• 대한수학회논문집
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• 제38권4호
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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.

• 대한수학회보
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• 제35권4호
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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.

• 호남수학학술지
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• 제30권4호
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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 $^*g-MEX_n$.

• 대한수학회보
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• 제38권3호
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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.

• 호남수학학술지
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• 제43권4호
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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.

• 대한조선학회논문집
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• 제35권4호
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• pp.98-108
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• 1998

중앙 단면도 등의 선박의 초기 구조설계는 여러 가지 이유로 2차원으로 설계되어 다른 설계부서에 도면으로 전달되고 있다. 본 연구에서는 기능이 서로 다른 여러 가지 컴퓨터 시스템사이의 데이터 교환을 위한 예제로, AutoCAD로 작성된 2차원의 초기 구조 설계 데이터를 구조해석(FEM) 시스템이나 상세설계 시스템(AutoDef)등의 다른 시스템에서 사용할 수 있는 데이터를 생성해 보았다. 이를 위해 STEP 제품모델의 방법에 따라 데이터가 정의 되었으며 2D 형상이나 3D 와이어프레임, 솔리드 모델등 다양한 형상을 다룰 수 있는 복합다양체 모델링 형상 도구인 ACIS가 사용되었다.

• 대한수학회지
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• 제35권4호
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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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• 제14권4호
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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.

• 대한조선학회논문집
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• 제32권4호
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• pp.9-18
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• 1995

국내에서 사용되고 있는 CAD/CAM 시스템들은 모두 도입한 제품들로, 그 구조가 폐쇄형으로 되어있기 때문에, 원천기술을 갖고있지 못한 후발 개발자들은 그 내부구조를 파악하기 어렵다. 근래에 정보기술분야에서 개방형 구조를 갖는 시스템들이 등장하여 좋은 기회를 제공하고 있다. 이 글에서는 개방형 구조를 갖는 형상모델러를 개발하기 위하여 그 시스템설계를 수행한 내용을 소개한다. 기존의 유사한 형상모델러들을 조사분석하여, 새로운 시스템이 갖추어야하는 기능들을 파악하였으며, 공학설계의 전 과정을 형상모델러가 유연하게 지원하기 위하여 복합다양체를 지원하는 자료구조를 갖는 것이 필요하다고 판단하였다. 이를 토대로 개방형 구조를 갖는 형상모델러의 골격에 대한 기준모델이 제안되었다. 이러한 기준모델과 자료구조, 그리고 공통의 개발환경은 시스템 개발을 위한 여러 사람의 참여와, 업무분담, 그리고 분담개발된 요소기능들의 통합을 지원하는 유효한 수단이 될 것이다.

• 호남수학학술지
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• 제39권4호
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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.