• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1249-1260
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• 2023

In the present paper, we study a semi-symmetric recurrent metric connection and verify its various geometric properties.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.641-652
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• 1998

Chung and et al. ([2].1991) introduced a new concept of a manifold, denoted by $^{\ast}g-SEX_n$, in Einstein's n-dimensional $^{\ast}g$-unified field theory. The manifold $^{\ast}g-SEX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{\lambda \nu}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor $^{\ast}g^{\lambda \nu}$. Recently, Chung and et al.([3],1998) obtained a concise tensorial representation of SE-curvature tensor defined by the SE-connection of $^{\ast}g-SEX_n$ and proved deveral identities involving it. This paper is a direct continuations of [3]. In this paper we derive surveyable tensorial representations of constracted curvature tensors of $^{\ast}g-SEX_n$ and prove several generalized identities involving them. In particular, the first variation of the generalized Bianchi's identity in $^{\ast}g-SEX_n$, proved in theorem (2.10a), has a great deal of useful physical applications.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.603-616
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• 2008

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.551-564
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• 2001

We view Weyl structures as generalizations of Riemannian metrics and study the critical points of geometric functional which involve scalar curvature, defined on the space of Weyl structures on a closed 4-manifold. The main goal here is to provide a framework to analyze critical Weyl structures by defining functionals, discussing function spaces and writing down basic formulas for the equations of critical points.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.655-665
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• 2021

In the present paper, we study the geometric properties of the invariant submanifold of an almost Kenmotsu structure whose Riemannian curvature tensor has (𝜅, 𝜇, 𝜈)-nullity distribution. In this connection, the necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu (𝜅, 𝜇, 𝜈)-space to be totally geodesic under the behavior of functions 𝜅, 𝜇, and 𝜈.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.98-108
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• 1998

Hull design data is currently prepared by a 2D CAD system and re-input to 3D CAD systems specialized for detail design or to a structural analysis system. In this paper, sharing design data among different CAD systems has been studied. Based on STEP methodology, a neutral model is generated from 2D AutoCAD drawings. To handle a geometric data of this model, the non-manifold model of ACIS is used because it can support various CAD data representation such as 2D graphic entities, 3D wireframe, 3D surface model, and solid B-Rep/CSG model. It is observed that a mon-manifold model can easily be transformed to a 3-D wireframe model for the hull detail design system AutoDef or a FE model for the structural analysis system Nastran.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.1045-1060
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• 1998

Recently, Chung and et al. ([11], 1991c) introduced a new concept of a manifold, denoted by ＊g-SE $X_{n}$ , in Einstein's n-dimensional ＊g-unified field theory. The manifold ＊g-SE $X_{n}$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor ＊ $g^{λν}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor ＊ $g^{λν}$. This paper is the first part of the following series of two papers: I. The SE-curvature tensor of ＊g-SE $X_{n}$ II. The contracted SE-curvature tensors of ＊g-SE $X_{n}$ In the present paper we investigate the properties of SE-curvature tensor of ＊g-SE $X_{n}$ , with main emphasis on the derivation of several useful generalized identities involving it. In our subsequent paper, we are concerned with contracted curvature tensors of ＊g-SE $X_{n}$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in ＊g-SE $X_{n}$ , which has a great deal of useful physical applications.tions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1721-1737
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• 2020

Human apparent age estimation has become a popular research topic and attracted great attention in recent years due to its wide applications, such as personal security and law enforcement. To achieve the goal of age estimation, a large number of methods have been pro-posed, where the models derived through the cumulative attribute coding achieve promised performance by preserving the neighbor-similarity of ages. However, these methods afore-mentioned ignore the geometric structure of extracted facial features. Indeed, the geometric structure of data greatly affects the accuracy of prediction. To this end, we propose an age estimation algorithm through joint feature selection and manifold learning paradigms, so-called Feature-selected and Geometry-preserved Least Square Regression (FGLSR). Based on this, our proposed method, compared with the others, not only preserves the geometry structures within facial representations, but also selects the discriminative features. Moreover, a deep learning extension based FGLSR is proposed later, namely Feature selected and Geometry preserved Neural Network (FGNN). Finally, related experiments are conducted on Morph2 and FG-Net datasets for FGLSR and on Morph2 datasets for FGNN. Experimental results testify our method achieve the best performances.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.4
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• pp.9-18
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• 1995

The use of CAD/CAM systems is growing fast in the shipbuilding industry. To develope a geometric modeler, the existing CAD/CAM systems have been analysed. Because existing systems have closed architectures, it is not easy to investigate the internal structures. However, new trends in the software engineering, open architectured systems, pose some possibility to develope the geometric modeler. Several geometric modelers are analysed to extract component functions and modules. ACIS of the Spatial Technology, AIS of the CAM-I consortium, the STEP part for the geometry and topology, CAD*I of the ESPRIT project, and domestic modelers are investigated. Based on this analysis, a reference model which shows the framework of the modeler is proposed. With the data structure supporting non-manifold topologies, the reference model can be used to encourage a cooperative development program.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.637-647
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• 2017

Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.