• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.705-718
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• 2022

In this paper, for bounded linear operators A, B, C satisfying [AB, B] = [BC, B] = [AB, BC] = 0 we study the Drazin invertibility of the sum of products formed by the three operators A, B and C. In particular, we give an explicit representation of the anti-commutator {A, B} = AB + BA. Also we give some conditions for which the sum A + C is Drazin invertible.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.459-465
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• 2018

Recently, Li et al proved that ${\Phi}$ which satisfies the following condition on factor von Neumann algebras $${\Phi}([[A,B]_*,C]_*)=[[{\Phi}(A),B]_*,C]_*+[[A,{\Phi}(B)]_*,C]_*+[[A,B]_*,{\Phi}(C)]_*$$ where $[A,B]_*=AB-BA^*$ for all $A,B{\in}{\mathcal{A}}$, is additive ${\ast}-derivation$. In this short note we show the additivity of ${\Phi}$ which satisfies the above condition on prime ${\ast}-algebras$.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.1230-1231
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• 2008

The effect of content of $Al_2O_3+Y_2O_3$ sintering additives on the densification behavior, mechanical and electrical properties of the pressureless-sintered $SiC-ZrB_2$ electroconductive ceramic composites was investigated. The $SiC-ZrB_2$ electroconductive ceramic composites were pressureless-sintered for 2 hours at 1,700[$^{\circ}C$] temperatures with an addition of $Al_2O_3+Y_2O_3$(6:4 mixture of $Al_2O_3$ and $Y_2O_3$) as a sintering aid in the range of 8${\sim}$20[wt%]. Phase analysis of $SiC-ZrB_2$ composites by XRD revealed mostly of ${\alpha}$-SiC(6H), $ZrB_2$ and In Situ YAG($Al_5Y_3O_{12}$). The relative density, flexural strength, Young's modulus and vicker's hardness showed the highest value of 89.01[%], 81.58[Mpa], 31.437[GPa] and 1.34[GPa] for $SiC-ZrB_2$ composites added with 16[wt%] $Al_2O_3+Y_2O_3$ additives at room temperature respectively. Abnormal grain growth takes place during phase transformation from ${\beta}$-SiC into ${\alpha}$-SiC was correlated with In Situ YAG phase by reaction between $Al_2O_3$ and $Y_2O_3$ additive during sintering. Compositional design and optimization of processing parameters are key factors for controlling and improving the properties of SiC-based electroconductive ceramic composites. In this paper, it is convinced that ${\beta}$-SiC based electroconductive ceramic composites for heaters or ignitors can be manufactured by pressureless sintering.

• Journal of Powder Materials
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• v.30 no.3
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• pp.262-267
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• 2023

Boron carbide (B₄C) is highly significant in the production of lightweight protective materials when added to aluminum owing to its exceptional mechanical properties. In this study, a method for fabricating Al-B₄C composites using high-energy ball milling and directed energy deposition (DED) is presented. Al-4 wt.% B4C composites were fabricated under 21 different laser conditions to analyze the microstructure and mechanical properties at different values of laser power and scan speeds. The composites fabricated at a laser power of 600 W and the same scan speed exhibited the highest hardness and generated the fewest pores. In contrast, the composites fabricated at a laser power of 1000 W exhibited the lowest hardness and generated a significant number of large pores. This can be explained by the influence of the microstructure on the energy density at different values of laser power.

• Journal of the Korean Ceramic Society
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• v.42 no.8 s.279
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• pp.567-574
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• 2005

Densification of SiC powder with additives of total amount of2, 4, 8 $wt\%$ Al-B-C was carried out by Spark Plasma Sintering (SPS). The unique features of the process are the possibilities of a very fast heating rate and a short holding time to obtain fully dense materials. The heating rate and applied pressure were kept at $100^{\circ}C/min$ and 40 MPa, while the sintering temperature and holding time varied from 1700 - $1800^{\circ}C$ for 10 - 40 min, respectively. The SPS-sintered specimens with different amount of Al-B-C at $1800^{\circ}C$ reached near-theoretical density. The $3C{\rightarrow}6H,\;15R{\rightarrow}4H$ phase transformation of SiC was enhanced by increasing the additive amount. The microstructure of SiC sintered up to $1750^{\circ}C$ consisted of fine equiaxed grains. In contrast, the growth of large elongated grains in small matrix grains was shown in sintered bodies at $1800^{\circ}C$, and the plate-like grains interlocking microstructure had been developed by increasing the holding time at $1800^{\circ}C$. The grain growth rate decreases with increasing amount of Al-B-C in SiC starting powder, however, the both of volume fraction and aspect ratio of large grains in sintered body increased.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.5
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• pp.808-815
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• 2008

