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The Geometry of the Space of Symmetric Bilinear Forms on ℝ2 with Octagonal Norm

  • Kim, Sung Guen
    • Kyungpook Mathematical Journal
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    • v.56 no.3
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    • pp.781-791
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    • 2016
  • Let $d_*(1,w)^2 ={\mathbb{R}}^2$ with the octagonal norm of weight w. It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on $d_*(1,w)^2$. We also show that the unit sphere of the space of symmetric bilinear forms on $d_*(1,w)^2$ is the disjoint union of the sets of smooth points, extreme points and the set A as follows: $$S_{{\mathcal{L}}_s(^2d_*(1,w)^2)}=smB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}extB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}A$$, where the set A consists of $ax_1x_2+by_1y_2+c(x_1y_2+x_2y_1)$ with (a = b = 0, $c={\pm}{\frac{1}{1+w^2}}$), ($a{\neq}b$, $ab{\geq}0$, c = 0), (a = b, 0 < ac, 0 < ${\mid}c{\mid}$ < ${\mid}a{\mid}$), ($a{\neq}{\mid}c{\mid}$, a = -b, 0 < ac, 0 < ${\mid}c{\mid}$), ($a={\frac{1-w}{1+w}}$, b = 0, $c={\frac{1}{1+w}}$), ($a={\frac{1+w+w(w^2-3)c}{1+w^2}}$, $b={\frac{w-1+(1-3w^2)c}{w(1+w^2)}}$, ${\frac{1}{2+2w}}$ < c < ${\frac{1}{(1+w)^2(1-w)}}$, $c{\neq}{\frac{1}{1+2w-w^2}}$), ($a={\frac{1+w(1+w)c}{1+w}}$, $b={\frac{-1+(1+w)c}{w(1+w)}}$, 0 < c < $\frac{1}{2+2w}$) or ($a={\frac{1=w(1+w)c}{1+w}}$, $b={\frac{1-(1+w)c}{1+w}}$, $\frac{1}{1+w}$ < c < $\frac{1}{(1+w)^2(1-w)}$).

Interfacial Reactions between W Thin Film and 6H-SiC during Heat Treatments (열처리에 따른 W 박막과 6H-SiC의 계면반응에 관한 연구)

  • Shin, Yang-Soo;Lee, Byung-Taek
    • Korean Journal of Materials Research
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    • v.8 no.6
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    • pp.545-550
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    • 1998
  • Phase reactions at W /6H- SiC interfaces during heat treatments were investigated by X- Ray diffractometer and transmission electron microscopy. No detectable reactions were found after annealing at up to 900$0^{\circ}C$ whereas formation of $W_5Si_3$ and $W_2C$$0^{\circ}C$ This result is consistent with a previous report that the reactions between 3C-SiC and W occurs at llOOoe, and suggests that $W_5Si_3$ and $W_2C$ are the stable phases in this temperature range.

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The Examination of Mortar Durability by Microbial Biomineralization (미생물의 생체광물형성작용에 따른 모르타르 내구성 검토)

  • Kim, Sung-Tae;Chun, Woo-Young;Kim, Wha-Jung
    • Proceedings of the Korea Concrete Institute Conference
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    • 2009.05a
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    • pp.525-526
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    • 2009
  • On this paper we induce calcite($CaCO_3$) precipitation using microbial biomineralization of the Sporosarcina pasteurii and evaluate required performance evaluation by adjusting it to mortar. As a result carbonation normal mortar test piece(C3S-W) and mortar test piece(C3S-S.p) mixed with Sporosarcina pasteurii, reaction of C3S-S.p was late than C3S-W. Also, in the case of carbonation experiment of C3S-S.p curing in the Urea-CaCl2 aqueous solution(Medium) during 28days and durability of the C3S-W, durability of the mortar test piece(C3S-S.p) mixed with Sporosarcina pasteurii become higher than normal mortar test piece(C3S-W).

