• Korean Journal of Mathematics
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• 제23권2호
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• pp.313-321
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• 2015

The manifold $^*g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 3-dimensional $^*g-ESX_3$ and to display a surveyable tnesorial representation of 3-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.

• 한국정보과학회논문지:소프트웨어및응용
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• 제36권11호
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• pp.960-966
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• 2009

다양체는 고차원 표본 데이터들 사이의 관계를 표현하기 위해 저차원 공간에서 생성된 구조로서 고차원 데이터인 영상과 3차원 인체 구성 데이터를 처리하는데 많이 사용되고 있다. 다양체 학습은 이러한 다양체를 생성하는 과정을 말한다. 그러나 다양체 학습을 이용한 포즈 추정은 학습하지 못한 실루엣 변화에 취약하다. 실루엣 변화는 2차원 영상에서 시점 변화, 포즈 변화, 사람 변화, 거리 변화, 잡영에 의해 발생되며, 이러한 변화를 하나의 다양체로 학습하기란 어렵다. 본 논문에서는 실루엣 변화를 유발하는 문제중 하나인 시점 변화에 대한 문제를 해결하고자 한다. 종래에 시점 변화에 상관 없이 포즈를 추정하는 방법에서는, 각 시점마다 다양체를 가지거나 사상 함수에서 시점에 관련한 요소들을 분리하석 별도의 다양체로 학습한다. 하지만 이러한 방법들은 복잡하고, 추정 과정에서 어떠한 시점의 다양체를통해 포즈를 추정할지 판단을 요구하며, 비교사 학습으로 인해 실루엣과 대응되는 3차원 인체 구성을 지정하기 어렵다. 본 논문에서는 시점 다양체, 포즈 다양체, 인체 구성 다양체를 편향된 다양체로 학습하여 사용하는 방법을 제안한다. 그리고 영상과 시점 다양체, 영상과 포즈 다양체, 인체 구성과 인체 구성 다양체, 포즈 다양체와 인체 구성 다양체 간에 사상 함수를 학습한다. 실험에서는 학습된 다양체와 사상 함수를 이용하여 24개의 시점에서 강인한 포즈 추정 결과를 보여주고 있다.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.485-495
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• 2022

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

• 대한수학회보
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• 제37권3호
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• pp.543-550
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• 2000

We prove that every generalized Landsberg manifold of scalar curvature R is a Riemannian manifold of constant curvature, provided that $R\neq\ 0$.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2013년도 춘계학술대회 논문집
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• pp.1123-1124
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• 2013

• International Journal of Fluid Machinery and Systems
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• 제6권3호
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• pp.121-136
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• 2013

This paper reports the 1-D fluid transient simulation results of the discharge flow conditions in a 6-cylinder reciprocating slurry pump. Two discharge manifold configurations are studied comparatively; a case with a hexagon shaped discharge manifold where each cylinder discharges at a single vertex, and a case where all the cylinders discharges are lumped together into a tank shaped manifold. In addition, the study examines the effect of two pulsation mitigation measures in the case of hexagonal manifold; a single inline orifice in one of the hexagon sides and a volumetric dampener at the manifold outlet. The study establishes the pressure and flow fluctuation characteristics of each configuration and decouples the pulsation characteristics of the pump and the discharge manifold.

• 대한수학회지
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• 제45권3호
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• pp.859-870
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• 2008

In the present paper, we investigate the geometric structures of the Dirichlet manifold composed of the Dirichlet distribution. We show that the Dirichlet distribution is an exponential family distribution. We consider its dual structures and give its geometric metrics, and obtain the geometric structures of the lower dimension cases of the Dirichlet manifold. In particularly, the Beta distribution is a 2-dimensional Dirich-let distribution. Also, we construct an affine immersion of the Dirichlet manifold. At last, we give the e-flat hierarchical structures and the orthogonal foliations of the Dirichlet manifold. All these work will enrich the theoretical work of the Dirichlet distribution and will be great help for its further applications.

• 대한수학회지
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• 제31권3호
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• pp.339-352
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• 1994

A sumbanifold M of a quaternionic Kaehlerian manifold $\tilde{M}^m$ of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

• 한국CDE학회논문집
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• 제3권3호
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• pp.154-160
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• 1998

In this study, we implement the prototype modeler with non-manifold data structure using Open Inventor. In these days, Open Inventor is a popular tool for computer graphics applications, even though Open Inventor could not store topological information including a non-manifold data structure which can represent an incomplete three dimensional shape such as a wireframe and a dangling surface during designing. Using Open Inventor, our modeler can handle a non-manifold model whose data structure is based on the radial edge data structure. A model editor is also implemented as an application which can construct a non-manifold model from two dimensional editing.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.965-977
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• 2016

The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.