• Proceedings of the Korean Magnestics Society Conference
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• 2004.06a
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• pp.110-111
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• 2004

• Proceedings of the Korean Magnestics Society Conference
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• 2000.09a
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• pp.508-509
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• 2000

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.778-781
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• 1995

The mixed ferrite $Ni_{x}Co_{1-x}Fe_{2}O_{4}$ have been investigated by X-ray and $M\"{o}ssbauer$ spectoscpy. From the results of X-ray diffraction measurement the structure for this system is spinel, and the lattice constant is in accord with Vegard's law. $M\"{o}ssbauer$ spectra of $Ni_{x}Co_{1-x}Fe_{2}O_{4}$ have been taken at various temperature ranging from 13 to 800 K. The isomer shifts indicate that the valence states of the irons at both A(tetrahedral) and B(octahedral) sithe are found to be in ferric high-spin states. The variation of magnetic hyperfine fields at the A and B sites are explained on the basis on A-B and B-B supertransferred hyperfine interactions. It is found that Debye temperatures for the A and B sites of $CoFe_{2}O_{4}$ and $NiFe_{2}O_{4}$ are found to be ${\theta}_{A}=734{\pm}5K,\;{\theta}_{B}=248{\pm}5K,\;and\;{\theta}_{A}=378{\pm}5K,\;{\theta}_{B}=357{\pm}5K$, respectively. Atomic migration of $Ni_{0.3}Co_{0.7}Fe_{2}O_{4}$ starts near 450 K and increases rapidly with increasing temperature to such a degree that 61 % of the ferric ions at the A site have moved over to the B site by 700 K.

• 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 the Korean Electrochemical Society
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• v.15 no.2
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• pp.67-73
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• 2012

Spherical lithium manganese oxide spinel, $LiMn_{2-x}M_xO_4$ (M = Al, Mg, B) prepared by wet-milling, spray-drying, and sintering process has been investigated as a cathode material for lithium ion batteries. As-prepared powders exhibit various surface morphologies and internal density in terms of boron (B) doping level. It is found that the dopant B drives the growth of the primary particle and minimizes the surface area of the powder. As a result, the dopant enhances the internal density of the particles. Electrochemical tests demonstrated that the capacity of the synthesized material at 5 C could be maintained up to 90% of that at 0.2 C. The cycle performance of the material showed that the initial capacity was retained up to 80% even after 500 cycles under the high temperature of $60^{\circ}C$.

• The Mathematical Education
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• v.22 no.1
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• pp.21-23
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• 1983

(1) Let f : XlongrightarrowX' be a homomorphism of BCK-algebras and let A,B be ideals of X and X' respectively such that f(A)⊂B. Then there is a unique homomorphism h : X/AlongrightarrowX'/B such that the diagram(equation omitted) commutes. (2) The class of all complexes of BCK-algebras becomes a category.

• Bulletin of the Korean Chemical Society
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• v.7 no.1
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• pp.29-35
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• 1986

An empirical formula for semiconductive metal oxides is proposed relating nonstoichiometric value x to a temperature or an oxygen partial pressure such that experimental data can be represented more accurately by the formula than by the well-known Arrhenius-type equation. The proposed empirical formula is log x = A + $B{\cdot}1000/T\;+\;C{\cdot}$exp$(-D{\cdot}1000/T)$ for a temperature dependence and $log\;{\times}\;=a\;+b{\cdot}log\;Po_2\;+\;c{\cdot}$exp$(-d{\cdot}log\;Po_2)$ for an oxygen partial pressure dependence. The A, B, C, D and a, b, c, d are parameters which are evaluated by means of a best-fitting method to experimental data. Subsequently, this empirical formula has been applied to the n-type metal oxides of $Zn_{1+x}O,\; Cd_{1+x}O,\;and\;PrO_{1.8003-x}$, and the p-type metal oxides of $CoO_{1+x},\; FeO_{1+x},\;and\;Cu_2O_{1+x}$. It gives a very good agreement with the experimental data through the best-fitted parameters within 6% of relative error. It is also possible to explain approximately qualitative characters of the parameters A, B, C, D and a, b, c, d from theoretical bases.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.

• Korean Journal of Materials Research
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• v.4 no.3
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• pp.268-279
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• 1994

The x-ray powtler pattern of single phase $Bi_2S_2CaCu_2O_{8+x}$ has been identified and fullyindexed using a pseudotetragonal subcell with a= 5.408, c = 30.83 $\AA$ and an incommensurate supercellwith reciprocal lattice vector, X$q^*$, given by $q^*=0.211b^*-c^*$. The x -ray powder pattern of the Pb-free110K superconductor phase "$Bi_2S_2CaCu_2O_{10+x}$" has many lines which belong t.o an incommensuratesupercell. Using elect.ron d~ffraction pImt.ographs as a indexing guide, an indexing scheme for the powderpattern has been obtained. The unit cell has a geometrically orthorhombic subcell a=5.411, b= 5.420, c=37.29(2) $\AA$. Supercell reflections have indices that are derived from the subcell k, 1 indices by addition uf$\pm q^*$, where $\pm q^*=0.211b^*-0.78c^*$The incommensurate con~ponent In the b dwection, $\delta$, is the same for both phases but on going from2212 to 2223 phase, the superlattic component in the c direction changes from commensurate($\varepsilon$=1) toincommensurate($\varepsilon$=0.78).X>$\varepsilon$=0.78).

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.319-324
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• 1998

The equation AX = BX implies $A^*X\;=\;B^X$ when A and B are normal (Fuglede-Putnam theorem). In this paper, the hypotheses on A and B can be relaxed by usin a Hilbert-Schmidt operator X: Let A be p-quasihyponormal and let $B^*$ be invertible p-quasihyponormal such that AX = XB for a Hilbert-Schmidt operator X and $|||A^*|^{1-p}||{\cdot}|||B^{-1}|^{1-p}||\;{\leq}\;1$.Then $A^*X\;=\;XB^*$.