• Korean Journal of Mathematics
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• v.18 no.4
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• pp.335-342
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• 2010

Let D be an integral domain with quotient field K,$\mathcal{I}(D)$ be the set of nonzero ideals of D, and $w$ be the star-operation on D defined by $I_w=\{x{\in}K{\mid}xJ{\subseteq}I$ for some $J{\in}\mathcal{I}(D)$ such that J is finitely generated and $J^{-1}=D\}$. The D is called a Pr$\ddot{u}$fer $v$-multiplication domain if $(II^{-1})_w=D$ for all nonzero finitely generated ideals I of D. In this paper, we show that D is a Pr$\ddot{u}$fer $v$-multiplication domain if and only if $(A{\cap}(B+C))_w=((A{\cap}B)+(A{\cap}C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $(A(B{\cap}C))_w=(AB{\cap}AC)_w$ for all $A,B,C{\in}\mathcal{I}(D)$, if and only if $((A+B)(A{\cap}B))_w=(AB)_w$ for all $A,B{\in}\mathcal{I}(D)$, if and only if $((A+B):C)_w=((A:C)+(B:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with C finitely generated, if and only if $((a:b)+(b:a))_w=D$ for all nonzero $a,b{\in}D$, if and only if $(A:(B{\cap}C))_w=((A:B)+(A:C))_w$ for all $A,B,C{\in}\mathcal{I}(D)$ with B, C finitely generated.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1757-1763
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• 2009

The composites were fabricated by adding 0, 15, 20, 25[vol.%] Zirconium Diboride(hereafter, $ZrB_2$) powders as a second phase to Silicon Carbide(hereafter, SiC) matrix. The physical, mechanical and electrical properties of electroconductive SiC ceramic composites by Spark Plasma Sintering(hereafter, SPS) were examined. Reactions between ${\beta}-SiC$ and $ZrB_2$ were not observed in the XRD analysis. The relative density of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 90.93[%], 74.62[%], 74.99[%] and 72.61[%], respectively. The XRD phase analysis of the electroconductive SiC ceramic composites reveals high of SiC and $ZrB_2$ and low of $ZrO_2$ phase. The lowest flexural strength, 108.79[MPa], shown in SiC+15[vol.%] $ZrB_2$ composite and the highest - 220.15[MPa] - in SiC+20[vol.%] $ZrB_2$composite at room temperature. The trend of the mechanical properties of the electroconductive SiC ceramic composites moves in accord with that of the relative density. The electrical resistivities of mono SiC, SiC+15[vol.%]$ZrB_2$, SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ composites are 4.57${\times}10^{-1}$, 2.13${\times}10^{-1}$, 1.53${\times}10^{-1}$ and 6.37${\times}10^{-2}$[${\Omega}$ cm] at room temperature, respectively. The electrical resistivity of mono SiC, SiC+15[vol.%]$ZrB_2$. SiC+20[vol.%]$ZrB_2$ and SiC+25[vol.%]$ZrB_2$ are Negative Temperature Coefficient Resistance(hereafter, NTCR) in temperature ranges from 25[$^{\circ}C$] to 100[$^{\circ}C$]. The declination of V-I characteristics of SiC+20[vol.%]$ZrB_2$ composite is 3.72${\times}10^{-1}$. It is convinced that SiC+20[vol.%]$ZrB_2$ composite by SPS can be applied for heater or electrode above 1000[$^{\circ}C$]

• Journal of the Korean Ceramic Society
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• v.47 no.6
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• pp.578-582
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• 2010

$ZrB_2$ has a melting point of $3245^{\circ}C$ and a relatively low density of $6.1\;g/cm^3$, which makes this a candidate for application to ultrahigh temperature environments over $2000^{\circ}C$. Beside these properties, $ZrB_2$ is known to have excellent resistance to thermal shock and oxidation compared with other non-oxide engineering ceramics. In order to enhance such oxidation resistance, SiC was frequently added to $ZrB_2$-based systems. Due to nonsinterability of $ZrB_2$-based ceramics, research on the sintering aids such as $B_4C$ or $MoSi_2$ becomes popular recently. In this study, densification and high-temperature properties of $ZrB_2$-SiC ceramics especially with $B_4C$ are investigated. $ZrB_2$-20 vol% SiC system was selected as a basic composition and $B_4C$ or C was added to this system in some extents. Mixed powders were sintered using hot pressing (HP). With sintered bodies, densification behavior and high-temperature (up to $1400^{\circ}C$) properties such as flexural strength, hardness, and so on were examined.

