• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.17-26
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• 2021

The purpose of this paper is to determine the structure of the crystallographic group 𝚷 of the 4-dimensional solvable Lie group Sol ⁴_m,n that the translation subgroup of 𝚷, 𝚪 := 𝚷; ∩ Sol⁴_m,n, is generated by the particular elements.

• Journal of Integrative Natural Science
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• v.14 no.3
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• pp.139-146
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• 2021

The purpose of this paper is to classify the torsion-free extensions 1→ℤ³→𝛱→ℤ_𝜱→1 with injective abstract kernel 𝜙 : ℤ_𝜱→Aut(ℤ³). From this classification, we handle the sufficient conditions so as to classify the crystallographic groups of Sol⁴_m,n.

• Journal of the Korean Ceramic Society
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• v.29 no.4
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• pp.328-334
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• 1992

TiO2 sols were prepared by hydrolysis and polymerization of titanium tetra-isopropoxide (TTIP) in the presence of diethanolamine (DEA). The optimal mole ratio of water to TTIP is 2 and the concentration of the TiO2 sol 0.7 M. Golden TiN films without cracks were obtained by dipping Si(110) wafers into the TiO2 sol and followed by nitridation in NH3 at 1100$^{\circ}C$ for 5 h. The TiN films were studied by an optical microscope, DTA, TGA and X-ray analysis.

• Journal of the Korean Ceramic Society
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• v.33 no.10
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• pp.1079-1088
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• 1996

Discontinuous ${\gamma}$-LiAlO2 fibers for fiber-reinforcing MCFC matrixes have been produced by the sol-gel process using the centrifugal spinning apparatus of the Rotary type. Gel fibers could be obtained through spinning of stable LiAlO2 complex polymetric sols under the optimum spinning conditions (hollow-disc rotating velocity 9000 rpm sol feeding rate of 4ml/min flowing N2 temperature of 4$0^{\circ}C$ and flowing N2 pressure of 4 bar). It was found that defect free and densified ${\gamma}$-LiAlO2 fibers with the relative density of 98% and the mean diameter of 4.7${\mu}{\textrm}{m}$ were prepared when the spinned fibers were heat-treated to 100$0^{\circ}C$ on the specified heating schedule. in particular the mean diameter and length of fibers could be controlled by the pressure of flowing N2 and the chopping-sieving method respectively.

• Journal of the Korean Ceramic Society
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• v.29 no.5
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• pp.357-366
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• 1992

Residual organics were considered as impurity in Sol-Gel method. The purpose of this study was to find the conditions to contain as much residual organics as possible in silica gel prepared from TEOS(tetraethylortho-silicate) by Sol-Gel method. Residual organics are to be expected to have reduction effect on synthesizing Si3N4 from silica gel. The results of this study are follows: 1) The maximum content of entrapped carbon was 19.8 wt.%(C/SiO2=0.25 wt.ratio) in silica gel synthesized under the conditions 1.5 fold mole water for incomplete hydrolysis, 2.5 fold mole phenol as a solvent and 0.1 fold mole HCl as a catalyst to TEOS. 2) Silica gel with organics entrapped by Sol-Gel method had a positive effect on the formation of Si3N4 compared with commercial silica gel. 3) Sintered body of synthesized $\alpha$-Si3N4 with Y2O3 and Al2O3 as additives at 175$0^{\circ}C$ in N2 atmosphere showed bending strength, 602$\pm$20 MPa and frature toughness 4.45$\pm$0.15 MPa.m1/2.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1121-1137
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• 2007

There are 7 types of 4-dimensional solvable Lie groups of the form ${\mathbb{R}^3}\;{\times}_{\varphi}\;{\mathbb{R}}$ which are unimodular and of type (R). They will have left. invariant Riemannian metrics with maximal symmetries. Among them, three nilpotent groups $({\mathbb{R}^4},\;Nil^3\;{\times}\;{\mathbb{R}\;and\;Nil^4)$ are well known to have lattices. All the compact forms modeled on the remaining four solvable groups $Sol^3\;{\times}\;{\mathbb{R}},\;Sol_0^4,\;Sol_0^'4\;and\;Sol_{\lambda}^4$ are characterized: (1) $Sol^3\;{\times}\;{\mathbb{R}}$ has lattices. For each lattice, there are infra-solvmanifolds with holonomy groups 1, ${\mathbb{Z}}_2\;or\;{\mathbb{Z}}_4$. (2) Only some of $Sol_{\lambda}^4$, called $Sol_{m,n}^4$, have lattices with no non-trivial infra-solvmanifolds. (3) $Sol_0^{'4}$ does not have a lattice nor a compact form. (4) $Sol_0^4$ does not have a lattice, but has infinitely many compact forms. Thus the first Bieberbach theorem fails on $Sol_0^4$. This is the lowest dimensional such example. None of these compact forms has non-trivial infra-solvmanifolds.

