• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.267-273
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• 2009

A representation for the Drazin inverse of an arbitrary square matrix in terms of the eigenprojection was established by Rothblum [SIAM J. Appl. Math., 31(1976) :646-648]. In this paper perturbation results based on the representation for the Darzin inverse $A^D\;=\;(A-X)^{-1}(I-X)$ are developed. Norm estimates of $\parallel(A+E)^D-A^D\parallel_2/\parallel A^D\parallel_2$ and $\parallel(A+E)^#-A^D\parallel_2/\parallel A^D\parallel_2$ are derived when IIEI12 is small.

• Journal of the Semiconductor & Display Technology
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• v.14 no.1
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• pp.13-17
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• 2015

$YAlO_3:Tb{_x}^{3+}$ has been synthesized by a combustion process and the concentration x of Tb was varied from 0.001 and 0.05 mol% per mole of YAlO3. The energy transfer of $^5D_3{\rightarrow}^7F_6$(385nm) and $^5D_4{\rightarrow}^7F_5$(544nm) transitions on the $YAlO_3:Tb{_x}^{3+}$(x =0.001, 0.05) have been investigated by using decay curves. The energy transfer mechanism was explained by Inokuti and Hirayama model. The results of calculation and fitting showed that values of n are 6.11(x=0.01) and 6.13(x=0.005). These indicate that the energy transfer mechanism between $Tb^{3+}$ ions is dipole-dipole interaction.

• Korean Journal of Crystallography
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• v.10 no.2
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• pp.110-113
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• 1999

x의 범위가 0.5

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.419-425
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• 1996

Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.543-549
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• 2001

We show that R[X] is a Krull (Resp. factorial) ring if and only if R is a normal Krull (resp, factorial) ring with a finite number of minimal prime ideals if and only if R is a Krull (resp. factorial) ring with a finite number of minimal prime ideals and R(sub)M is an integral domain for every maximal ideal M of R. As a corollary, we have that if R[X] is a Krull (resp. factorial) ring and if D is a Krull (resp. factorial) overring of R, then D[X] is a Krull (resp. factorial) ring.

• Journal of the Korean Chemical Society
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• v.34 no.6
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• pp.548-554
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• 1990

Temperature effects on the fluorescence emission spectra of 0.01 M Eu(III) ion with ClO$_4$, Cl$^-$, NO$_3$ were studied. Relative intensity change of hypersensitive band ($^5D0\; {\to}\;^7F_2$) and nonhypersensitive band ($^5D0 \;{\to}\;^7F_1$) was quite remarkable with temperature and ligand. The relative intensity change was interpreted as the change of formation constant and used to calculation the enthalpy change of $Eu(H_2O)_X^{3+}$+ to EuL(H$_2O)_{X-1}^{2+}$ complex. $\Delta{H}$ of $Eu(H_2O)_X^{3+}$ to EuCl(H$_2O)_{X-1}^{2+}$ was roughly 15 kJ/mol and temperature independent, but $\Delta{H}$ of EuNO$_3(H_2O)_{X-1}^{2+}$ was changed with temperature; -11 kJ/mol at 25$^{\circ}C$ and 47 kJ/mol at 250$^{\circ}C$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.10
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• pp.2187-2193
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• 2002

We present a novel method for 3D microfabrication with LIGA process that utilizes a deep X-ray mask in which a micro-actuator is integrated. The integrated micro-actuator oscillates the X-ray absorber, which is formed on the shuttle mass of the micro-actuator, during X-ray exposures to modify the absorbed dose profile in X-ray resist, typically PMMA. 3D PMMA microstructures according to the modulated dose contour are revealed after GG development. An X-ray mask with integrated comb drive actuator is fabricated using deep reactive ion etching, absorber electroplating, and bulk micromachining with silicon-on-insulator (SOI) wafer. 1mm $\times$ 1 mm, 20 $\mu$m thick silicon shuttle mass as a mask blank is supported by four 1 mm long suspension beams and is driven by the comb electrodes. A 10 $\mu$m thick, 50 $\mu$m line and spaced gold absorber pattern is electroplated on the shuttle mass before the release step. The fundamental frequency and amplitude are around 3.6 kHz and 20 $\mu$m, respectively, for a do bias of 100 V and an ac bias of 20 $V_{p-p}$ (peak-peak). Fabricated PMMA microstructure shows 15.4 $\mu$m deep, S-shaped cross section in the case of 1.6 kJ $cm^{-3}$ surface dose and GG development at 35$^{\circ}C$ for 40 minutes.

• Journal of the Korean Chemical Society
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• v.55 no.4
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• pp.697-702
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• 2011

The new layered perovskite manganites $La_{0.5}Sr_{1.5}Mn_{0.5}Cr_{0.5-x}Fe_xO_4$ (x=0.15, 0.3) have been prepared by standard ceramic method. The powder X-ray diffraction studies show that the phases crystallize with tetragonal unit cell in the space group I4/mmm. The electrical transport properties suggest that the phases show insulating behaviour and the electrical conduction in the phases occurs by a 3D variable range hopping mechanism. The magnetic properties suggest that both the phases are antiferromagnetic.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.73-82
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• 2022

Let K be a field of characteristic zero. We first show that images of the linear derivations and the linear 𝓔-derivations of the polynomial algebra K[x] = K[x₁, x₂, …, x_n] are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear 𝓔-derivations are not unity. In addition, we prove that the images of D and 𝛿 are Mathieu-Zhao spaces of the polynomial algebra K[x] if D = ∑ⁿ_i=1 (a_ix_i + b_i)∂_i and 𝛿 = I - 𝜙, 𝜙(x_i) = λ_ix_i + 𝜇_i for a_i, b_i, λ_i, 𝜇_i ∈ K for 1 ≤ i ≤ n. Finally, we prove that the image of an affine 𝓔-derivation of the polynomial algebra K[x₁, x₂] is a Mathieu-Zhao space of the polynomial algebra K[x₁, x₂]. Hence we give an affirmative answer to the LFED Conjecture for the affine 𝓔-derivations of the polynomial algebra K[x₁, x₂].

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.551-561
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• 2010

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic $\mathbb{Q}P^n$ in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, where m = 2n, with the Reeb vector $\xi$ belonging to the distribution $\mathfrak{D}$, where $\mathfrak{D}$ denotes a subdistribution in the tangent space $T_xM$ such that $T_xM$ = $\mathfrak{D}{\bigoplus}\mathfrak{D}^{\bot}$ for any point $x{\in}M$ and $\mathfrak{D}^{\bot}=Span{\xi_1,\;\xi_2,\;\xi_3}$.