• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of Biosystems Engineering
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• v.30 no.4 s.111
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• pp.202-209
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• 2005

The output of Stirling engine is influenced by the regenerator effectiveness. The regenerator effectiveness is influenced by heat transfer and flow friction loss of the regenerator matrix. In this paper, in order to provide a basic data for the design of regenerator matrix, characteristics of heat transfer and flow friction loss were investigated by a packed method of matrix in the oscillating flow as the same condition of operation in a Stirling engine. As matrices, 6 kinds of steel wires, 4 kinds of combined steel wires, 8 kinds of combined steel wires with screen meshes were used. The results are summarized as follows; Among 6 kinds of steel wires $({\phi}0.7\;mm,\;{\phi}0.9\;mm,\;{\phi}1.2\;mm,\;{\phi}\;1.6\;mm,\;{\phi}2.0\;mm,\;{\phi}2.7\;mm),$ the two steel wires $({\phi}0.7\;mm,\;{\phi}0.9\;mm)$ showed the highest in effectiveness. Among 4 kinds of combined steel wires $({\phi}l.6-{\phi}l.2\;mm,\;{\phi}1.2-{\phi}l.6\;mm,\;{\phi}0.9-{\phi}l.2\;mm,\;{\phi}l.2-{\phi}0.9\;mm),\;the\;{\phi}1.2-{\phi}0.9\;mm$ showed the highest in effectiveness. Among 8 kinds of combined steel wires with screen meshes $(150-{\phi}0.9\;mm,\;150-{\phi}l.2\;mm,\;{\phi}0.9\;mm-150,\;{\phi}1.2\;mm-150,\;150-{\phi}0.9\;mm-150,\;150-{\phi}1.2\;mm-150,\;150-{\phi}l.6\;mm-150,\;150-{\phi}2.0\;mm-150),\;the\;{\phi}l.2\;mm-150$ showed the highest in effectiveness.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.461-470
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• 1995

In this paper a capacitance matrix method is developed for the Poisson equation on a rectangle $$ (1-1) Lu \equiv -(u_{xx} + u_{yy} = f, (x, y) \in \Omega \equiv (0, 1) \times (0, 1) $$ with the homogeneous Dirichlet boundary condition $$ (1-2) u = 0, (x, y) \in \partial\Omega $$ where $\partial\Omega$ is the boundary of the region $\Omega$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.843-851
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• 2009

The purpose of this paper is to show that for each integer k where $1{\geq}k{\geq}2^{n-1}$, there exists an $n{\times}n(0,1)$-matrix A with exactly PerA = k. Thus we introduce a constructive approch for such matrices. Using the permanent of (0,1)-matrix, we decomposed the number n! with an linear combination of the power of 2. That coefficient is an stiring number.

• Korean Journal of Materials Research
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• v.18 no.7
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• pp.362-366
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• 2008

The precipitation behavior in Mg-6 wt%Zn-1 wt%Y alloy annealed at different temperatures of $200^{\circ}C$ and $400^{\circ}C$ has been characterized by high resolution transmission electron microscope. When the alloy is annealed at $200^{\circ}C$ for 6 hr, the plate- and the rod-shaped ${\beta}_2'$ phases are precipitated in the matrix. The orientation relationship of plate-shaped precipitates with the matrix exhibits a [$11{\bar{2}}0]{\beta}_2$ || [$10{\bar{1}}0$]Mg, $(0001){\beta}_2'$ || (0001)Mg. While the rod-shaped precipitates have two kinds of the orientation relationships with the matrix, i.e. $[11{\bar{2}}0]{\beta}_2'$||[0001] Mg, $(0001){\beta}_2'||(11{\bar{2}}0)$ Mg and $[11{\bar{2}}0]{\beta}_2'$||[0001] Mg, $({\bar{1}}106){\beta}_2'||(10{\bar{1}}0)$ Mg. With increasing annealing time at $200^{\circ}C$ the ${\beta}_1'$ phases are also precipitated in the matrix and the orientation relationship exhibits a $[010]{\beta}_1'$ || [0001]Mg, $(603){\beta}_1'$ || ($01{\bar{1}}0$)Mg between the ${\beta}_1'$ precipitate and the matrix. The icosahedral phases are precipitated in the alloy annealed at $400^{\circ}C$ and exhibit a $[I2]_I$ || [0001]Mg relationship with the matrix.

