• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1285-1301
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• 2018

In this paper, we mainly consider the determinantal representations of the unique solution and the general solution to the restricted system of quaternion matrix equations $$\{{A_1X=C_1\\XB_2=C_2,}\;{{\mathcal{R}}_r(X){\subseteq}T_1,\;{\mathcal{N}}_r(X){\supseteq}S_1$$, respectively. As an application, we show the determinantal representations of the general solution to the restricted quaternion matrix equation $$AX+Y B=E,\;{\mathcal{R}}_r(X){\subseteq}T_1,\;{\mathcal{N}}_(X){\supseteq}S_1,\;{\mathcal{R}}_l(Y){\subseteq}T_2,\;{\mathcal{N}}_l (Y){\supseteq}S_2$$. The findings of this paper extend some known results in the literature.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.499-516
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• 2020

In this paper, we denote by L the block matrix linear relation, acting on the Banach space X ⊕ Y, of the form ${\mathcal{L}}=\(\array{A&B\\C&D}\)$, where A, B, C and D are four linear relations with dense domains. We first try to determine the conditions under which a block matrix linear relation becomes a demicompact block matrix linear relation (see Theorems 4.1 and 4.2). Second we study Shechter spectra using demicompact linear relations and relatively demicompact linear relations (see Theorem 5.1).

• Journal of Korean Society on Water Environment
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• v.22 no.2
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• pp.271-276
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• 2006

The outbreak cases of Cryptosporidium or Giardia from drinking water in abroad have drawn attentions on the public health. It is well known that Cryptosporidium is the most resistant organism against chlorine disinfection. To guesstimate the levels of Cryptosporidium and Giardia in Korean surface water, 1~2 samples from 22 drinking water sources in four Korean major rivers of Han, Keum, Nakdong, and Youngsan were monitored. In addition, two sites in Kyunganchon, a contaminated river were monitored for comparison. In source waters, detection rates of Cryptosporidium and Giardia were 15% (6/39) and 21% (5/24) with the range of 1~3 oocysts/10 L and 1~6 cysts/10 L, respectively. In Kyunganchon, they were 60% (6/10) and 70% (7/10) in the range of 1~9 oocysts/10 L and 10~72 cysts/10 L, respectively. When one of the source waters in Han river was monitored monthly, Cryptosporidium were found mostly in cold season. Matrix of the samples gave influence on the recoveries of the spiked protozoa. The recoveries of both Cryptosporidium and Giardia increased in the samples of Kyunganchon, known as contaminated area. However, protozoan recovery did not show significant relation with turbidity, the index of matrix contamination, which implies that there are additional unveiled features of matrix affecting the recoveries of the protozoa. The protozoan distribution in Kyunganchon showed significant relations with Cl. perfringens, anaerobic and spore forming indicator bacteria of fecal contamination by regression analysis, but not with turbidity, the general indicator of water quality.

• Korean Journal of Environmental Agriculture
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• v.36 no.4
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• pp.263-268
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• 2017

BACKGROUND: Lespedeza cuneata G. Don is a well-known medicinal plant. In this study, the biological activities of L. cuneata extracts were investigated. METHODS AND RESULTS: L. cuneata shoot was extracted with 30% ethanol and further fractionated with organic solvents. Total phenolic and flavonoid content, antioxidant activity, and matrix metalloproteinase inhibition effect of the extract and fractions were measured. Among the tested extract and fractions, the highest contents of total phenolic and flavonoids were found in ethyl acetate fraction (117.8 mg GAE/g and 35.9 mg QE/g, respectively). Ethyl acetate fraction showed the highest DPPH and ABTS radical scavenging activity, and the antioxidant activity of the other fractions followed the order n-hexane fraction>ethanol extract>methyl chloroform>n-butanol fraction. Inhibitory effect on the expression of matrix metalloproteinases (MMP1 and MMP3) was highest in the fraction of ethyl acetate, and n-butanol fraction also significantly inhibited the expression of MMP3. Antioxidant activities of L. cuneata extracts were significantly positively related to their phenolic and flavonoid content. CONCLUSION: Ethyl acetate fraction of L. cuneata ethanol extract showed potent antioxidant and matrix metalloproteinases inhibitory activities. Those activities might be related to the high total phenolic and flavonoid content of the extract.

• Corrosion Science and Technology
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• v.16 no.3
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• pp.128-140
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• 2017

Aluminum alloy matrix may be used for manufacturing lighter automobiles. However, galvanic corrosion may occur between the rivet joint combining aluminum alloy matrix and a CFRP (carbon fiber reinforced plastic) laminate. The possibility of galvanic corrosion may be investigated by measuring galvanic couple currents. Two types of galvanic current measuring methods were used. One method is to use potentiodynamic polarization curves and the other is the ZRA (zero resistance ammeter) method. For galvanic corrosion experiments graphite, a major component of CFRP, was used with carbon steel (rivets) and 6061 aluminum alloys. Regardless of carbon steel, Ni deposited carbon steel, and 316L stainless steels we also investigated the possibility of reduction in galvanic corrosion. Results revealed that even though Ni deposited carbon steel or 316L stainless rivet may slightly increase galvanic current density between those and Al matrix, substitute rivets for carbon steel may be considerably useful for reducing overall galvanic corrosion.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.34-42
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• 1986

An interface of a circular arc formed by two isotropic, homogeneous elastic materials is investigated. It is shown that L integral satisfies the conservation law for the interface if it is perfectly bonded, in frictionless contact or separated such as in a crack with the origin of the coordinate system being located at the center of the circular arc. The property of path independence of the L integral is applied to an interfacial crack problem, to obtain the stress intensity factors, where the interfacial crack is located along the arc of the circular inclusion embedded in infinite matrix. It is assumed here that the contact zone exist as in the model proposed by Comninou, thus removing the overlapping of the materials along the interface. Another example is shown for case of a circular interfacial crack in the matrix of finite size, where the stress intensity factors are determined by computing a value of the L integral numerically along the path far from the crack tip.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.127-136
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• 2013

The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $k$ and $l$.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.197-204
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• 2005

For two distinct rank-1 matrices A and B, a rank-1 matrix C is called a separating matrix of A and B if the rank of A + C is 2 but the rank of B + C is 1 or vice versa. In this case, rank-1 matrices A and B are said to be separable. We show that every pair of distinct Boolean rank-l matrices are separable.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.529-539
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• 2016

In this paper, we obtain solution for the first order matrix dynamical system and also we provide set of necessary and sufficient conditions for complete controllability and complete observability of the Sylvester matrix dynamical system.

• Journal of Korean Society of Environmental Engineers
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• v.28 no.1
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• pp.26-33
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• 2006

This study investigated the characteristics of the biofilm removal by free chlorine or monochloramine. The simulated drinking water distribution pipes on which biofilms had been formed were supplied with tap water containing 0.5, 1.0, 2.0 mg/L of free chlorine or monochloramine residuals. The biofilm removal was characterized by measurement of attached HPC and biomass on pipe surfaces. Chlorine was more effective in both inactivation of attached viable heterotrophic bacteria and removal of biofilm biomass compared to monochloramine. Biofilm matrix was not much eliminated from the surfaces by monochloramine disinfection. Free chlorine residual of 2.0 mg/L was found to be effective in biomass removal. However, biofilm level as low as $10CFU/cm^2$ of attached HPC and $5{\mu}g/cm^2$ of biomass still remained on the surfaces at 2.0 mg/L of chlorine residual. The measurement of biomass appeared to be a useful means in evaluating the characteristics of biofilm removal.