• Interaction and multiscale mechanics
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• 제2권1호
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• pp.1-14
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• 2009

This paper proposes an interaction field concept based on the field theory of plasticity. Relative deformation between two arbitrary scales, e.g., macro and micro fields, is defined which can be implemented in the crystal plasticity-based constitutive framework. Differential geometrical quantities responsible for describing dislocations and defects in the interaction field are obtained, based on which dislocation density and incompatibility tensors are further derived. It is shown that the explicit interaction exists in the curvature or incompatibility tensor field, whereas no interaction in the torsion or dislocation density tensor field. General expressions of the interaction fields over multiple scales with more than three scale levels are derived and implemented into the present constitutive equation.

• 한국수학사학회지
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• 제18권2호
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• pp.1-8
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• 2005

본 논문의 목적은 호프의 삶과 업적을 수학사적인 관점에서 조명하는 데 있다. 호프는 리만 다양체의 곡률과 위상의 관련성을 주목한 선각자이다. 곡률의 부호가 다양체의 국소적 성질과 대역적 성질을 연결하는 고리임을 알고 이에 대해 연구하였고 이와 관련된 예상문제들을 발표하여 기하학의 발전에 기여하였다. 이 논문에서는 호프 이전의 미분 기하학과 호프의 생애와 업적을 살펴보기로 한다.

• 대한수학회논문집
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• 제35권3호
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• pp.999-1018
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• 2020

In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from Kähler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.

• 대한수학회논문집
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• 제35권4호
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• pp.1203-1219
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• 2020

Jin [7] defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an (ℓ, m)-type connection. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (ℓ, m)-type connection in [7]. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an (ℓ, m)-type connection.

• 대한의용생체공학회:의공학회지
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• 제43권6호
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• pp.375-381
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• 2022

Brain-computer interface (BCI) is a technology that allows users with motor disturbance to control machines by brainwaves without a physical controller. Motor imagery (MI)-BCI is one of the popular BCI techniques, but it needs a long calibration time for users to perform a mental task that causes high fatigue to the users. MI is reported as showing a similar neural mechanism as motor execution (ME) and motor observation (MO). However, integrative investigations of these three tasks are rarely conducted. In this study, we propose a new paradigm that incorporates three tasks (MI, ME, and MO) and conducted a comparative analysis. For this study, we collected Electroencephalograms (EEG) of motor imagery/execution/observation from 28 healthy subjects and investigated alpha event-related (de)synchronization (ERD/ERS) and classification accuracy (left vs. right motor tasks). As result, we observed ERD and ERS in MI, MO and ME although the timing is different across tasks. In addition, the MI showed strong ERD on the contralateral hemisphere, while the MO showed strong ERD on the ipsilateral side. In the classification analysis using a Riemannian geometry-based classifier, we obtained classification accuracies as MO (66.34%), MI (60.06%) and ME (58.57%). We conclude that there are similarities and differences in fundamental neural mechanisms across the three motor tasks and that these results could be used to advance the current MI-BCI further by incorporating data from ME and MO.