• Korean Journal of Materials Research
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• v.18 no.1
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• pp.51-56
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• 2008

The crystal structures and morphologies of precipitates in $L1_0$-ordered TiAl intermetallics containing nitrogen were investigated by transmission electron microscopy (TEM). Under aging at an approximate temperature of 1073 K after quenching from 1423 K, TiAl hardens appreciably due to the nitride precipitation. TEM observations revealed that needle-like precipitates, which lie only in one direction parallel to the [001] axis of the $L1_0$-TiAl matrix, appear in the matrix preferentially at the dislocations. Selected area electron diffraction (SAED) pattern analyses showed that the needle-shaped precipitate is perovskite-type $Ti_3AlN$ (P-phase). The orientation relationship between the P-phase and the $L1_0$-TiAl matrix was found to be $(001)_P//(001)_{TiAl}\;and\;[010]_P//[010]_{TiAl}$. By aging at higher temperatures or for longer periods at 1073 K, plate-like precipitates of $Ti_2AlN$ (H-phase) with a hexagonal structure formed on the {111} planes of the $L1_0$-TiAl matrix. The orientation relationship between the $Ti_2AlN$ and the $L1_0$-TiAl matrix is $(0001)_H//(111)_{TiAl}\;and\;_H//_{TiAl}$.

• Mass Spectrometry Letters
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• v.4 no.1
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• pp.21-23
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• 2013

The effects of trifluoroacetic acid (TFA) were evaluated on the generation of multiply charged ions of cytochrome c in a 2-nitrophloroglucinol (2-NPG) matrix in high-vacuum, matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The presence of 1% TFA in the 2-NPG matrix solution was more effective in generating multiply charged protein ions than matrix solutions containing 0.1% or 0% TFA. Regarding the matrix itself, with 1% TFA, 2-NPG was significantly more effective in generating multiply charged ions than 2,5-dihydroxybenzoic acid (2,5-DHB). The maximum charge state of cytochrome c was +8 when using a 2-NPG matrix containing 1% TFA.

• Bulletin of the Korean Chemical Society
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• v.35 no.12
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• pp.3482-3488
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• 2014

Matrix-induced mass bias and its effect on the accuracy of isotope ratio measurements have been examined for a quadrupole-based inductively coupled plasma-mass spectrometer (Q ICP-MS). Matrix-induced mass bias effect was directly proportional to % mass difference, and its magnitude varied for element and nebulizer flow rate. For a given element and conditions in a day, the effect was consistent. The isotope ratio of Cd106/Cd114 under $200{\mu}g\;g^{-1}$ U matrix deviated from the natural value significantly by 3.5%. When Cd 111 and Cd114 were used for the quantification of Cd with isotope dilution (ID) method, the average of differences between the calculated and measured concentrations was -0.034% for samples without matrix ($0.076{\mu}g\;g^{-1}$ to $0.21{\mu}g\;g^{-1}$ for the period of 6 months). However, the error was as large as 1.5% for samples with $200{\mu}g\;g^{-1}$ U. The error in ID caused by matrix could be larger when larger mass difference isotopes are used.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.949-968
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• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.125-135
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• 2004

One of the intriguing and fundamental algorithmic graph problems is the computation of the strongly connected components of a directed graph G. In this paper we first introduce a simple procedure for determining the location of the nonzero elements occurring in $B^{-1}$ without fully inverting B, where EB\;{\equiv}\;(b_{ij)\;and\;B^T$ are diagonally dominant matrices with $b_{ii}\;>\;0$ for all i and $b_{ij}\;{\leq}\;0$, for $i\;{\neq}\;j$, and then, as an application, show that all of the strongly connected components of a directed graph G can be recognized by the location of the nonzero elements occurring in the matrix $C(G)\;=\;(D\;-\;A(G))^{-1}$. Here A(G) is an adjacency matrix of G and D is an arbitrary scalar matrix such that (D - A(G)) becomes a diagonally dominant matrix.