ${B_t}$ such that $(X_t-A_t)/B_t \to^D n(0,1)$ as $t \to 0 (resp. t \to \infty)$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.29-42
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• 2018

In this paper, we investigate the stability of two functional equations f(ax+by + cz) - abf(x + y) - bcf(y + z) - acf(x + z) + bcf(y) - a(a - b - c)f(x) - b(b - a)f(-y) - c(c - a - b)f(z) = 0, f(ax+by + cz) + abf(x - y) + bcf(y - z) + acf(x - z) - a(a + b + c)f(x) - b(a + b + c)f(y) - c(a + b + c)f(z) = 0 by applying the direct method in the sense of Hyers and Ulam.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.875-883
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• 2012

Let $\mathbb{F}_q$ be a finite field with q elements and $\mathbb{F}_q((X^{-1}))$ be the field of all formal Laurent series with coefficients lying in $\mathbb{F}_q$. This paper concerns with the size of the set of points $x{\in}\mathbb{F}_q((X^{-1}))$ with their partial quotients $A_n(x)$ both lying in a given subset $\mathbb{B}$ of polynomials in $\mathbb{F}_q[X]$ ($\mathbb{F}_q[X]$ denotes the ring of polynomials with coefficients in $\mathbb{F}_q$) and deg $A_n(x)$ tends to infinity at least with some given speed. Write $E_{\mathbb{B}}=\{x:A_n(x){\in}\mathbb{B},\;deg\;A_n(x){\rightarrow}{\infty}\;as\;n{\rightarrow}{\infty}\}$. It was shown in [8] that the Hausdorff dimension of $E_{\mathbb{B}}$ is inf{$s:{\sum}_{b{\in}\mathbb{B}}(q^{-2\;deg\;b})^s$ < ${\infty}$}. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg $A_n(x)$ tends to infinity.

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