• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1357-1365
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• 2009

In this study, we enhance the numerical approach of Lee et al.$^{(1)}$ to spherical indentation technique for property evaluation of hyper-elastic rubber. We first determine the friction coefficient between rubber and indenter in a practical viewpoint. We perform finite element numerical simulations for deeper indentation depth. An optimal data acquisition spot is selected, which features sufficiently large strain energy density and negligible frictional effect. We then improve two normalized functions mapping an indentation load vs. deflection curve into a strain energy density vs. first invariant curve, the latter of which in turn gives the Yeoh-model constants. The enhanced spherical indentation approach produces the rubber material properties with an average error of less than 3%.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1607-1620
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• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.231-244
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• 2023

We study the modularity and holomorphic anomaly equation for Hodge-Gromov-Witten invariants of elliptic curves.

• Journal of Korea Multimedia Society
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• v.5 no.2
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• pp.158-166
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• 2002

In this paper, we proposed a contour shape description method which use the CFR(contour fluctuation ratio) feature. The CFR is the ratio of the line length to the curve length of a contour segment. The line length means the distance of two end points on a contour segment, and the curve length means the sum of distance of all adjacent two points on a contour segment. We should acquire rotation and scale invariant contour segments because each CFR is computed from contour segments. By using the interleaved contour segment of which length is proportion to the entire contour length and which is generated from all the points on contour, we could acquire rotation and scale invariant contour segments. The CFR can describes the local or global feature of contour shape according to the unit length of contour segment. Therefore we describe the shape of objects with the feature vector which represents the distribution of CFRs, and calculate the similarity by comparing the feature vector of corresponding unit length segments. We implemented the proposed method and experimented with rotated and scaled 165 fish images of fifteen types. The experimental result shows that the proposed method is not only invariant to rotation and scale but also superior to NCCH and TRP method in the clustering power.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.9
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• pp.98-105
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• 2002

Some materials exhibit a rising K-R curve, while the K-R curve for other materials is flat. The shape of the K-R curve depends on material behavior and, to a lesser extent, on the configuration of the cracked structure. The K-R curve for an ideally brittle material is flat because the surface energy is an invariant material property. However, the K-R curve can take on a variety of shapes when nonlinear material behavior accompanies fracture. Five different hot-rolled thin plates are tested to investigate K-R curve behavior. A special experimental apparatus is used to prevent specimens from buckling.

• Journal of Korea Multimedia Society
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• v.25 no.8
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• pp.991-998
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• 2022

Recently, object recognition using image/video signals is rapidly spreading on autonomous driving and mobile phones. However, the actual input image/video signals are easily exposed to a poor illuminance environment. A recent researches for improving illumination enable to estimate and compensate the illumination parameters. In this study, we propose VE-DCE (video enhancement zero-reference deep curve estimation) to improve the illumination of low-light images. The proposed VE-DCE uses unsupervised learning-based zero-reference deep curve, which is one of the latest among learning based estimation techniques. Experimental results show that the proposed method can achieve the quality of low-light video as well as images compared to the previous method. In addition, it can reduce the computational complexity with respect to the existing method.

• Economic and Environmental Geology
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• v.5 no.2
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• pp.77-86
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• 1972

The system NaAlSiO_4-KAlSiO_4-SiO_2-H_2O, Bowen's "Petrogeny's Residua System" of course is extremely important in understanding the phase relationships of igneous and metamorphic rock in the continental crust. The phase relationships in this system, however, have not been completely established in the P-T range above the Mohorovicic discontinuity. They need to be established. In this study, the most probable sequence of P-T curves around a quaternary invariant point(~5Kb/${\sim}635^{\circ}C$) in the system using Schreinemakers' rule, is deduced, essentially on the basis of Morse's(1969a and b) experimental data. Possible modifications of the sequence of the P-T curves considering likely changes of the invariant chemogram are also considered. It is concluded that the sequence of P-T curves around the invariant point (~5Kb/${\sim}635^{\circ}C$) is (L), (Anl), (Or), (V), (Ne) and (Ab) on the P-T projection, where the P-T curve (L) is extended towards lower P-T regions, and the (Anl) curve is extended towards a region of higher temperature and lower pressure from the invariant point respectively.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1407-1419
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• 2021

The Iwasawa decomposition NAK of the Lie group G = SO₀(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

• East Asian mathematical journal
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• v.30 no.5
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• pp.583-597
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• 2014

In this paper, we study an area-preserving piecewise linear map with the feature of dangerous border collision bifurcations. Using this map, we study dynamical properties occurred in the invariant set, specially related to the boundary of KAM-tori, and the existence and stabilities of periodic orbits. The result shows that elliptic regions having periodic orbits and chaotic region can be divided by smooth curve, which is an unexpected result occurred in area preserving smooth dynamical systems.

• Transactions of Materials Processing
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• v.31 no.4
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• pp.214-228
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• 2022

The yield criterion, or called yield function, plays an important role in the study of plastic working of a sheet because it governs the plastic deformation properties of the sheet during plastic forming process. In this paper, we propose a novel anisotropic yield function useful for describing the plastic behavior of various anisotropic sheets. The proposed yield function includes the anisotropic version of the second stress invariant J₂ and the third stress invariant J₃. The anisotropic yield function newly proposed in this study is as follows. F(J₂)+ αG(J₃)+ βH (J₂ × J₃) = k^m The proposed yield function well explains the anisotropic plastic behavior of various sheets by introducing the parameters α and β, and also exhibits both symmetrical and asymmetrical yield surfaces. The parameters included in the proposed model are determined through an optimization algorithm from uniaxial and biaxial experimental data under proportional loading path. In this study, the validity of the proposed anisotropic yield function was verified by comparing the yield surface shape, normalized uniaxial yield stress value, and Lankford's anisotropic coefficient R-value derived with the experimental results. Application for the proposed anisotropic yield function to aluminum sheet shows symmetrical yielding behavior and to pure titanium sheet shows asymmetric yielding behavior, it was shown that the yield curve and yield behavior of various types of sheet materials can be predicted reasonably by using the proposed new yield anisotropic function.