The composites were fabricated 61[vol.%] ${\beta}$-SiC and 39[vol.%] $TiB_2$ powders with the liquid forming additives of 8, 12, 16[wt%] $Al_2O_3+Y_2O_3$ as a sintering aid by pressureless annealing at 1650[$^{\circ}C$] for 4 hours. The present study investigated the influence of the content of $Al_2O_3+Y_2O_3$ sintering additives on the microstructure, mechanical and electrical properties of the pressureless annealed SiC-$TiB_2$ electroconductive ceramic composites. Reactions between SiC and transition metal $TiB_2$ were not observed in the microstructure and the phase analysis of the pressureless annealed SiC-$TiB_2$ electroconductive ceramic composites. Phase analysis of SiC-$TiB_2$ composites by XRD revealed mostly of ${\alpha}$-SiC(6H), ${\beta}$-SiC(3C), $TiB_2$, and In Situ YAG($Al_2Y_3O_{12}$). The relative density of SiC-$TiB_2$ composites was lowered due to gaseous products of the result of reaction between SiC and $Al_2O_3+Y_2O_3$. There is another reason which pressureless annealed temperature 1650[$^{\circ}C$] is lower $300{\sim}450[^{\circ}C]$ than applied pressure sintering temperature $1950{\sim}2100[^{\circ}C]$. The relative density, the flexural strength, the Young's modulus and the Vicker's hardness showed the highest value of 82.29[%], 189.5[Mpa], 54.60[Gpa] and 2.84[Gpa] for SiC-$TiB_2$ composites added with 16[wt%] $Al_2O_3+Y_2O_3$ additives at room temperature. Abnormal grain growth takes place during phase transformation from ${\beta}$-SiC into ${\alpha}$-SiC was correlated with In Situ YAG phase by reaction between $Al_2O_3$ and $Y_2O_3$ additive during sintering. The electrical resistivity showed the lowest value of 0.0117[${\Omega}{\cdot}cm$] for 16[wt%] $Al_2O_3+Y_2O_3$ additives at 25[$^{\circ}C$]. The electrical resistivity was all negative temperature coefficient resistance (NTCR) in the temperature ranges from $25^{\circ}C$ to 700[$^{\circ}C$]. The resistance temperature coefficient of composite showed the lowest value of $-2.3{\times}10^{-3}[^{\circ}C]^{-1}$ for 16[wt%] additives in the temperature ranges from 25[$^{\circ}C$] to 100[$^{\circ}C$].

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2015-2022
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• 2008

The effect of content of $Al_2O_3+Y_2O_3$ sintering additives on the densification behavior, mechanical and electrical properties of the pressureless-sintered $SiC-ZrB_2$ electroconductive ceramic composites was investigated. The $SiC-ZrB_2$ electroconductive ceramic composites were pressurless-sintered for 2 hours at 1,700[$^{\circ}C$] temperatures with an addition of $Al_2O_3+Y_2O_3$(6 : 4 mixture of $Al_2O_3$ and $Y_2O_3$) as a sintering aid in the range of $8\;{\sim}\;20$[wt%]. Phase analysis of $SiC-ZrB_2$ composites by XRD revealed mostly of $\alpha$-SiC(6H), $ZrB_2$ and In Situ YAG($Al_5Y_3O_{12}$). The relative density, flexural strength, Young's modulus and vicker's hardness showed the highest value of 89.02[%], 81.58[MPa], 31.44[GPa] and 1.34[GPa] for $SiC-ZrB_2$ composites added with 16[wt%] $Al_2O_3+Y_2O_3$ additives at room temperature respectively. Abnormal grain growth takes place during phase transformation from $\beta$-SiC into $\alpha$-SiC was correlated with In Situ YAG phase by reaction between $Al_2O_3$ and $Y_2O_3$ additive during sintering. The electrical resistivity showed the lowest value of $3.l4{\times}10^{-2}{\Omega}{\cdot}cm$ for $SiC-ZrB_2$ composite added with 16[wt%] $Al_2O_3+Y_2O_3$ additives at 700[$^{\circ}C$]. The electrical resistivity of the $SiC-TiB_2$ and $SiC-ZrB_2$ composite was all negative temperature coefficient resistance (NTCR) in the temperature ranges from room temperature to 700[$^{\circ}C$]. Compositional design and optimization of processing parameters are key factors for controlling and improving the properties of SiC-based electroconductive ceramic composites.

