• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.2
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• pp.148-155
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• 2014

In this paper a commute time embedding is implemented by organizing patches according to the graph-based metric, and its properties are investigated via changing the number of nodes on the graph.. It is shown that manifold embedding methods generate the intrinsic geometric structures when waveforms such as speech or music instrumental sound signals are embedded on the low dimensional Euclidean space. Basically manifold embedding algorithms only project the training samples on the graph into an embedding subspace but can not generalize the learning results to test samples. They are very effective for data clustering but are not appropriate for classification or recognition. In this paper a commute time guided transform is adopted to enhance the generalization ability and its performance is analyzed by applying it to the classification of 6 kinds of music instrumental sounds.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.205-214
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• 2016

Any open Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we will prove that, given any open Riemann surface, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. This result along with [5] now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension ${\geq}3$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.157-161
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• 2007

We show that there is an equivariant symplectic embedding of a two-torus with a nontrivial action into a symplectic manifold with a symplectic circle action if and only if the circle action on the manifold is non-Hamiltonian. This is a new equivalent condition for non-Hamiltonian action and gives us a new insight to solve the famous conjecture by Frankel and McDuff.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.939-947
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• 2012

In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-297
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• 2002

It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.

• Journal of KIISE:Software and Applications
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• v.31 no.2
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• pp.182-188
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• 2004

This paper proposes to synthesize facial images from a few parameters for the pose and the expression of their constituent components. This parameterization makes the representation, storage, and transmission of face images effective. But it is difficult to parameterize facial images because variations of face images show a complicated nonlinear manifold in high-dimensional data space. To tackle this problem, we use an LLE (Locally Linear Embedding) technique for a good representation of face images, where the relationship among face images is preserving well and the projected manifold into the reduced feature space becomes smoother and more continuous. Next, we apply a snake model to estimate face feature values in the reduced feature space that corresponds to a specific pose and/or expression parameter. Finally, a synthetic face image is obtained from an interpolation of several neighboring face images in the vicinity of the estimated feature value. Experimental results show that the proposed method shows a negligible overlapping effect and creates an accurate and consistent synthetic face images with respect to changes of pose and/or expression parameters.

• Journal of Korea Multimedia Society
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• v.17 no.1
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• pp.34-42
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• 2014

In this paper an embedding algorithm based on commute time is implemented by organizing patches according to the graph-based metric, and its performance is analyzed by comparing with the results of principal component analysis embedding. It is usual that the dimensionality reduction be done within some acceptable approximation error. However this paper shows the proposed manifold embedding method generates the intrinsic geometry corresponding to the signal despite severe approximation error, so that it can be applied to the areas such as pattern classification or machine learning.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.103-112
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• 2003

We consider multiplier ideals on CR manifolds, which is associated to Kiremidjian's work on CR embedding problem. Similar to the Kohn's result, we found that the multipliers form a nontrivial radical ideal.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.809-817
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• 1998

We investigate when the product of two smooth manifolds admits a weakly Lagrangian embedding. Prove that, if $M^m$ and $N^n$ are smooth manifolds such that M admits a weakly Lagrangian embedding into ${\mathbb}C^m$ whose normal bundle has a nowhere vanishing section and N admits a weakly Lagrangian immersion into ${\mathbb}C^n$, then $M \times N$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$. As a corollary, we obtain that $S^m {\times} S^n$ admits a weakly Lagrangian embedding into ${\mathbb}C^{m+n}$ if n=1,3. We investigate the problem of whether $S^m{\times}S^n$ in general admits a weakly Lagrangian embedding into ${\mathbb} C^{m+n}$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.799-808
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• 1999

We investigate when the .product of two smooth manifolds admits a weakly Lagrangian embedding. Assume M, N are oriented smooth manifolds of dimension m and n,. respectively, which admit weakly Lagrangian immersions into $C^m$ and $C^n$. If m and n are odd, then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$ In the case when m is odd and n is even, we assume further that $\chi$(N) is an even integer. Then $M\;{\times}\;N$ admits a weakly Lagrangian embedding into $C^{m+n}$. As a corollary, we obtain the result that $S^n_1\;{\times}\;S^n_2\;{\times}\;...{\times}\;S^n_k$, $\kappa$>1, admits a weakly Lagrang.ian embedding into $C^n_1+^n_2+...+^n_k$ if and only if some ni is odd.