• Current Optics and Photonics
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• v.1 no.6
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• pp.587-597
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• 2017

The extraction of the valid measurement region from the interference fringe pattern is a significant step when measuring gear tooth flank form deviation with grazing incidence interferometry, which will affect the measurement accuracy. In order to overcome the drawback of the conventionally used method in which the object image pattern must be captured, an improved segmentation approach is proposed in this paper. The interference fringe patterns feature, which is smoothed by the nonlinear diffusion, would be extracted by the structure tensor first. And then they are incorporated into the vector-valued Chan-Vese model to extract the valid measurement region. This method is verified in a variety of interference fringe patterns, and the segmentation results show its feasibility and accuracy.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1315-1327
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• 2011

Let M be a real hypersurface of a complex space form with almost contact metric structure (${\phi}$, ${\xi}$, ${\eta}$, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},\;{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when $R_{\xi}{\phi}S=R_{\xi}S{\phi}$ holds on M, where S denotes the Ricci tensor of type (1,1) on M.

• Journal of Korea Society of Digital Industry and Information Management
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• v.19 no.3
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• pp.245-251
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• 2023

Facial expression recognition plays a significant role in understanding human emotional states. With the advancement of AI and computer vision technologies, extensive research has been conducted in various fields, including improving customer service, medical diagnosis, and assessing learners' understanding in education. In this study, we develop a model that can infer emotions in real-time from a webcam using transfer learning with TensorFlow.js and MobileNet. While existing studies focus on achieving high accuracy using deep learning models, these models often require substantial resources due to their complex structure and computational demands. Consequently, there is a growing interest in developing lightweight deep learning models and transfer learning methods for restricted environments such as web browsers and edge devices. By employing MobileNet as the base model and performing transfer learning, our study develops a deep learning transfer model utilizing JavaScript-based TensorFlow.js, which can predict emotions in real-time using facial input from a webcam. This transfer model provides a foundation for implementing facial expression recognition in resource-constrained environments such as web and mobile applications, enabling its application in various industries.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1245-1252
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• 2011

Consider the $L^2$-adjoint $s_g^{'*}$ of the linearization of the scalar curvature $s_g$. If ker $s_g^{'*}{\neq}0$ on an n-dimensional compact manifold, it is well known that the scalar curvature $s_g$ is a non-negative constant. In this paper, we study the structure of the level set ${\varphi}^{-1}$(0) and find the behavior of Ricci tensor when ker $s_g^{'*}{\neq}0$ with $s_g$ > 0. Also for a nontrivial solution (g, f) of $z=s_g^{'*}(f)$ on an n-dimensional compact manifold, we analyze the structure of the regular level set $f^{-1}$(-1). These results give a good understanding of the given manifolds.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.217-224
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• 1999

In this paper the properties of the Finsler metrics compatible with an f-structure are investigated.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.339-348
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• 2000

We introduce the notion of the Finsler metrics compat-ible with a special Riemannian structure f of type (1,1) satisfying f6+f2=0 and investigate the properties of Finsler space with them.

• Proceedings of the Korean Vacuum Society Conference
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• 1994.06a
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• pp.146-146
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• 1994

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.855-867
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• 1998

In the present paper, we introduce the notions of quaternionically planar curves and quaternionically projective transformations to the case of almost quaternionic manifold with symmetric affine connection. Also, we obtain an invariant tensor field under the quaternionically projective transformation, and show that a quaternionic Kahlerian manifold with such a vanishing tensor field is of constant Q-sectional curvature.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.127-135
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• 2017

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 5-dimensional $^*g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the first class.

• Korean Journal of Mathematics
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• v.23 no.2
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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.