• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.08a
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• pp.218-218
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• 2012

Recently, hexagonal manganites have attracted much attention because of the coexistence of ferroelectricity and antiferromagnetic (AFM) order. The crystal structure of hexagonal manganites consists of $MnO_5$ polyhedra in which $Mn^{3+}$ ion is surrounded by three oxygen atoms in plane and two apical oxygen ions. The Mn ions within Mn-O plane form a triangular lattice and couple the spins through the AFM superexchange interaction. Due to incomplete AFM coupling between neighboring Mn ions in the triangular lattice, the system forms a geometrically-frustrated magnetic state. Among hexagonal manganites, $YMnO_3$, in particular, is the best known experimentally since the f states are empty. In addition, for applications, $YMnO_3$ thin films have been known as promising candidates for non-volatile ferroelectric random access memories. However, $YMnO_3$ has low magnetic order temperature (~70 K) and A-type AFM structure, which hinders its applications. We have synthesized $YMn1_{-x}Cr_xO_3$ (x = 0, 0.05 and 0.1) samples by the conventional solid-state reaction. The powders of stoichiometric proportions were mixed, and calcined at $900^{\circ}C$ for $YMn1_{-x}Cr_xO_3$ for 24 h. The obtained powders were ground, and pressed into 5-mm-thick disks of 1/2-inch diameter. The disks were directly put into the oven, and heated up to $1,300^{\circ}C$ and sintered in air for 24 h. The phase of samples was checked at room temperature by powder x-ray diffraction using a Rigaku Miniflex diffractometer with Cu $K{\alpha}$ radiation. All the magnetization measurements were carried out with a superconducting quantum-interference-device magnetometer. Our experiments point out that the Cr-doped samples show the characteristics of a spin-glass state at low temperatures.

• The korean journal of orthodontics
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• v.29 no.2 s.73
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• pp.251-265
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• 1999

Various types of horizontal reference planes are used for diagnosis, treatment planning and evaluation of treatment results. But these reference Planes lack accuracy and repro-ducibility, and are mainly for Caucasian. Unlike the adult patients who have completed growth, the horizontal reference planes for growing children may change continuously during growth. Therefore this must be considered in selecting the horizontal reference plane. The purpose of this study was to Investigate the angle formed by the Sella-Nasion(SN) plane and Frankfort-Horizontal(FH) plane and evaluate the angle formed by FH plane and other horizontal reference planes in relation to different skeletal maturity and malocclusion types. 540 subjects with no orthodontic treatment history were chosen, and hand -wrist X-rays and lateral cephalometric X-rays were taken. According to SMA(Skeletal Maturity Assessment) of hand-wrist X-rays, the subjects were classified into 3 skeletal maturity groups : SMI 1-4 for group A, SMI 5-7 for group B and SMI 8-11 for group C. A second classification was made according to cephalometric analysis of lateral cephalograms. The subjects were classified into 3 malocclusion groups : Skeletal Class I, II and III malocclusion group. 10 measurements were evaluated. The results were as follows. 1. The angle formed by the SN plane and FH plane showed no difference among skeletal maturity groups, malocclusion groups, and between .sexes. 2. The angles formed by the SN plane and FH plane were $8.27^{\circ}{\pm}2.31^{\circ}$ for males and $8.59^{\circ}{\pm}2.24^{\circ}$ for females. The average value for females and males was $8.42^{\circ}{\pm}2.28^{\circ}$. 3. The angle formed by the FH plane and palatal plane was almost constant showing no difference among skeletal maturity groups, malocclusion groups, and between sexes($1.09^{\circ}{\pm}3.21^{\circ}$).

• Journal of the Microelectronics and Packaging Society
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• v.21 no.4
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• pp.45-49
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• 2014

In this study, we grew non-polar ZnO nanostructure on (1-102) R-plane sapphire substrates. As for growth method of ZnO, we used hydrothermal synthesis which is known to have the advantages of low cost and easy process. For growth of non-polar, the deposited AZO seed buffer layer with of 80 nm on R-plane sapphire by radio frequency magnetron sputter was annealed by RTA(rapid thermal annealing) in the argon atmosphere. After that, we grew ZnO nanostructure on AZO seed layer by the added hexamethylenetramine (HMT) solution and sodium citrate at $90^{\circ}C$. With two types of additives into solution, we investigated the structures and shapes of ZnO nanorods. Also, we investigate the possibility of formation of 2D non-polar ZnO layer by changing the ratio of two additives. As a result, we could get the non-polar A-plane ZnO layer with well optimized additives' concentrations.

