• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.173-187
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• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.35-46
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• 2021

The purpose of this paper is to study invariant pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparallel submanifold of a para-Kenmotsu manifold and I obtained some equivalent conditions of invariant submanifolds of para-Kenmotsu manifolds under some conditions which the submanifolds are totally geodesic. Finally, a non-trivial example of invariant submanifold of paracontact metric manifold is constructed in order to illustrate our results.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.152-166
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• 2021

In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D1 ⊕ {V}, D2 ⊕ {V} and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.699-715
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• 2022

We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension 2, and exhibit connections to various problems in dimension 3.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.201-210
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• 2024

This paper is concerned with the study of spacetimes satisfying div 𝓜 = 0, where "div" denotes the divergence and 𝓜 is the m-projective curvature tensor. We establish that a perfect fluid spacetime with div 𝓜 = 0 is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with div 𝓜 = 0 represents a generalized Robertson-Walker spacetime.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.85-92
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• 2024

In this work we give the necessary and sufficient conditions for f-biharmonic curves in three-dimensional generalized symmetric spaces.

• Journal of Korea Game Society
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• v.17 no.5
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• pp.89-102
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• 2017

With the increase in interest in health in the society, a variety of fusion studies have been conducted by ICT to sports. This study develops a smart bicycle that is run only when a rider maintains balance, and proposes an interface of studio space where the smart bicycle can be experienced. The studio consists of interactive smart bike, a geodesic dome for immersion of content for a single person, and virtual reality content that is implemented to enjoy various sceneries in real space. This study contributes to attempts of design and production of studio that is optimized to interactive space of smart bike for single person. This studio has a scalable interface, which can be applicable to various other interactive contents for sportainmnet.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.2
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• pp.364-370
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• 2011

This paper propose a novel method for tracking moving object based on covariance matrix and Riemannian Manifolds. With image backgrounds continuously changed, we use the covariance matrices to extract features for tracking nonrigid object undergoing transformation and deformation. The covariance matrix can make fusion of different types of features and has its small dimension, therefore we enable to handle the spatial and statistical properties as well as the component correlation. The proposed method can estimate the position of the moving object by employing the covariance matrix of object region as a feature vector and comparing the candidate regions. Rimannian Geometry is efficiently adapted to object deformation and change of shape and improve the accuracy by using geodesic distance to predict the estimated position with the minimum distance. The experimental results have shown that the proposed method correctly tracked the moving object.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.273-280
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• 2005

The design of structural engineering optimization is to minimize the cost. This problem has many objective functions formulating section and shape as a function of the included discrete variables. simulated annealing, genetic algerian and TABU algerian are searching methods for optimum values. The object of this reserch Is comparing the result of TABU algorithm, and verifying the efficiency of TABU algorithm in structural optimization design field. For the purpose, this study used a solid truss of 25 elements having 10 nodes, and size optimization for each constraint and load condition of Geodesic ome, and shape optimization of Cable Dome for verifying spatial structures by the application of TABU algorithm.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.11b
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• pp.3-8
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• 1999

In this paper, we propose a new connected operator using morphological grayscale reconstruction for region-based coding. First, an effective method of reference-image creation is proposed, which is based on the size as well as the contrast. The conventional connected operators are good for removing small regions, but have a serious drawback for low-contrast regions that are larger than the structuring element. That is, when the conventional connected operators are applied to these regions. the simplification becomes less effective or several meaningful regions are merged to one region. To avoid this, the conventional geodesic dilation is modified to propose an adaptive operator. To reduce the effect of inappropriate propagation, pixels reconstructed to the original values are excluded in the dilation operation. Experimental results have shown that the proposed algorithm achieves better performance in terms of the reconstruction of flat zones. The picture quality has also been improved by about 7dB, compared to the conventional methods.