• Journal of the Korean Magnetics Society
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• v.16 no.5
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• pp.245-248
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• 2006

[ $Tb_{3-x}Bi_xFe_5O_{12}$ ] has been studied by x-ray diffraction (XRD), vibrating sample magnetometer, $M\"{o}ssbauer$ spectroscopy. The crystal structures were found to be a cubic garnet structure with space group Ia3d. The lattice constants increase linearly with increasing bismuth concentration. With increase of bismuth substitution, the $N\'{e}el$ temperature increases but the compensation temperature decreases. We have observed the negative magnetization in Bi-TbIG system which has not been reported in garnet systems. $M\"{o}ssbauer$ spectra were measured at various temperatures from 4.2 K to $N\'{e}el$ temperature. The isomer shifts at room temperature are ${\sim}0.26mm/s$ which is consistent with ferric state.

• Journal of the Korean Electrochemical Society
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• v.6 no.4
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• pp.266-270
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• 2003

The $LiN_{0.8}Co_{0.2}O_2$ has shown outstanding electrochemical properties. The microstructure of $LiN_{0.8}Co_{0.2}O_2$ cathode was investigated by using TEM (transmission electron microscopy) and X-ray diffraction techniques. The $LiN_{0.8}Co_{0.2}O_2$ was produced by sol-gel method to synthesize fine particles less than $1{\mu}m$ in the average diameter. In this study, emphasis was given to the examination and interpretation of the microstructural change during charge-discharge cycling experiments, which appeared to be one of the main causes of early degradation of rechargeable batteries. Results showed that the $1{\mu}m$ cathode produced by sol-gel method had high reversible capacity and excellent cycling stability due to its homogeneous distribution of Ni and Co cations on u atomic scale. In particular, the $1{\mu}m$ cathode did not show severe strain induced structural defects or cubic spinel disordering during cycling experiments, which had been observed in the conventional $LiCoO_2$ cathode. The $LiNi_{0.8}Co_{0.2-x}M_x[M=Al]$ compounds show good reversibility but low discharge capacity.

• Bulletin of the Korean Chemical Society
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• v.27 no.1
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• pp.65-70
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• 2006

An amperometric glucose biosensor has been developed based on the use of the nanoporous composite film of sol-gel-derived zirconia and perfluorosulfonated ionomer, Nafion, for the encapsulation of glucose oxidase (GOx) on a platinized glassy carbon electrode. Zirconium isopropoxide (ZrOPr) was used as a sol-gel precursor for the preparation of zirconia/Nafion composite film and the performance of the resulting glucose biosensor was tuned by controlling the water content in the acid-catalyzed hydrolysis of sol-gel stock solution. The presence of Nafion polymer in the sol-gel-derived zirconia in the biosensor resulted in faster response time and higher sensitivity compared to those obtained at the pure zirconia- and pure Nafion-based biosensors. Because of the nanoporous nature of the composite film, the glucose biosensor based on the zirconia/Nafion composite film can reach 95% of steady-state current less than 5 s. In addition, the biosensor responds to glucose linearly in the range of 0.03-15.08 mM with a sensitivity of 3.40 $\mu$A/mM and the detection limit of 0.037 mM (S/N = 3). Moreover, the biosensor exhibited good sensor-to-sensor reproducibility (~5%) and long-term stability (90% of its original activity retained after 4 weeks) when stored in 50 mM phosphate buffer at pH 7 at 4 ${^{\circ}C}$.

• Membrane Journal
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• v.18 no.2
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• pp.176-184
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• 2008

Nano-porous ceramic membranes was synthesized by the sol-gel method. Gas permeation of hydrogen and nitrogen was determined by single composition gas. Pore size $0.1{\mu}m$ and porosity 32% of flat type ${\alpha}-Al_2O_3$ substrate was manufactured. An intermediate ${\gamma}-Al_2O_3$ layer with pore size of 4 nm was formed by dip-coating. Polymeric silica sol was synthesized by acid catalyzed hydrolysis and condensation of tetra-ethyl-ortho-silicate. Supported membranes on alumina were prepared by dipping and calcining. He, $N_2$ permeation experiments with nanoporous sol-gel modified supported ceramic membranes were peformed to determine the gas transport characteristics. $He/N_2$ permselectivity around $100{\sim}160$ and helium permeation in the order of $10^{-7}mol/m^2{\cdot}s{\cdot}Pa$ were measured in the temperature range of $303{\sim}363K$.