• Interaction and multiscale mechanics
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• v.2 no.1
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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.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.15-30
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• 2009

The theoretical framework of the interaction fields for multiple scales based on field theory is applied to one-dimensional problem mimicking dislocation substructure sensitive intra-granular inhomogeneity evolution under fatigue of Cu-added steels. Three distinct scale levels corresponding respectively to the orders of (A)dislocation substructures, (B)grain size and (C)grain aggregates are set-up based on FE-RKPM (reproducing kernel particle method) based interpolated strain distribution to obtain the incompatibility term in the interaction field. Comparisons between analytical conditions with and without the interaction, and that among different cell size in the scale A are simulated. The effect of interaction field on the B-scale field evolution is extensively examined. Finer and larger fluctuation is demonstrated to be obtained by taking account of the field interactions. Finer cell size exhibits larger field fluctuation whereas the coarse cell size yields negligible interaction effects.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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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.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.795-809
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• 2020

In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.205-221
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• 2023

The main goal of the paper is the introduction of the notion of conformal hemi-slant submersions from almost contact metric manifolds onto Riemannian manifolds. It is a generalization of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. Our main focus is conformal hemi-slant submersion from cosymplectic manifolds. We tend also study the integrability of the distributions involved in the definition of the submersions and the geometry of their leaves. Moreover, we get necessary and sufficient conditions for these submersions to be totally geodesic, and provide some representative examples of conformal hemi-slant submersions.

• Journal of Biomedical Engineering Research
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• v.43 no.6
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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.