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.63-71
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• 2005

Equilibrium geometries, electronic structures, and energies of borocarbon clusters (binary compounds of carbon and boron), an unexplored class of molecules with highly unusual characteristics and potential for further development, have been investigated by means of B3LYP/6-311+G$^*$ density functional theory computations. A large number of B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ clusters with planar and non-planar monocyclic and polycyclic rings, as well as cage structures, have been systematically studied. Unexpectedly, planar forms are predicted not only to be the most stable structures, but also, in many cases, to have unprecedented planar heptacoordinate boron (p-heptaB) and planar heptacoordinate carbon (p-heptaC) arrangements. All these pheptaB and p-heptaC have 6π electrons and are aromatic according to the nucleus independent chemical shift (NICS). This novel bonding pattern is analyzed in terms of natural bond orbital (NBO) analysis. For virtually all possible B$_7$C${_1}^{1-}$, B$_6C_2$, and B$_5C_{3}\,^{1+}$ combinations, the p-heptaB arrangements are the more stable than other type structures.

• Journal of the Korean Ceramic Society
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• v.31 no.7
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• pp.739-744
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• 1994

The B4C-C system was investigated to gain an understanding of the sintering behaviors of B4C. In order to get sintered density of 97% TD, sintering temperature of 225$0^{\circ}C$ was necessary. Since such a high temperature operation is actually difficult on a commercial basis, our objective was to examine the possibility of decreasing the sintering temperature by adding SiC. The addition of SiC in B4C increases the sintering rate about at 210$0^{\circ}C$ and results in a fine microstructure with more than 98% relative density on 55 wt% B4C-40wt% SiC-5 wt% C composition. The probability of liquid phase sintering was investigated, but the evidences of liquid phase formation were not observed with XRD and TEM observation. It was proposed that the addition of SiC and carbon to B4C reduce interface energy during sintering, which results in enhanced grain-boundary diffusion. Thus, the enhanced grain-boundary diffusion and retarded grain growth by SiC improve densification.

• Proceedings of the KIEE Conference
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• 2004.11a
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• pp.191-193
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• 2004

The composites were fabricated, respectively, using 61vol.% SiC-39vol.% $TiB_2$ and using 61vol.% SiC-39vol.% $ZrB_2$ powders with the liquid forming additives of 12wt% $Al_2O_3+Y_2O_3$ by hot pressing annealing at $1650^{\circ}C$ for 4 hours. Reactions between SiC and transition metal $TiB_2$, $ZrB_2$ were not observed in this microstructure. The result of phase analysis of composites by XRD revealed SiC(6H, 3C), $TiB_2$, $ZrB_2$ and $YAG(Al_5Y_3O_{12})$ crystal phase on the SiC-$TiB_2$, and SiC-$ZrB_2$ composites. The ${\beta}\;{\alpha}$-SiC phase transformation was occurred on the $SiC-TiB_2$, $SiC-ZrB_2$ composites. The relative density, the flexural strength and Young's modulus showed respectively value of 98.57%, 226.06Mpa and $86.37{\times}10^3Mpa$ in SiC-$ZrB_2$ composites.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.04a
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• pp.135-140
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• 1997

The influences of ZrB$_2$ additions to SiC on microstructural, DDM(Electrical Discharge Machining), mechanical and electrical properties were investigated. composites were prepared by adding 15, 30, 45 vol.% ZrB$_2$particles as a second phase to SiC matrix. SiC-ZrB$_2$ composites obtained by hot pressing for high temperature structural application were fully dense with the relative densities over 99%. The fracture toughness of the composites were increased with the ZrB$_2$contents. In case of composite containing 30vol.% ZrB$_2$, the flexural strength and fracture toughness showed 45% and 60% increase, respectively compared to that of monolithic SiC sample. The electrical resistivities of SiC-ZrB$_2$ composites decreased significantly with the ZrB$_2$ contents. The electrical resistivity of SiC-30vol.% ZrB$_2$ composite showed 6.50$\times$10$^{-4}$ $\Omega$.cm. Cutting velocity of EDM of SiC-ZrB$_2$ composites are directly proportional to duty factor of pulse width. Surface roughness, however, are not all proportional to pulse width. Higher-flexural strength composites show a trend toward smaller crater volumes, leaving a smoother surface; the average surface roughness of the SiC-ZrB$_2$ 15 vol.% composite with the flexural strengthe of 375㎫ was 3.2${\mu}{\textrm}{m}$, whereas the SiC-ZrB$_2$ 30.vol% composite of 457㎫ was 1.35${\mu}{\textrm}{m}$. In the SEM micrographs of the fracture surface of SiC-ZrB$_2$ composites, the SiC-ZrB$_2$ two phases are distinct; the white phase is the ZrB$_2$and the gray phase is the SiC matrix. In the SEM micrographs of the EDM surface, however, these phases are no longer distinct because of thicker recast layer of resolidified-melt-formation droplets present. It is shown that SiC-ZrB$_2$ composites are able to be machined without surface cracking.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.1303-1304
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• 2007