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Ohmic Contact Formation of SiC for Harsh Environment MEMS Using a TiW Thin-film (TiW 박막을 이용한 극한 환경 MEMS용 3C-SiC의 Ohmic contact 형성)

  • Chung, Soo-Yong;Noh, Sang-Soo;Chung, Gwiy-Sang
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2004.04b
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    • pp.133-136
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    • 2004
  • In this study, the characteristics of 3C-SiC ohmic contact were investigated. Titanium-tungsten(TiW) films were used for contact metalization. The ohmic contact resistivity between 3C-SiC and TiW was measured by HP4155 and then calculated with the circular transmission line method(C-TLM). And also the physical properties of TiW and the interface between TiW and 3C-SiC were analyzed using XRD and AES. TiW films make a good role of a diffusion barrier and their contact properties with 3C-SiC are stable at high temperature.

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Properties of Al2O3-SiCw Composites Fabricated by Three Preparation Methods (제조방법에 따른 Al2O3-SiCw 복합체의 특성)

  • Lee, Dae-Yeop;Yoon, Dang-Hyok
    • Journal of the Korean Ceramic Society
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    • v.51 no.5
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    • pp.392-398
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    • 2014
  • $Al_2O_3$-SiC composites reinforced with SiC whisker ($SiC_w$) were fabricated using three different methods. In the first, $Al_2O_3-SiC_w$ starting materials were used. In the second, $Al_2O_3-SiC_w$-SiC particles ($SiC_p$) were used, which was intended to enhance the mechanical properties by $SiC_p$ reinforcement. In the third method, reaction-sintering was used with mullite-Al-C-$SiC_w$ starting materials. After hot-pressing at $1750^{\circ}C$ and 30 MPa for 1 h, the composites fabricated using $Al_2O_3-SiC_w$ and $Al_2O_3-SiC_w-SiC_p$ showed strong mechanical properties, by which the effects of reinforcement by $SiC_w$ and $SiC_p$ were confirmed. On the other hand, the mechanical properties of the composite fabricated by reaction-sintering were found to be inferior to those of the other $Al_2O_3$-SiC composites owing to its relatively lower density and the presence of ${\gamma}-Al_2O_3$ and ${\gamma}-Al_{2.67}O_4$. The greatest hardness and $K_{1C}$ were 20.37 GPa for the composite fabricated using $Al_2O_3-SiC_w$, and $4.9MPa{\cdot}m^{1/2}$ using $Al_2O_3-SiC_w-SiC_p$, respectively, which were much improved over those from the monolithic $Al_2O_3$.

Application of White Light Emitting Diodes to Produce Uniform Scions and Rootstocks for Grafted Fruit Vegetable Transplants (과채류 접목 시 균일한 접수와 대목 생산을 위한 백색 LED의 적용)

  • Hwang, Hyunseung;Chun, Changhoo
    • Journal of Bio-Environment Control
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    • v.31 no.1
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    • pp.14-21
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    • 2022
  • Uniform scions and rootstocks should be produced to ensure grafting success. Light quality is an important environmental factor that regulates seedling growth. The effects of warm- and cool-white light emitting diode (LED) ratios on seedling growth were investigated. Scions and rootstocks of cucumber, tomato, and watermelon were grown in a closed transplant production system using LED as the sole lighting source. The LED treatments were W1C0 (only warm-white), W1C1 (warm-white: cool-white = 1:1), W3C1 (warm-white: cool-white = 3:1), and W5C2 (warm-white: cool-white = 5:2). The seedlings grown in W1C1 had the shortest hypocotyls, and the seedlings grown in W1C0 had the longest hypocotyls among the three tested vegetables. The hypocotyls of watermelon scions, watermelon rootstocks, and tomato rootstocks were shortest in W1C1, followed by those in W3C1, W5C2, and W1C0, but there was no significant difference between W3C1 and W5C2, which remained the same as the ratio of cool-white LEDs increased. In addition, tomato scions had the first and second longest hypocotyls in W1C0 and W3C1, respectively, and the shortest hypocotyls in W5C2 and W1C1, along with W5C2 and W1C1, although the difference was not significant. The stem diameter was highest in W1C0 except for tomato seedlings and rootstocks of watermelon. The shoot fresh weight of scions and rootstocks of cucumber and watermelon and the root fresh weight of cucumber scions were lowest in W1C1. These results indicated that different ratios of LED lighting sources had a strong effect on the hypocotyl elongation of seedlings.

