• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.3
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• pp.55-62
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• 2017

Non-negative matrix factorization (NMF) is one of the typical parts-based representation in which images are expressed as a linear combination of basis vectors that show the lcoal features or objects in the images. In this paper, we represent face images using various NMF methods and recognize their face identities based on extracted features using a learning vector quantization. We analyzed the various NMF methods by comparing extracted basis vectors. Also we confirmed the availability of NMF to the face recognition by verification of recognition rate of the various NMF methods.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.600-602
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• 1997

In this study, a hybrid neural net consisting of an Adaptive LVQ(ALVQ) algorithm and MLP is proposed to perform speaker identification task. ALVQ is a new learning procedure using adaptively feature vector sequence instead of only one feature vector in training codebooks initialized by LBG algorithm and the optimization criterion of this method is consistent with the speaker classification decision rule. ALVQ aims at providing a compressed, geometrically consistent data representation. It is fit to cover irregular data distributions and computes the distance of the input vector sequence from its nodes. On the other hand, MLP aim at a data representation to fit to discriminate patterns belonging to different classes. It has been shown that MLP nets can approximate Bayesian "optimal" classifiers with high precision, and their output values can be related a-posteriori class probabilities. The different characteristics of these neural models make it possible to devise hybrid neural net systems, consisting of classification modules based on these two different philosophies. The proposed method is compared with LBG algorithm, LVQ algorithm and MLP for performance.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.3
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• pp.322-326
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• 2004

This paper describes a new iris recognition method based on a shift-invariant wavelet sub-images. For the feature representation, we first preprocess an iris image for the compensation of the variation of the iris and for the easy implementation of the wavelet transform. Then, we decompose the preprocessed iris image into multiple subband images using a shift-invariant wavelet transform. For feature representation, we select a set of subband images, which have rich information for the classification of various iris patterns and robust to noises. In order to reduce the size of the feature vector, we quantize. each pixel of subband images using the Lloyd-Max quantization method Each feature element is represented by one of quantization levels, and a set of these feature element is the feature vector. When the quantization is very coarse, the quantized level does not have much information about the image pixel value. Therefore, we define a new similarity measure based on mutual information between two features. With this similarity measure, the size of the feature vector can be reduced without much degradation of performance. Experimentally, we show that the proposed method produced superb performance in iris recognition.

• East Asian mathematical journal
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• v.17 no.2
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• pp.253-264
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• 2001

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.601-612
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• 2017

Let Q be the frame g-loop quiver, i.e. a generalized ADHM quiver obtained by replacing the two loops into g loops. The vector space M of representations of Q admits an involution ${\ast}$ if orthogonal and symplectic structures on the representation spaces are endowed. We prove equivalence between semisimplicity of representations of the ${\ast}-invariant$ subspace N of M and the orbit-closedness with respect to the natural adjoint action on N. We also explain this equivalence in terms of King's stability [8] and orthogonal decomposition of representations.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.365-386
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• 2005

Let L be the free Lie superalgebra generated by a $Z_2$-graded vector space V over C. Suppose that g is a Lie superalgebra gl(m, n) or q(n). We study the g-module structure on the kth homogeneous component Lk of L when V is the natural representation of g. We give the multiplicities of irreducible representations of g in Lk by using the character of Lk. The multiplicities are given in terms of the character values of irreducible (projective) representations of the symmetric groups.

• ETRI Journal
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• v.28 no.2
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• pp.219-222
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• 2006

Virtual source location information (VSLI) has been newly utilized as a spatial cue for compact representation of multichannel audio. This information is represented as the azimuth of the virtual source vector. The superiority of VSLI is confirmed by comparison of the spectral distances, average bit rates, and subjective assessment with a conventional cue.

• Journal of Broadcast Engineering
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• v.19 no.2
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• pp.166-173
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• 2014

Recently, human action recognition have been developed for various broadcasting and video process. Since a video can consist of various scenes, keypoint approaches have been more attracted than template based methods for real application. Keypoint approahces tried to find regions having motion in video, and made 3-dimensional patches. Then, descriptors using histograms were computed from the patches, and a classifier based on machine learning method was applied to detect actions in video. However, a single classifier was difficult to handle various human actions. In order to improve this problem, approaches using multi classifiers were used to detect and to recognize objects. Thus, we propose a new human action recognition using decision-level fusion with support vector machine and sparse representation. The proposed method extracted descriptors based on keypoint approach from a video, and acquired results from each classifier for human action recognition. Then, we applied weights which were acquired by training stage to fuse each results from two classifiers. The experiment results in this paper show better result than a previous fusion method.

• Research in Mathematical Education
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• v.18 no.4
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• pp.289-305
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• 2014

The current mathematical education calls for a learning environment from the constructionism perspective that actively creates mathematical objects. This research first analyzes JavaMAL's expression 'move' that enables students to express the agent's behavior constructively before they learn vector as a formal concept. Since expression 'move' is based on a coordinate, it naturally corresponds with the expression of vectors used in school mathematics and lets students take an embodied approach to the concept of vector. Furthermore, as a design tool, expression 'move' can be used in various activities that include vector structure. This research studies the educational significance entailed in JavaMAL's expression 'move'.