The composites were fabricated, respectively, using 61[vol.%]SiC-39[vol.%]$TiB_2$ and using 61[vol.%]SiC-39[vol.%]$ZrB_2$ powders with the liquid forming additives of 12[wt%] $Al_{2}O_{3}+Y_{2}O_{3}$ by hot pressing annealing at $1650[^{\circ}C]$ for 4 hours. Reactions between SiC and transition metal $TiB_2$, $ZrB_2$ were not observed in this microstructure. ${\beta}{\rightarrow}{\alpha}$-SiC phase transformation was occurred on the SiC-$TiB_2$ and SiC-$ZrB_2$ composite. The relative density, the flexural strength and Young's modulus showed the highest value of 98.57[%], 226.06[Mpa] and 86.38[Gpa] in SiC-$ZrB_2$ composite at room temperature respectively. The electrical resistivity showed the lowest value of $7.96{\times}10^{-4}[{\Omega}{\cdot}cm]$ for SiC-$ZrB_2$ composite at $25[^{\circ}C]$. The electrical resistivity of the SiC-$TiB_2$ and SiC-$ZrB_2$ composite was all positive temperature coefficient resistance (PTCR) in the temperature ranges from $25[^{\circ}C]$ to $700[^{\circ}C]$. The resistance temperature coefficient of composite showed the value of $6.88{\times}10^{-3}/[^{\circ}C]$ and $3.57{\times}10^{-3}/[^{\circ}C]$ for SiC-$ZrB_2$ and SiC-$TiB_2$ composite in the temperature ranges from $25[^{\circ}C]$ to $700[^{\circ}C]$.

• Journal of Powder Materials
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• v.1 no.1
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• pp.15-20
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• 1994

The effect of SiC addition on sintering behaviors and microstructures of TiB2 ceramics were studied. The sintering of TiB2 was limited due to the surface diffusion and rapid grain growth at high temperature. However the addition of SiC to TiB2 ceramics improved the densification to above 99% of the theoretical density. The sintering of TiB2-SiC composite starts at 120$0^{\circ}C$ with the melting of the oxides in particle surface as impurities. After the reduction of the oxide by additional cabon at above 140$0^{\circ}C$, the grain boundary diffusion through the interface of TiB2-SiC play an important role. TEM observation showed neither chemical reactions nor other phases formed at the TiB2-SiC interfaces but the microcracks were observed due to the mismatch of thermal expansion between TiB2-SiC.

• Applied Biological Chemistry
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• v.43 no.1
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• pp.39-45
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• 2000

The stability of vitamin A, $B_1,\;B_2,\;B_6$, C in aqueous multivitamin solutions was carried out by means of estimation of reaction velocity and the results are described in this paper. The stability of vitamin A, $B_1$ and C due to thermal degradation method in aqueous multivitamin solutions was evaluated at 40, 50, 60 and $70^{\circ}C$ up to 40 days. The shelf-lives of vitamin A, B₁ and C in this preparation, calculated using the Arrhenius equation, were 1493, 449 and 639 days at $25^{\circ}C$ respectively. Examination was made on the effect of initial concentration of vitamin $B_2$$(C_0)$ on light fading of vitamin $B_2$ in aqueous multivitamin solutions and it was found that the fading progressed according to the following formula : $-{\frac {dc}{dt}}=K_c\;{\frac C{C_0}}$ where Kc is apparent light-fading rate constant relate to $C_0$. Photodecomposition of vitamin $B_6$ in aqueous multivitamin solutions was apparently first order kinetics and was stable in polyethylene>brown color>glass container to sunlight. Photodecomposition of vitamin $B_6$ in four seasons also investigated.