Studies on Lipids in Fresh-Water Fishes 8. Comparison of Lipid Components among Wild and Cultured Carp (Cyprinus carpio) and Israeli Carp (Cyprinus carpio nudus) (담수어의 지질에 관한 연구 8. 천연 및 양식 잉어와 이스라엘 잉어의 지질성분 비교)

  • CHOI Jin-Ho;RHIM Chae-Hwan;BAE Tae-Jin;YOON Tai-Heon;LEE Kang-Ho
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.18 no.5
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    • pp.447-454
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    • 1985
  • As a part of serial study for comparing lipid components in freshwater fishes, this work was undertaken to compare the lipid components among wild and cultured carp, Cyprinus carpio, and Israeli carp, Cyprinus carpio nudus. The lipid components of cultured carp were analyzed and compared with those of wild and Israeli carp. In the content of total lipid, the lipid content in cultured carp was slightly lower than that in wild one, but similar to that in Israeli carp. The lipid contents in viscera of wild and cultured carp were 2 times higher than those in edible portion, but the lipid content in viscera of Israeli carp showed a similar trend to that in edible portion. In the fatty acid composition of neutral lipid in edible portion, percentages of $C_{18:1},\;C_{18:2},\;C_{18:3},\;C_{22:5}\;and\;C_{22:6}$ in cultured carp wire higher than those in wild one, while percentages of $C_{16:0},\;C_{18:0},\;C_{16:1},\;C_{20:4}\;and\;C_{20:5}$ lower, and percentage of $C_{18:2}$ in Israeli carp was noticeably higher than that in wild and cultured carp. In the case of phospholipid in edible portion, percentages of $C_{18:0},\;C_{18:1},\;C_{18:2},\;C_{18:3}\;and\;_C{22:6}$ in cultured carp were higher than those in wild one, while percentages of $C_{16:0},\;C_{16:1},\;C_{20:4},\;C_{20:5}\;and\;C_{22:5}$ lower. The unsaturation (TUFA/TSFA) of neutral lipid in cultured carp was slightly higher than that in wild one, but slightly lower than that in Israeli carp. In the case of phospholipid, the unsaturation showed a similar trend to that of neutral lipid. The essential fatty acid content(TEFA) of neutral lipid in edible portion of cultured carp was higher than that of wild one, but that in viscera lower. In the case of phospholipid in edible portion, the essential fatty acid content in Israeli carp was slightly higher than that in wild and cultured carp, and that in wild one was higher than that in cultured one. The w3 highly unsaturated fatty acid contents(w3 HUFA) of neutral lipid almost showed a similar trend to the essential fatty acid contents in wild and cultured carp, and Israeli carp. In the case of phospholipid, the w3 HUFA in Israeli carp was considerably higher than those in cultured and wild carp. In the ratio (A/C) of fatty acid content(A) in cultured carp to that(C) in diet, the A/C ratios of $C_{20:5}\;w3(0.12),\;C_{22:5}\;w6(0.53),\;C_{22:5}\;w3(0.68)\;and\;C_{22:6}\;w3(0.26)$ were much lower and in the ratio (B/C) of fatty acid content (B) in Israeli carp, the B/C ratios of $C_{18:3}\;w3(0.61),\;C_{20:5}\;w3(0.11),\;C_{22:4}\;w6(0.16),\;C_{22:5}\;w6(0.07)\;and\;C_{22:6}\;w3(0.79)$ were also lower than the other fatty acid. Consequently, it is considered that the ratios of w3 HUFA is related to the biosynthesis of polyenoic acid and growth rates of cultured and Israeli carp.