• Journal of Powder Materials
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• v.17 no.1
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• pp.13-22
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• 2010

The unique features of spark plasma sintering process are the possibilities of a very fast heating rate and a short holding time to obtain fully dense materials. $\beta$-SiC powder with 0, 2, 6, 10 wt% of $\alpha$-SiC particles (seeds) and 4 wt% of Al-B-C (sintering aids) were spark plasma sintered at $1700-1850^{\circ}C$ for 10 min. The heating rate, applied pressure and sintering atmosphere were kept at $100^{\circ}C/min$, 40 MPa and a flowing Ar gas (500 CC/min). Microstructural development of SiC as function of seed content and temperature during spark plasma sintering was investigated quantitatively and statistically using image analysis. Quantitative image analyses on the sintered SiC ceramics were conducted on the grain size, aspect ratio and grain size distribution of SiC. The microstructure of SiC sintered up to $1700^{\circ}C$ consisted of equiaxed grains. In contrast, the growth of large elongated SiC grains in small matrix grains was shown in sintered bodies at $1750^{\circ}C$ and the plate-like grains interlocking microstructure had been developed by increasing sintering temperature. The introduction of $\alpha$-SiC seeds into $\beta$-SiC accelerated the grain growth of elongated grains during sintering, resulting in the plate-like grains interlocking microstructure. In the $\alpha$-SiC seeds added in $\beta$-SiC, the rate of grain growth decreased with $\alpha$-SiC seed content, however, bulk density and aspect ratio of grains in sintered body increased.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.2
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• pp.80-84
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• 2003

The mechanical and electrical properties of the hot-pressed and pressureless annealed SiC-Ti $B_2$electroconductive ceramic composites were investigated as functions of the liquid additives of $Al_2$ $O_3$+ $Y_2$ $O_3$. The result of phase analysis for the SiC-Ti $B_2$ composites by XRD revealed $\alpha$-SiC(6H), Ti $B_2$, and YAG(A $l_{5}$ $Y_3$ $O_{12}$ ) crystal phase. The relative density of SiC-Ti $B_2$ composites was increased with increased $Al_2$ $O_3$+ $Y_2$ $O_3$ contents. The fracture toughness showed the highest value of 6.04 Mpa $m^{\frac{1}{2}}$ for composites added with l2wt% A1$_2$ $O_3$+ $Y_2$ $O_3$ additives at room temperature. The electrical resistivity showed the lowest value of 6.2$\times$10$^{-3}$ $\Omega$ㆍcm for composite added with l6wt% $Al_2$ $O_3$+ $Y_2$ $O_3$ additives at room temperature. The electrical resistivity of the SiC-Ti $B_2$ composites was all positive temperature cofficient resistance(PTCR) in the temperature ranges from $25^{\circ}C$ to $700^{\circ}C$.

• Korean Journal of Materials Research
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• v.22 no.6
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• pp.316-320
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• 2012

$Co_3O_4$, $Al_2O_3$ and $Co_3O_4$/$Al_2O_3$ mesoporous powders were prepared by a sol-gel method with starting matierals of aluminum isopropoxide and cobalt (II) nitrate. A P123 template is employed as an active organic additive for improving the specific surface area of the mixed oxide by forming surfactant micelles. A transition metal cobalt oxide supported on alumina with and without P123 was tested to find the most active and selective conditions as a heterogeneous catalyst in the reaction of styrene epoxidation. A bBlock copolymer-P123 template was added to the staring materials to control physical and chemical properties. The properties of $Co_3O_4$/$Al_2O_3$ powder with and without P123 were characterized using an X-ray diffractometer (XRD), a Field-Emission Scanning Electron Microscope (FE-SEM), a Bruner-Emmertt-Teller (BET) surface analyzer, and $^{27}Al$ MAS NMR spectroscopy. Powders with and without P123 were compared in catalytic tests. The catalytic activity and selectivity were monitored by GC/MS, $^1H$, and $^{13}C$-NMR spectroscopy. The performance for the reaction of epoxidation of styrene was observed to be in the following order: [$Co_3O_4$/$Al_2O_3$ with P123-1173 K > $Co_3O_4$/$Al_2O_3$ with P123-973 K > $Co_3O_4$-973 K>$Co_3O_4$/$Al_2O_3$-973 K > $Co_3O_4$/$Al_2O_3$ with P123-1473 K > $Al_2O_3$-973 K]. The existence of ${\gamma}$-alumina and the nature of the surface morphology are related to catalytic activity.