• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.269-331
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• 2015

For a fixed positive integer g, we let $\mathcal{P}_g=\{Y{\in}\mathbb{R}^{(g,g)}{\mid}Y=^tY>0\}$ be the open convex cone in the Euclidean space $\mathbb{R}^{g(g+1)/2}$. Then the general linear group GL(g, $\mathbb{R}$) acts naturally on $\mathcal{P}_g$ by $A{\star}Y=AY^tA(A{\in}GL(g,\mathbb{R}),\;Y{\in}\mathcal{P}_g)$. We introduce a notion of polarized real tori. We show that the open cone $\mathcal{P}_g$ parametrizes principally polarized real tori of dimension g and that the Minkowski modular space 𝔗g = $GL(g,\mathbb{Z}){\backslash}\mathcal{P}_g$ may be regarded as a moduli space of principally polarized real tori of dimension g. We also study smooth line bundles on a polarized real torus by relating them to holomorphic line bundles on its associated polarized real abelian variety.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.419-422
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• 2005

Global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of primary resonance, in which an excitation frequency is near natural frequencies, is considered. The damping force is not included in the analysis. The renormalization-group technique for KAM tori is used to obtain the criteria for large-scale stochasticity in the system.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1199-1211
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• 2012

In this paper we give an introduction to the theory of universal central extensions of perfect Lie algebras. In particular, we will provide a model for the universal coverings of Lie tori and we show that automorphisms and derivations lift to the universal coverings. We also prove that the universal covering of a Lie ${\Lambda}$-torus of type ${\Delta}$ is again a Lie ${\Lambda}$-torus of type ${\Delta}$.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.336-346
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• 2000

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.65-90
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• 2024

In this paper, we introduce the notion of the stability of automorphic forms for the general linear group and relate the stability of automorphic forms to the moduli space of real tori and the Jacobian real locus.

• (The) Research of the performance art and culture
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• no.43
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• pp.325-356
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• 2021

This study is to analyze the current status of transmission and musical characteristics of Naeseo-deulilsori in Changwon, and the purpose of this study is to illuminate the value of deulilsori in Naeseo region, so that it can be continuously inherited. Naeseo-deulsori consists of the Mosimgi-sori, Nonmaegi-sori, and Chingchingi-sori. Mosimgi-sori, which is called when planting a seedling, is divided into 6 types according to the order and situation of work. ① rice planting sound, ② rice planting sound called in the morning, ③ rice planting sound called at lunch time, ④ rice planting sound called after lunch, ⑤ rice planting sound called when it is raining or cloudy, ⑥ rice planting sound called at sunset. Mosimgi-sori, which is called when planting a seedling, is based on Menali-tori, but partly influenced by Yugjabaegi-tori. However, it was typical Menali-tori in the slow The sound of rice planting in the nearby Haman region, but as the speed increased in the fast The sound of rice planting, the characteristics of Menali-tori faded and la↘mi perfect fourth descending frequently appeared. In the sound of rice planting in Goseong, both slow and fast sounds were strongly influenced by Yugjabaegi-tori. In the end, the sound of rice planting in the Naeseo region is less Yugjabaegi-tori than in the Goseong region and stronger than in Haman region. This combination of tori is a musical bargaining phenomenon that appears in the border region, and it can be said to be a geographical and regional characteristic of the Naeseo region. Nonmaegi-sori has the same sound as 'Sangsadeio' throughout the nearby Goseong and Haman regions. However, in Nonmaegi-sori in the Naeseo region, a strong Gyeong-tori tendency is found in the sound received. Looking at the flow of the melody of Nonmaegi-sori, it seems that the pitch has been changed by the intestines in recent years, and this modified melodic form has continued as it is. In order to guarantee locality, this part seems to need to be corrected in the future.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.707-715
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• 1994

This study presents thickness optimization for the pressure vessel domes subject to internal pressure and axial force simultaneously. The considered typical pressure vessel domes are ellipsoidal and tori-spherical domes with skirt and nozzle part. These pressure vessel domes under loading have higher stress concentration on geometric discontinuity parts. Therefore, thickness optimization of axi-symmetric pressure vessel domes is essentially concerned on minimizing this stress concentration. The objective function is minimization of weight of pressure vessel dome. The design variable is thickness of dome and cylinder. Considered constraint is Von Mises equivalent stress. In the optimization procedure, ANSYS code is used. The equivalent and hoop stress of original shape domes are compared with those of optimal shape domes. And optimal thicknesses for pressure vessel domes are presented.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.951-965
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• 2006

In this paper, we study a topological mirror symmetry on noncommutative complex tori. We show that deformation quantization of an elliptic curve is mirror symmetric to an irrational rotation algebra. From this, we conclude that a mirror reflection of a noncommutative complex torus is an elliptic curve equipped with a Kronecker foliation.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.149-154
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• 1986

• Journal of the Korean Mathematical Society
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• v.26 no.1
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• pp.117-142
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• 1989