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Effects of Dietary Nutrient on the Biological Index and Serum Chemistry of Juvenile Olive Flounder Paralichthys olivaceus Achieving Compensatory Growth

  • Cho, Sung-Hwoan
    • Fisheries and Aquatic Sciences
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    • v.15 no.1
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    • pp.69-72
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    • 2012
  • Effects of dietary nutrient content on the biological index and serum chemistry of olive flounder Paralichthys olivaceus achieving compensatory growth were investigated. Six treatments were prepared in triplicate. Fish were hand-fed with the control (C) diet twice daily for 8 weeks (8W-C) or fish were starved for 2 weeks and then hand-fed with the C, high protein (HP), high carbohydrate (HC), high lipid (HL), or intermediate protein, carbohydrate and lipid (IPCL) diets for 6 weeks, referred to as 6W-C, 6W-HP, 6W-HC, 6W-HL, and 6W-IPCL, respectively. Weight gain of fish in the 8W-C, 6W-HP, and 6W-IPCL treatments was higher than that of fish in the 6W-C treatment. Condition factor (CF) of the fish in the 6W-HP, 6W-HC and 6W-IPCL treatments was higher than that of fish in the 8W-C and 6W-C treatments. The hepatosomatic index (HSI) of fish in the 6W-HC, 6W-HL and 6W-IPCL treatments was higher than that of the fish in the 8W-C, 6W-C and 6W-HP treatments. Serum chemistry except triiodothyronine ($T_3$) was not significantly different among the treatments. In conclusion, CF and HSI of the fish could be indices reflecting compensatory growth, whereas $T_3$ seemed to play a partial role in achieving compensatory growth.

Ohmic contact formation of single crystalline 3C-SiC for high temperature MEMS applications (초고온 MEMS용 단결정 3C-SiC의 Ohmic Contact 형성)

  • Chung, Gwiy-Sang;Chung, Su-Yong
    • Journal of Sensor Science and Technology
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    • v.14 no.2
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    • pp.131-135
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    • 2005
  • This paper describes the ohmic contact formation of single crystalline 3C-SiC thin films heteroepitaxially grown on Si(001) wafers. In this work, a TiW (Titanium-tungsten) film as a contact matieral was deposited by RF magnetron sputter and annealed with the vacuum and RTA (rapid thermal anneal) process respectively. Contact resistivities between the TiW film and the n-type 3C-SiC substrate were measured by the C-TLM (circular transmission line model) method. The contact phases and interface the TiW/3C-SiC were evaulated with XRD (X-ray diffraction), SEM (scanning electron microscope) and AES (Auger electron spectroscopy) depth-profiles, respectively. The TiW film annealed at $1000^{\circ}C$ for 45 sec with the RTA play am important role in formation of ohmic contact with the 3C-SiC substrate and the contact resistance is less than $4.62{\times}10^{-4}{\Omega}{\cdot}cm^{2}$. Moreover, the inter-diffusion at TiW/3C-SiC interface was not generated during before and after annealing, and kept stable state. Therefore, the ohmic contact formation technology of single crystalline 3C-SiC using the TiW film is very suitable for high temperature MEMS applications.

Research on operation stability of 7kW Inverter for short distance vehicle using SiC Hybrid module (SiC 하이브리드 모듈을 적용한 근거리용 7kW Inverter 동작 안정성에 대한 연구)

  • Jeon, Joon-Hyeok;Kyoung, Sin-Su;Kim, Hee-Jun
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.12 no.5
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    • pp.499-506
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    • 2019
  • This paper is concerned with the operating stability of 7kW inverter using SIC hybrid module and verifies the validity of the simulation results by comparing the result of the loss equation and the simulation result, Simulation results using Si module and SiC hybrid module are compared to compare switch loss and diode loss. Through the loss equation calculation, the conduction loss of SiC Hybrid module is 168W, switching loss is 9.3W, diode loss is 10.5nW, When compared with the simulation results, similar values were shown. As a result of comparing the simulation results of the Si module and the SiC Hybrid module, The total device loss of the Si module was 246.2W, and the total device loss of the SiC Hybrid module was 189.9W. The loss difference was 56.3W, which was about 0.8W. thereby verifying the reverse recovery characteristics of the SiC SBD. In addition, temperature saturation test was conducted to confirm the stability of SiC Hybrid module and Si module under high temperature saturation, In the case of the Si module, the output power was stopped at 4kW, and the SiC Hybrid module was confirmed to operate at 7kW. Based on this, an efficiency graph and a temperature graph are presented, and the Si module is graphed up to 4kW and the SiC Hybrid module is graphed up to 7kW.