• Imaging Science in Dentistry
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• v.51 no.4
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• pp.389-398
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• 2021

Purpose: This study introduces a standardized 2-plane approach using 8 landmarks to assess alveolar bone levels in mice using micro-computed tomography. Materials and Methods: Bone level differences were described as distance from the cemento-enamel junction (CEJ) to alveolar bone crest (ABC) and as percentages of vertical bone height and vertical bone loss, comparing mice infected with Porphyromonas gingivalis (Pg) to controls. Eight measurements were obtained per tooth: 2 in the sagittal plane (mesial and distal) and 6 in the coronal plane (mesiobuccal, middle-buccal, distobuccal, mesiolingual, middle-lingual, and distolingual). Results: Significant differences in the CEJ-to-ABC distance between Pg-infected mice and controls were found in the coronal plane (middle-lingual, mesiobuccal, and distolingual for the first molar; and mesiobuccal, middle-buccal, and distolingual for the second molar). In the sagittal plane, the distal measurement of the second molar was different. The middle-buccal, mesiobuccal, and distolingual sites of the first and second molars showed vertical bone loss relative to controls; the second molar middle-lingual site was also different. In the sagittal plane, the mesial sites of the first and second molars and the distal site of the second molar showed loss. Significantly different vertical bone height percentages were found for the mesial and distal sites of the second molar (sagittal plane) and the middle-lingual and distolingual sites of the first molar(coronal plane). Conclusion: A reliable, standardized technique for linear periodontal assessments in mice is described. Alveolar bone loss occurred mostly on the lingual surface of the coronal plane, which is often omitted in studies.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.17-24
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• 2002

It will be described the discovery of fundamental algebras such as complex numbers and the quaternions. Cardano(1539) was the first to introduce special types of complex numbers such as 5$\pm$$\sqrt{-15}$. Girald called the number a$\pm$$\sqrt{-b}$ solutions impossible. The term imaginary numbers was introduced by Descartes(1629) in “Discours la methode, La geometrie.” Euler knew the geometrical representation of complex numbers by points in a plane. Geometrical definitions of the addition and multiplication of complex numbers conceiving as directed line segments in a plane were given by Gauss in 1831. The expression “complex numbers” seems to be Gauss. Hamilton(1843) defined the complex numbers as paire of real numbers subject to conventional rules of addition and multiplication. Cauchy(1874) interpreted the complex numbers as residue classes of polynomials in R[x] modulo $x^2$＋1. Sophus Lie(1880) introduced commutators [a, b] by the way expressing infinitesimal transformation as differential operations. In this paper, it will be studied general quaternion algebras to finding of algebraic structure in Algebras.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07a
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• pp.531-534
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• 2002

NiO buffer layers for YBCO coated conductors were deposited on hi-axially textured Ni substrates by MOCVD(metal organic chemical vapor deposition) method, using single solution source. To establish the processing condition, oxygen partial pressure and deposition temperature were changed. The surface orientation and degree of texture were estimated by X-ray diffraction, X-ray pole figure and atomic force microscopy. The FWHMs of in-plane and out-of-plane of the NiO films were about 10$^{\circ}$. The surface roughness was a function of deposition temperature. The AFM surface roughness of NiO films is in the range of 3∼10 nm, when NiO films was grown at 450∼530$^{\circ}C$.

• Proceedings of the Korean Magnestics Society Conference
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• 2003.06a
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• pp.58-59
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• 2003

We have developed a simple model allowing further clarifications of the magnetoresistance (MR) contribution to the giant magnetoimpedance (GMI) effect in thin films. The theoretical considerations are the following. It is absolutely assumed that a thin film with no magnetic domain structure and a high frequency ac current I = I$\sub$0/e$\^$iwt/ flowing parallel to the Z direction in the plane of the film. The sample has the thickness 2a in the X direction, thus the Y direction in the plane of the sample and perpendicular to the current direction. The transverse permeability ${\mu}$$\sub$Y/ in the Y direction is uniform. In the case of GMI effect, the total impedance Z = R + iX can be written as.

• Journal of Magnetics
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• v.5 no.3
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• pp.76-80
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• 2000

Soft x-ray standing waves produced by a multilayer interference substrate add depth-sensitivity to magnetic circular dichroism to resolve changes in Co magnetism across a 10${\AA}$ distance from the Co center to the Co-Pd interface of a Pd/Co/Pd trilayer having in-plane magnetization. Large enhancements of in-plane orbital and spin magnetic moments, as well as the number of d holes, are strongly localized in a thin interface layer. These results provide new insight into the phenomenon of magnetic anisotropy at buried interfaces, and suggest a broad applicability of such standing wave measurements to interface magnetism studies.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.11
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• pp.80-87
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• 1993

In this paper, the fields of double-plane steps in rectangular waveduides are analyzed using the modified TE$_{mn}$$^{x}$ mode-matching method. The characteristics of rectangular waveguide having double-plane steps are investigated with accomdating the effects of higher-order modes generated by discontinuities. In comparison with the generalized TE$_{mn}$-TM$_{mn}$ mode analysis, the modified TE$_{mn}$$^{x}$ mode-matching method consumes less memory and CPU time and provides improved convergence behavior. The results obtained in this manner coinside with that of the TE$_{mn}$-TM$_{mn}$ mode-matching method.