• Korean Journal of Crystallography
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• v.16 no.1
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• pp.11-20
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• 2005

Six basic symmetries and five Bravais lattices existing in the two-dimensional lattice are derived and then ten two-dimensional point groups are classified by each of five Bravais lattices. Finally seventeen two-dimensional space groups belonging to the ten point groups are studied.

• Coupled systems mechanics
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• v.7 no.1
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• pp.61-77
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• 2018

This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.6
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• pp.843-849
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• 2010

This paper presents definition of symmetry of a ship section where three symmetries are proposed: material, geometric, and load symmetries. Precise terminologies of centroid, moment plane, and neutral axis plane are also defined. It is suggested that force vector equilibrium as well as force equilibrium are necessary condition to determine new position of neutral axis due to translational and rotational mobility. It is also stated that new reference datum of ENMP(elastic neutral moment plane), PNMP(fully plastic moment plane), ENAP(elastic neutral axis plane), and INAP(inelastic neutral moment plane) are required to define asymmetric section properties such as second moment of area, elastic section modulus, yield moment, fully plastic moment, and ultimate moment. Since collision-induced damage and flooding-induced biaxial bending moment produce typical asymmetry of section, the section properties are calculated for a typical VLCC. Geometry asymmetry is determined from ABS and DNV rules and two moment planes of 0/30 degs are assumed for load asymmetry. It is proved that the property reduction ratios directly calculated from second moment of area are usually larger than area reduction ratio. Reduction ratio of ultimate moment capacity shows almost linearly proportional to area reduction ratio. Mobility of elastic and inelastic neutral axis planes is visually provided.

• Transactions on Electrical and Electronic Materials
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• v.12 no.2
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• pp.68-71
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• 2011

[ $Ti_{1-x}W_xO_{2-y}$ ]solid solutions with compositions of x = 0.01(TW-1), x = 0.02(TW-2), x = 0.03(TW-3) and x = 0.04(TW-4) were prepared at 1,073 K in air under atmospheric pressure. All the solutions exhibited tetragonal symmetries. Nonstoichiometric chemical formulas have been obtained from oxidation-reduction titration and the partial substitution of $W^{6+}$ ions mainly caused the formation of $Ti^{3+}$ ion, rather than oxygen excess. Resistivities of the samples were highly dependent on humidity. The increase of the W amount resulted in an increase of $Ti^{3+}$ content, decrease of resistivity values and finally degradation of photocatalytic activities.

• East Asian mathematical journal
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• v.39 no.3
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• pp.349-354
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• 2023

The motivation in this paper comes from the recent results about Bell inequalities and topological insulators from group theory. Symmetries which are interested in group theory could be mainly used to find material structures. In this point of views, we study group extending by adding one relator which is easily called an equation. So a relative group extension by a adding relator is aspherical if the natural injection is one-to-one and the group ring has no zero divisor. One of concepts of asphericity means that a new group by a adding relator is well extended. Also, we consider that several equations and relative presentations over torsion-free groups are related to zero divisors.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.28 no.10
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• pp.642-647
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• 2015

The perovskite solid solutions of the $Sr_{1-x}Mg_xFe{^{3+}}_{1-{\tau}}Fe{^{4+}}_{\tau}O_{3-y}$ system (x=0.0, 0.1, 0.2, and 0.3) were synthesized in $N_2$ at $1,150^{\circ}C$. X-ray powder diffraction study assured that all the four samples had cubic symmetries(SM-0: $3.865{\AA}$, SM-1: $3.849{\AA}$, SM-2: $3.833{\AA}$, and SM-3: $3.820{\AA}$) and that the lattice volumes decreased steadily from $57.7{\AA}^3$ to $55.7{\AA}^3$ with x values. The nonstoichiometric chemical formulas were determined by Mohr salt analysis and with the increase of x values the amounts of $Fe^{4+}$ ion and oxygen were decreased simultaneously. Thermal analysis showed that SM-0 started to lose its oxygen at $450^{\circ}C$ and SM-1, Sm-2, and SM-3 began to lose their oxygen at around $350{\sim}400^{\circ}C$. SM-0 showed almost reversible weight change in the cooling process. All the samples exhibited semiconducting behaviors in the temperature range of $10{\sim}400^{\circ}C$. Conductivities of the 4 samples were decreased in the order of SM-0, SM-1, SM-2, and SM-3 at constant temperature. The activation energies of the conductions were in the range of 0.176 eV~0.244 eV.

• Proceedings of the Korean Magnetic Resonance Society Conference
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• 2002.08a
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• pp.70-71
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• 2002

Exchange-coupled cluster of transition-metal ions are relevant to many different scientific areas, ranging from chemistry to solid-state physics, biology, material science and has been the subject of much research in recent years(1,2). Single crystal EPR spectroscopy works as a very effective tool for the measurement of J values for small exchange interactions. This makes EPR technique very suitable for detection of weak exchange coupling transmitted over long distances via extended atomic and melecular bridges. Large polyoxometallates (3) may provide ideal structural environments for the study of interactions between paramagnetic ions. The detailed nature of magnetic interaction (positive sign and magnitude of J~0.006 $cm^{-1}$ /) was clearly determined for di-copper(II) system by single crystal EPR spectroscopy (4). The single-triplet (S-T) transitions are forbidden by different symmetries of the wave functions. However, when the singlet ground state is mixed into triplet states, the S-T transitions can be allowed and observed as weak lines. These weak S-T lines are positioned symmetrically with respect to the main transitions in the distance equals to 2J from the center of the spectrum. This lines allow one to determine the J-value with very high accuracy when │J│ ＜ hv 0.32 $cm^{-1}$ /. Unfortunately, the S-T transitions in the single crystal were detected by EPR method only in a few complexes until now. We have measured single-triplet transition lines for several magnetically coupled cluster systems and determined their J values accurately. The temperature dependency of J was studied by monitoring the changes in S-T.

• Transactions on Electrical and Electronic Materials
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• v.13 no.1
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• pp.39-42
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• 2012

To study the physical and chemical properties, solid solutions of $(Sr_{1-x}Ba_x)NdFe{^{3+}}_{1-\tau}Fe{^{4+}}_{\tau}O_{4-y}$ system with x=0.0(SBN-0), 0.1(SBN-1), 0.2(SBN-2) and 0.3(SBN-3) were synthesized in air at 1,473 K and annealed in air at 1,073 K for 24 h. X-ray powder diffraction assured that the four samples had tetragonal symmetries (I4/mmm). Their lattice volumes increased gradually with x values. Nonstoichiometric chemical formulas were formulated using the data such as $\tau$(amount of $Fe^{4+}$ ion) and y(oxygen deficiency) values using Mohr salt analysis. It was found out that all the four samples had excessive oxygen (4-y>4.0). All the samples started to lose some of their oxygen at around 613K(TG/DTA thermal analysis). They exhibited semiconductivities in the temperature range of around 283-1173K. All the four specimens had sufficient tensile strength to endure the force of 19.6 N (2 kg of weights) and the conductivity values of the ECIAs which were painted on pieces of glass with the area of $150mm^2$ ($10mm{\times}15mm$) and it was in the order of ECIA-0${\rightarrow}$ECIA-1${\rightarrow}$ECIA-2${\rightarrow}$ECIA-3 at a constant temperature.